PCA, Singular Value Decomposition & Association Rules implementation in Python¶
In [1]:
import pandas as pan
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn import decomposition
import operator
PCA for Reduced Dimensionality in Clustering¶
Data loading and normalization¶
In [2]:
# Function to load and normalize data
def Getdata():
# reading data column names
colnames = np.genfromtxt('segmentation_names.txt', dtype=str)
# reading data file
fil = pan.read_csv("segmentation_data.txt", sep=',', names=colnames)
# showing data types
print fil.dtypes
print fil.describe()
# Min'max normalization function
minmax = lambda x: ((x-x.min())/(x.max()-x.min()) * (1-0) + 0) if x.dtypes==np.float64 else x
data = fil.apply(minmax) # applying function
print data.describe()
# reading clasess
ynames = ['label','class']
y = pan.read_csv('segmentation_classes.txt',sep='\t', names=ynames)
print y
return colnames, data, ynames, y
In [3]:
# getting data with the function Getdata
colnames, data, ynames, y = Getdata()
REGION-CENTROID-COL float64
REGION-CENTROID-ROW float64
REGION-PIXEL-COUNT int64
SHORT-LINE-DENSITY-5 float64
SHORT-LINE-DENSITY-2 float64
VEDGE-MEAN float64
VEDGE-SD float64
HEDGE-MEAN float64
HEDGE-SD float64
INTENSITY-MEAN float64
RAWRED-MEAN float64
RAWBLUE-MEAN float64
RAWGREEN-MEAN float64
EXRED-MEAN float64
EXBLUE-MEAN float64
EXGREEN-MEAN float64
VALUE-MEAN float64
SATURATION-MEAN float64
HUE-MEAN float64
dtype: object
REGION-CENTROID-COL REGION-CENTROID-ROW REGION-PIXEL-COUNT \
count 2100.000000 2100.000000 2100.0
mean 124.940476 123.483333 9.0
std 72.858637 57.431428 0.0
min 1.000000 11.000000 9.0
25% 62.000000 81.000000 9.0
50% 121.000000 122.000000 9.0
75% 188.250000 171.250000 9.0
max 254.000000 251.000000 9.0
SHORT-LINE-DENSITY-5 SHORT-LINE-DENSITY-2 VEDGE-MEAN VEDGE-SD \
count 2100.000000 2100.000000 2100.000000 2100.000000
mean 0.014921 0.004550 1.890820 5.708299
std 0.041024 0.023573 2.649453 44.989359
min 0.000000 0.000000 0.000000 0.000000
25% 0.000000 0.000000 0.722222 0.349603
50% 0.000000 0.000000 1.277776 0.833333
75% 0.000000 0.000000 2.222221 1.807406
max 0.333333 0.222222 29.222221 991.718400
HEDGE-MEAN HEDGE-SD INTENSITY-MEAN RAWRED-MEAN RAWBLUE-MEAN \
count 2100.000000 2.100000e+03 2100.000000 2100.000000 2100.000000
mean 2.406772 7.904224e+00 37.047654 32.806667 44.205556
std 3.469954 5.347107e+01 38.135291 34.994538 43.510119
min 0.000000 -1.589457e-08 0.000000 0.000000 0.000000
25% 0.833332 4.216377e-01 7.472222 7.000000 9.666667
50% 1.444444 9.897442e-01 21.666666 19.666668 27.777779
75% 2.555556 2.251852e+00 53.277778 47.333332 65.000000
max 44.722225 1.386329e+03 143.444440 137.111110 150.888890
RAWGREEN-MEAN EXRED-MEAN EXBLUE-MEAN EXGREEN-MEAN VALUE-MEAN \
count 2100.000000 2100.000000 2100.000000 2100.000000 2100.000000
mean 34.130741 -12.722963 21.473704 -8.750741 45.162381
std 36.303768 11.588214 19.654107 11.606996 42.900582
min 0.000000 -49.666668 -12.444445 -33.888890 0.000000
25% 6.222222 -18.583333 4.305556 -17.000000 11.777778
50% 20.444445 -10.888889 19.666666 -11.000000 28.666666
75% 46.388888 -4.222222 36.111110 -3.222222 65.000000
max 142.555560 9.888889 82.000000 24.666666 150.888890
SATURATION-MEAN HUE-MEAN
count 2100.000000 2100.000000
mean 0.427259 -1.365147
std 0.228458 1.544278
min 0.000000 -3.044175
25% 0.284934 -2.188539
50% 0.375064 -2.052625
75% 0.540228 -1.565745
max 1.000000 2.912480
REGION-CENTROID-COL REGION-CENTROID-ROW REGION-PIXEL-COUNT \
count 2100.000000 2100.000000 2100.0
mean 0.489883 0.468681 9.0
std 0.287979 0.239298 0.0
min 0.000000 0.000000 9.0
25% 0.241107 0.291667 9.0
50% 0.474308 0.462500 9.0
75% 0.740119 0.667708 9.0
max 1.000000 1.000000 9.0
SHORT-LINE-DENSITY-5 SHORT-LINE-DENSITY-2 VEDGE-MEAN VEDGE-SD \
count 2100.000000 2100.000000 2100.000000 2100.000000
mean 0.044762 0.020476 0.064705 0.005756
std 0.123071 0.106079 0.090666 0.045365
min 0.000000 0.000000 0.000000 0.000000
25% 0.000000 0.000000 0.024715 0.000353
50% 0.000000 0.000000 0.043726 0.000840
75% 0.000000 0.000000 0.076046 0.001822
max 1.000000 1.000000 1.000000 1.000000
HEDGE-MEAN HEDGE-SD INTENSITY-MEAN RAWRED-MEAN RAWBLUE-MEAN \
count 2100.000000 2100.000000 2100.000000 2100.000000 2100.000000
mean 0.053816 0.005702 0.258272 0.239271 0.292968
std 0.077589 0.038570 0.265854 0.255228 0.288359
min 0.000000 0.000000 0.000000 0.000000 0.000000
25% 0.018634 0.000304 0.052091 0.051053 0.064065
50% 0.032298 0.000714 0.151046 0.143436 0.184094
75% 0.057143 0.001624 0.371418 0.345219 0.430781
max 1.000000 1.000000 1.000000 1.000000 1.000000
RAWGREEN-MEAN EXRED-MEAN EXBLUE-MEAN EXGREEN-MEAN VALUE-MEAN \
count 2100.000000 2100.000000 2100.000000 2100.000000 2100.000000
mean 0.239421 0.620323 0.359133 0.429304 0.299309
std 0.254664 0.194578 0.208102 0.198222 0.284319
min 0.000000 0.000000 0.000000 0.000000 0.000000
25% 0.043648 0.521922 0.177353 0.288425 0.078056
50% 0.143414 0.651119 0.340000 0.390892 0.189985
75% 0.325409 0.763060 0.514118 0.523719 0.430781
max 1.000000 1.000000 1.000000 1.000000 1.000000
SATURATION-MEAN HUE-MEAN
count 2100.000000 2100.000000
mean 0.427259 0.281874
std 0.228458 0.259252
min 0.000000 0.000000
25% 0.284934 0.143644
50% 0.375064 0.166461
75% 0.540228 0.248198
max 1.000000 1.000000
label class
0 GRASS 0
1 GRASS 0
2 GRASS 0
3 GRASS 0
4 GRASS 0
5 GRASS 0
6 GRASS 0
7 GRASS 0
8 GRASS 0
9 GRASS 0
10 GRASS 0
11 GRASS 0
12 GRASS 0
13 GRASS 0
14 GRASS 0
15 GRASS 0
16 GRASS 0
17 GRASS 0
18 GRASS 0
19 GRASS 0
20 GRASS 0
21 GRASS 0
22 GRASS 0
23 GRASS 0
24 GRASS 0
25 GRASS 0
26 GRASS 0
27 GRASS 0
28 GRASS 0
29 GRASS 0
... ... ...
2070 PATH 1
2071 PATH 1
2072 WINDOW 2
2073 WINDOW 2
2074 WINDOW 2
2075 WINDOW 2
2076 WINDOW 2
2077 WINDOW 2
2078 WINDOW 2
2079 WINDOW 2
2080 WINDOW 2
2081 WINDOW 2
2082 WINDOW 2
2083 WINDOW 2
2084 WINDOW 2
2085 WINDOW 2
2086 WINDOW 2
2087 WINDOW 2
2088 WINDOW 2
2089 WINDOW 2
2090 WINDOW 2
2091 WINDOW 2
2092 WINDOW 2
2093 CEMENT 3
2094 CEMENT 3
2095 CEMENT 3
2096 CEMENT 3
2097 CEMENT 3
2098 CEMENT 3
2099 CEMENT 3
[2100 rows x 2 columns]
Using Kmeans¶
In [13]:
# Implementing Kmeans from sklearn
y_pred = KMeans(n_clusters=7, random_state=33).fit_predict(data)
kmeans = KMeans()
kmeans.fit_predict(data)
Out[13]:
array([3, 3, 3, ..., 7, 7, 0])
In [14]:
print 'Centoids: \n:', kmeans.cluster_centers_
Centoids:
: [[ 2.66067793e-01 3.85492424e-01 9.00000000e+00 7.67676746e-02
2.12121212e-02 7.98421515e-02 4.24663623e-03 6.28383167e-02
5.14115240e-03 1.54919455e-01 1.44074458e-01 1.93718481e-01
1.24041661e-01 7.09628001e-01 3.54360076e-01 3.46173325e-01
1.93975097e-01 4.25887844e-01 1.97267894e-01]
[ 5.35098814e-01 1.50166667e-01 9.00000000e+00 2.77777769e-02
1.66666667e-03 3.02281387e-02 5.42887957e-04 2.67660451e-02
5.86661900e-04 8.23246433e-01 7.79716377e-01 8.94170356e-01
7.88760696e-01 2.70665440e-01 6.66372551e-01 2.89386481e-01
8.94170356e-01 2.11804171e-01 1.25065773e-01]
[ 7.52265126e-01 5.32705128e-01 9.00000000e+00 3.99999988e-02
3.38461538e-02 1.10336359e-01 1.41035712e-02 1.06809355e-01
1.54142562e-02 3.00861595e-01 2.79690816e-01 3.52871870e-01
2.65704173e-01 5.91750869e-01 4.52191858e-01 3.08270342e-01
3.52955704e-01 3.02475106e-01 1.64674515e-01]
[ 5.13993692e-01 8.08936588e-01 9.00000000e+00 7.74410751e-02
5.05050505e-03 5.44737633e-02 1.40719343e-03 4.63349822e-02
1.40097198e-03 1.08789943e-01 9.14029557e-02 9.24140773e-02
1.42676436e-01 6.79161019e-01 7.90017879e-02 8.21286885e-01
1.34900800e-01 4.14491323e-01 8.92332630e-01]
[ 3.02489781e-01 5.32371795e-01 9.00000000e+00 5.27065511e-02
4.48717949e-02 1.01182936e-01 9.48264629e-03 8.40154954e-02
1.11164652e-02 4.01836307e-01 3.71642496e-01 4.73720152e-01
3.54164576e-01 4.97217448e-01 5.71322275e-01 2.12272354e-01
4.73720152e-01 3.01140161e-01 1.63936224e-01]
[ 8.20975220e-01 3.90384615e-01 9.00000000e+00 1.92307687e-02
3.84615385e-02 5.68057202e-02 1.24900031e-02 3.14440976e-02
6.78120274e-03 4.82171955e-02 3.69654660e-02 7.20091760e-02
3.37812511e-02 7.40860007e-01 2.57200230e-01 4.71117371e-01
7.26216434e-02 6.98691234e-01 1.83818522e-01]
[ 2.33870249e-01 4.56986216e-01 9.00000000e+00 2.63157887e-02
1.31578947e-02 3.82086408e-02 2.39853690e-03 2.81604614e-02
1.96496537e-03 2.52655270e-02 1.63140837e-02 4.20205521e-02
1.61012425e-02 7.64069693e-01 2.18045117e-01 5.10664722e-01
4.29313341e-02 8.14264730e-01 1.74144577e-01]
[ 5.68040655e-01 5.08928571e-01 9.00000000e+00 7.14285693e-03
7.14285714e-03 1.97854434e-02 4.77200179e-04 1.48713388e-02
1.00377064e-03 2.43093216e-02 2.83572588e-02 2.79823269e-02
1.64903680e-02 8.54157784e-01 1.55117652e-01 5.20534035e-01
2.95287187e-02 2.81163316e-01 3.41843742e-01]]
In [ ]:
# plotting kmeans clusters vs actual
plt.figure(figsize=(12, 12))
plt.subplot(221)
plt.scatter(data[:, 9], data[:, 14], c= y_pred)
plt.ylabel(str(colnames[9]))
plt.xlabel(str(colnames[14]))
plt.title('KMeans')
plt.subplot(222)
plt.scatter(data[:, 9], data[:, 14], c= np.asarray(y['class']))
plt.xlabel(str(colnames[14]))
plt.title('Actual')
plt.subplot(223)
plt.scatter(data[:, 0], data[:, 9], c= y_pred)
plt.ylabel(str(colnames[0]))
plt.xlabel(str(colnames[9]))
plt.subplot(224)
plt.scatter(data[:, 0], data[:, 9], c= np.asarray(y['class']))
plt.xlabel(str(colnames[9]))
#plt.show()
plt.savefig("kmeans1.png")
plt.figure(figsize=(12, 12))
plt.subplot(221)
plt.scatter(data[:, 11], data[:, 18], c= y_pred)
plt.ylabel(str(colnames[11]))
plt.xlabel(str(colnames[18]))
plt.title('KMeans')
plt.subplot(222)
plt.scatter(data[:, 11], data[:, 18], c= np.asarray(y['class']))
plt.xlabel(str(colnames[18]))
plt.title('Actual')
plt.subplot(223)
plt.scatter(data[:, 16], data[:, 1], c= y_pred)
plt.ylabel(str(colnames[16]))
plt.xlabel(str(colnames[1]))
plt.subplot(224)
plt.scatter(data[:, 16], data[:, 1], c= np.asarray(y['class']))
plt.xlabel(str(colnames[1]))
#plt.show()
plt.savefig("kmeans2.png")
In [22]:
Image(filename='kmeans1.png')
Out[22]:
In [21]:
Image(filename='kmeans2.png')
Out[21]:
Implementing Dimensionality reduction using PCA¶
In [8]:
# setting PCA from sklearn decomposition package
pca = decomposition.PCA(n_components=len(colnames))
# reducing dimensionality
DTtrans = pca.fit(data).transform(data)
# variance captured by component
print 'Variance ratio: \n', pca.explained_variance_ratio_ , '\n'
# we need to take the first 6 component to get 95% of the variance
print '\nVariance Captured with 6 components %0.3f' % sum(pca.explained_variance_ratio_[:6])
print 'Variance Captured with 7 components %0.3f \n' % sum(pca.explained_variance_ratio_[:7])
np.set_printoptions(precision=2,suppress=True)
print '\nData in lower dimension:\n', DTtrans
Variance ratio: [ 0.61 0.13 0.1 0.05 0.04 0.02 0.02 0.02 0.01 0.01 0. 0. 0. 0. 0. 0. 0. 0. 0. ] Variance Captured with 6 components 0.941 Variance Captured with 7 components 0.960 Data in lower dimension: [[-0.69 0.53 -0.25 ..., 0. 0. 0. ] [-0.67 0.51 -0.34 ..., -0. -0. 0. ] [-0.71 0.77 0.16 ..., -0. 0. 0. ] ..., [-0.51 -0.13 0.08 ..., 0. 0. 0. ] [-0.48 -0.09 0.16 ..., 0. 0. 0. ] [-0.44 -0.11 0.05 ..., 0. 0. 0. ]]
Kmeas in lower dimension¶
In [9]:
y_pred = KMeans(n_clusters=7, random_state=33).fit_predict(DTtrans[:,:7])
kmeans = KMeans()
kmeans.fit_predict(DTtrans[:,:7])
print 'Centoids: \n:', kmeans.cluster_centers_
plt.figure(figsize=(12, 12))
plt.subplot(221)
plt.scatter(DTtrans[:, 1], DTtrans[:, 2], c= y_pred)
plt.ylabel('PC1')
plt.xlabel('PC2')
plt.title('KMeans')
plt.subplot(222)
plt.scatter(DTtrans[:, 1], DTtrans[:, 2], c= np.asarray(y['class']))
plt.xlabel('PC2')
plt.title('Actual')
plt.subplot(223)
plt.scatter(DTtrans[:, 1], DTtrans[:, 3], c= y_pred)
plt.ylabel('PC1')
plt.xlabel('PC3')
plt.subplot(224)
plt.scatter(DTtrans[:, 1], DTtrans[:, 3], c= np.asarray(y['class']))
plt.xlabel('PC3')
#plt.show()
#plt.savefig("kmeans_PCA_1.png")
plt.figure(figsize=(12, 12))
plt.subplot(221)
plt.scatter(DTtrans[:, 1], DTtrans[:, 4], c= y_pred)
plt.ylabel('PC1')
plt.xlabel('PC4')
plt.title('KMeans')
plt.subplot(222)
plt.scatter(DTtrans[:, 1], DTtrans[:, 4], c= np.asarray(y['class']))
plt.xlabel('PC4')
plt.title('Actual')
plt.subplot(223)
plt.scatter(DTtrans[:, 1], DTtrans[:, 5], c= y_pred)
plt.ylabel('PC1')
plt.xlabel('PC5')
plt.subplot(224)
plt.scatter(DTtrans[:, 1], DTtrans[:, 5], c= np.asarray(y['class']))
plt.xlabel('PC5')
#plt.show()
#plt.savefig("kmeans_PCA_2.png")
Centoids: : [[ 0.18 0.04 0.27 0.18 0.03 0.02 0. ] [-0.6 -0.35 -0.12 -0.13 -0.12 -0.02 -0.04] [ 1.41 0.09 -0.04 -0.17 -0.03 -0.01 -0.02] [ 0.44 -0.11 -0.17 0.23 -0.05 -0.01 0.02] [-0.63 0.56 -0.41 -0.07 -0.07 0.02 0.02] [-0.21 -0.24 -0.15 0.06 0.13 -0.01 0.03] [-0.61 0.65 0.08 -0.06 0.04 0.01 0.04] [-0.5 -0.12 0.37 -0.1 0.02 0. -0.02]]
Out[9]:
<matplotlib.text.Text at 0xa6d9da0>
In [11]:
Image(filename='kmeans_PCA_1.png')
Out[11]:
In [12]:
Image(filename='kmeans_PCA_2.png')
Out[12]:
Discussion¶
In [ ]:
''' In general kmeans seems that is doing a good job identifying categories. However there is some confussion for some topics that are "close". The images are divided into two columns. The first one to the left belongs to the clusters created by kmeans, the second column is the actual class. In the first image above the relation between features mean intensity and exblue-mean is shown. There are some categories that are perfectly identify by kmeans colored in green and blue. But in the cluster were there is some overlap among the actual classes, kmeans seems to try to divide the space without recognizing this overlap. The same effect is posible to se in the second row with region-control-col and intensity-mean features.
PCA helped in reducing the ammount of data that is requiered to perform the analysis and still get similar results. When dealing with lare amount of data PCA would improve the time rquiered to perform the analysis. From the images we may see that the clusters a good, but the overlap still makes hard for kmeans to assign an instance to its corresponding class
Association Rule Discovery¶
In [27]:
''' Apriori implementation '''
from numpy import *
def loadDataSet():
return [[1, 3, 4], [2, 3, 5], [1, 2, 3, 5], [2, 5]]
def createC1(dataSet):
C1 = []
for transaction in dataSet:
for item in transaction:
if not [item] in C1:
C1.append([item])
C1.sort()
return map(frozenset, C1)#use frozen set so we
#can use it as a key in a dict
def scanD(D, Ck, minSupport):
ssCnt = {}
for tid in D:
for can in Ck:
if can.issubset(tid):
if not ssCnt.has_key(can): ssCnt[can]=1
else: ssCnt[can] += 1
numItems = float(len(D))
retList = []
supportData = {}
for key in ssCnt:
support = ssCnt[key]/numItems
if support >= minSupport:
retList.insert(0,key)
supportData[key] = support
return retList, supportData
def aprioriGen(Lk, k): #creates Ck
retList = []
lenLk = len(Lk)
for i in range(lenLk):
for j in range(i+1, lenLk):
L1 = list(Lk[i])[:k-2]; L2 = list(Lk[j])[:k-2]
L1.sort(); L2.sort()
if L1==L2: #if first k-2 elements are equal
retList.append(Lk[i] | Lk[j]) #set union
return retList
def apriori(dataSet, minSupport = 0.5):
C1 = createC1(dataSet)
D = map(set, dataSet)
L1, supportData = scanD(D, C1, minSupport)
L = [L1]
k = 2
while (len(L[k-2]) > 0):
Ck = aprioriGen(L[k-2], k)
Lk, supK = scanD(D, Ck, minSupport)#scan DB to get Lk
supportData.update(supK)
L.append(Lk)
k += 1
return L, supportData
def generateRules(L, supportData, metric='confidence', minMetric=0.7): #supportData is a dict coming from scanD
bigRuleList = []
for i in range(1, len(L)):#only get the sets with two or more items
for freqSet in L[i]:
H1 = [frozenset([item]) for item in freqSet]
if (i > 1):
rulesFromConseq(freqSet, H1, supportData, bigRuleList, metric, minMetric)
else:
calcMetric(freqSet, H1, supportData, bigRuleList, metric, minMetric)
return bigRuleList
def calcMetric(freqSet, H, supportData, brl, metric='confidence', minMetric=0.7):
prunedH = [] #create new list to return
for conseq in H:
conf = supportData[freqSet]/supportData[freqSet-conseq] #calc confidence
lift = conf/supportData[conseq] #calc lift
if (metric == 'confidence'):
if (conf >= minMetric):
print freqSet-conseq,'-->',conseq,'conf:',conf,' lift:',lift
brl.append((freqSet-conseq, conseq, conf, lift))
prunedH.append(conseq)
elif (metric == 'lift'):
if (lift >= minMetric):
print freqSet-conseq,'-->',conseq,'conf:',conf,' lift:',lift
brl.append((freqSet-conseq, conseq, conf, lift))
prunedH.append(conseq)
return prunedH
def rulesFromConseq(freqSet, H, supportData, brl, metric='confidence', minMetric=0.7):
m = len(H[0])
if (len(freqSet) > (m + 1)): #try further merging
Hmp1 = aprioriGen(H, m+1)#create Hm+1 new candidates
Hmp1 = calcMetric(freqSet, Hmp1, supportData, brl, metric, minMetric)
if (len(Hmp1) > 1): #need at least two sets to merge
rulesFromConseq(freqSet, Hmp1, supportData, brl, metric, minMetric)
def pntRules(ruleList, itemMeaning):
for ruleTup in ruleList:
for item in ruleTup[0]:
print itemMeaning[item]
print " -------->"
for item in ruleTup[1]:
print itemMeaning[item]
print "[confidence: %f, lift: %f]" % (ruleTup[2], ruleTup[3])
print #print a blank line
Loading data¶
In [14]:
# loading playlists
fil = open('playlists.txt', 'r')
lines = fil.readlines()
fil.close()
#building playlist data
l = lines[0]
ll = l.replace('\n','').strip().split(' ')
playlist = []
for line in lines:
line = line.replace('\n','').strip().split(' ')
temp = []
for li in line:
temp.append(int(li))
playlist.append(temp)
playlist
ply = np.asarray(playlist)
print 'Playlists: \n',ply
# loading song names
fi = open('song_names.txt', 'r')
lines = fi.readlines()
fi.close()
#Building song names
songs = {}
for line in lines:
li = line.replace('\n','').strip().split('\t')
# spliting artist name from song title
song = li[-1].split('::')
# storing artist name and song title
temp = []
temp.append(song[1])
temp.append(song[0])
# creating key for the song/artist data
songs[int(li[0])] = temp
print '\nSongs examples:\n',songs[1]
print songs[1345]
Playlists: [[0, 1, 2, 3, 4, 5, 6, 7, 8] [9, 10, 11] [12, 13, 14, 15] ..., [1735, 104, 2422, 2235, 31, 1721, 41, 2346, 2420, 193, 11, 48, 196, 195, 1694, 39, 480, 29, 40] [2422, 31, 2418, 188, 2338] [2347]] Songs examples: ['Rick-Ross', 'Aston-Martin-Music'] ['The-Greg-Kihn-Band', 'Breakup-Song']
In [29]:
songs
Out[29]:
{0: ['Gucci-Mane', 'Gucci-Time'],
1: ['Rick-Ross', 'Aston-Martin-Music'],
2: ['T.I.', 'Get-Back-Up'],
3: ['Usher', 'Hot-Toddy'],
4: ['Willow', 'Whip-My-Hair'],
5: ['Jeremih', 'Down-On-Me'],
6: ['Wiz-Khalifa', 'Black-And-Yellow'],
7: ['Soulja-Boy', 'Blowing-Me-Kisses'],
8: ['Lloyd', 'Lay-It-Down'],
9: ['Rihanna', "Who's-That-Chick"],
10: ['Far-East-Movement', 'Like-A-G6'],
11: ['Usher', "DJ-Got-Us-Fallin'-In-Love"],
12: ['Miguel', 'All-I-Wants-Is-You'],
13: ['Ne-Yo', 'Champagne-Life'],
14: ['Drake', 'Find-Your-Love'],
15: ['Nicki-Minaj', 'Your-Love'],
16: ['Outkast', 'Ms.-Jackson'],
17: ['Maxi-Priest', 'Close-To-You'],
18: ['Nicki-Minaj', 'Right-Thru-Me'],
19: ['Usher', 'You-Make-Me-Wanna...'],
20: ['Rihanna', "What's-My-Name"],
21: ['Ne-Yo', 'One-In-A-Million'],
22: ['Will.I.Am', 'Check-It-Out'],
23: ['Mary-J.-Blige', 'Be-Without-You'],
24: ['Trey-Songz', 'Bottoms-Up'],
25: ['Usher', 'There-Goes-My-Baby'],
26: ['Drake', 'Up-All-Night'],
27: ['Bruno-Mars', 'Liquor-Store-Blues'],
28: ['Kanye-West', '"Monster"'],
29: ['Bruno-Mars', 'Just-The-Way-You-Are'],
30: ['Kanye-West', 'Runaway'],
31: ['Eminem', 'Love-The-Way-You-Lie'],
32: ['Black-Eyed-Peas', 'Boom-Boom-Pow'],
33: ['Jazmine-Sullivan', "Holding-You-Down-(Goin'-In-Circles)"],
34: ['Chris-Brown-&-Tyga', 'Deuces'],
35: ['DJ-Khaled', '"All-I-Do-Is-Win"'],
36: ['Sean-Kingston', 'Letting-Go-(Dutty-Love)'],
37: ['Fabolous', 'You-Be-Killin-Em'],
38: ['Drake', 'Fancy'],
39: ['Rihanna', 'Only-Girl-(In-The-World)'],
40: ['Katy-Perry', 'California-Gurls'],
41: ['Taio-Cruz', 'Dynamite'],
42: ['Taio-Cruz', 'Break-Your-Heart'],
43: ['Usher', 'OMG'],
44: ['Chris-Brown', 'Yeah-3X'],
45: ['Justin-Bieber', 'Somebody-To-Love'],
46: ['Jeremih', 'I-Like'],
47: ['B.o.B', 'Airplanes'],
48: ['Jason-Mraz', "I'm-Yours"],
49: ['Owl-City', 'Fireflies'],
50: ['Jamie-Foxx', 'Blame-It'],
51: ['Alicia-Keys', "Un-Thinkable-(I'm-Ready)"],
52: ['Sade', 'Soldier-Of-Love'],
53: ['John-Legend-&-The-Roots', 'Wake-Up-Everybody'],
54: ['Beyonce', 'Single-Ladies-(Put-A-Ring-On-It)'],
55: ['Mariah-Carey', 'We-Belong-Together'],
56: ['Ludacris', 'My-Chick-Bad'],
57: ['Gyptian', 'Hold-Yuh'],
58: ['Usher', 'Lil-Freak'],
59: ['J.-Holiday', 'Bed'],
60: ['Usher', 'U-Got-It-Bad-'],
61: ['Beyonce', 'Halo'],
62: ['B.o.B.', 'Nothing-On-You'],
63: ['Usher', 'Yeah'],
64: ['Puff-Daddy-&-The-Family', "I'll-Be-Missing-You"],
65: ['2Pac', 'Changes'],
66: ['Tarrus-Riley', "She's-Royal"],
67: ['Trey-Songz', "Can't-Be-Friends"],
68: ['The-Notorious-B.I.G.', 'Hypnotize'],
69: ['Tanto-Metro-&-Devonte', 'Everyone-Falls-In-Love'],
70: ['Rick-Ross', "Blowin'-Money-Fast-(B.M.F.)"],
71: ['Jason-DeRulo', 'Whatcha-Say'],
72: ['Jason-DeRulo', "Ridin'-Solo"],
73: ['Trey-Songz', 'Say-Aah'],
74: ['Flo-Rida', "Club-Can't-Handle-Me"],
75: ['Lil-Wayne', 'Right-Above-It'],
76: ['Travie-McCoy', 'Billionaire'],
77: ['Drake', '"Forever"'],
78: ['Pitbull', 'Hey-Baby-(Drop-It-To-The-Floor)'],
79: ['Eminem', 'No-Love'],
80: ['Waka-Flocka-Flame', 'No-Hands'],
81: ['Plies', 'Shawty'],
82: ['Britt-Nicole', 'Hanging-On'],
83: ['Drake', 'Over'],
84: ['Kanye-West', 'Stronger'],
85: ['The-Game', 'Hate-It-Or-Love-It'],
86: ["Lil'-Jon-&-The-Eastside-Boyz", 'Get-Low'],
87: ['Musical-Youth', 'Pass-The-Dutchie'],
88: ['T-Pain', "I'm-Sprung"],
89: ['Keri-Hilson', 'Pretty-Girl-Rock'],
90: ['Ciara', 'Ride'],
91: ['Edward-Maya', 'Stereo-Love'],
92: ['Joe', 'I-Wanna-Know'],
93: ['Timbaland', 'Say-Something'],
94: ['Akon', 'Beautiful'],
95: ['Dr.-Dre', "Nuthin'-But-A-G-Thang"],
96: ['Young-Jeezy', 'Lose-My-Mind'],
97: ['The-Notorious-B.I.G.', 'Mo-Money-Mo-Problems'],
98: ['Ne-Yo', 'Sexy-Love'],
99: ['Usher', 'Confessions-Part-II'],
100: ['Drake', 'Best-I-Ever-Had'],
101: ['Sean-Paul', 'Temperature'],
102: ['T.I.', 'Got-Your-Back'],
103: ['Chino-&-Nacho', 'Nina-Bonita'],
104: ['Nelly', 'Just-A-Dream'],
105: ['Tanya-Stephens', "It's-A-Pity"],
106: ['Pink', 'So-What'],
107: ['Rihanna', 'Rude-Boy'],
108: ['Luther-Vandross', 'Here-And-Now'],
109: ['Mindi-Abair', 'Come-As-You-Are'],
110: ['Walter-Beasley', 'Oh-Yeah'],
111: ['Bernie-Williams', 'Ritmo-De-Otono'],
112: ['Stevie-Wonder', 'Superstition'],
113: ['Yvonne-Elliman', "If-I-Can't-Have-You"],
114: ['Hezekiah-Walker', 'God-Favored-Me-(Part-I)'],
115: ['Marvin-Sapp', 'He-Has-His-Hands-On-You'],
116: ['Brian-Culbertson', 'Go'],
117: ['Kyle-Wolverton', "Can't-Stop-The-Feeling"],
118: ['Nick-Colionne', 'Always-Thinking-Of-You'],
119: ['David-Benoit', 'Botswana-Bossa-Nova'],
120: ['Ramsey-Lewis', 'The-In-Crowd'],
121: ['La-Original-Banda-El-Limon', 'Derecho-De-Antiguedad'],
122: ['Pitbull', 'Bon-Bon'],
123: ['Titanes-De-Durango', 'Soy-Enamorado'],
124: ['Chuy-Lizarraga-Y-Su-Banda-Tierra-Sinaloense',
'La-Peinada-(La-Peinadita)'],
125: ['Banda-Los-Recoditos', 'La-Escuelita'],
126: ['Banda-El-Recodo-De-Don-Cruz-Lizarraga', 'Me-Gusta-Todo-De-Ti'],
127: ['Cumbre-Nortena', 'Te-Amo'],
128: ['Viento-Y-Sol', 'Par-De-Anillos'],
129: ['Grupo-Montez-De-Durango', 'Espero'],
130: ['Tierra-Cali', 'Amor-Te-Amo'],
131: ['Intocable', 'Ensename-A-Olvidarte'],
132: ['La-Original-Banda-Limon', 'Al-Menos'],
133: ['War', 'Low-Rider'],
134: ['El-Trono-De-Mexico', 'Te-Ves-Fatal'],
135: ['Jenni-Rivera', 'Culpable-O-Inocente'],
136: ['Dorrough-Music', 'Ice-Cream-Paint-Job'],
137: ['Dr.-Dre', 'The-Next-Episode'],
138: ['2Pac', 'How-Do-U-Want-It'],
139: ['Black-Eyed-Peas', 'Imma-Be'],
140: ['2Pac', 'California-Love'],
141: ['2Pac', 'I-Get-Around'],
142: ['Spencer-Day', 'Till-You-Come-To-Me'],
143: ['Kenny-Lattimore', 'And-I-Love-Her'],
144: ['Kenny-G', 'Fall-Again'],
145: ['Kanye-West', 'Heartless'],
146: ['Black-Eyed-Peas', 'I-Gotta-Feeling'],
147: ['Keri-Hilson', 'Knock-You-Down'],
148: ['T.I.', 'Whatever-You-Like'],
149: ['Jesse-Cook', 'Bogota-By-Bus'],
150: ['Paul-Brown', 'The-Rhythm-Method'],
151: ['Rick-Braun', 'Tijuana-Dance'],
152: ['Alicia-Keys', 'No-One'],
153: ['Chris-Brown', 'With-You'],
154: ['Sade', 'Babyfather'],
155: ['Corinne-Bailey-Rae', 'Closer'],
156: ['Rick-Braun', 'Christiane'],
157: ['El-Trono-De-Mexico', 'Te-Recordare'],
158: ['Banda-MS', 'Increible'],
159: ['Grupo-Bryndis', '"Quizas-Si,-Quizas-No"'],
160: ['Sergio-Vega', 'Millonario-De-Amor'],
161: ['Paul-Brown-&-Marc-Antoine', 'Brother-Earl'],
162: ['Ne-Yo', 'Mad'],
163: ['Jay-Z', 'Empire-State-Of-Mind'],
164: ['Twista', "Let's-Make-A-Movie"],
165: ['Bobby-McFerrin', 'Say-Ladeo'],
166: ['Peter-White', 'Bueno-Funk'],
167: ['Corinne-Bailey-Rae', 'Put-Your-Records-On'],
168: ['KT-Tunstall', 'Suddenly-I-See'],
169: ['KT-Tunstall', 'Fade-Like-A-Shadow'],
170: ['Robert-Plant', 'Angel-Dance'],
171: ['Jay-Soto', 'Groovalicious'],
172: ['The-Philippe-Saisse-Trio', 'Do-It-Again'],
173: ['The-Jazzmasters', 'Touch-And-Go'],
174: ['Chris-Standring', 'Bossa-Blue'],
175: ['Norman-Brown', 'Sending-My-Love'],
176: ['Eric-Darius', 'Uptown-Swagger'],
177: ['Paul-Brown', '24\\/7'],
178: ['The-Rolling-Stones', 'Gimme-Shelter'],
179: ['The-Rolling-Stones', "(I-Can't-Get-No)-Satisfaction"],
180: ['The-Rolling-Stones', "Jumpin'-Jack-Flash"],
181: ['The-Rolling-Stones', 'Beast-Of-Burden'],
182: ['The-Bellamy-Brothers', 'Redneck-Girl'],
183: ['Johnny-Paycheck', 'Take-This-Job-And-Shove-It'],
184: ['Selena', 'Amor-Prohibido'],
185: ["Booker-T.-&-The-MG's", 'Green-Onions'],
186: ['Shakira', 'She-Wolf-\\/-Loba'],
187: ['Nelly-Furtado', 'Say-It-Right'],
188: ['OneRepublic-&-Timbaland', 'Apologize'],
189: ['Cee-Lo-Green', 'F**k-You'],
190: ['Linkin-Park', 'Shadow-Of-The-Day'],
191: ['Pitbull', 'Hotel-Room-Service'],
192: ['Selena', 'Baila-Esta-Cumbia'],
193: ['Kesha', 'Tick-Tock'],
194: ['Nickelback', 'Rockstar'],
195: ['Mike-Posner', "Please-Don't-Go"],
196: ['Katy-Perry', 'Teenage-Dream'],
197: ['Lady-Gaga', 'Poker-Face'],
198: ['Willie-Nelson', 'Whiskey-River'],
199: ['Lady-Gaga', 'Alejandro'],
200: ['Michael-Jackson', 'The-Way-You-Make-Me-Feel'],
201: ['50-Cent', 'In-Da-Club'],
202: ['The-Temper-Trap', 'Sweet-Disposition'],
203: ['The-Beatles', 'Let-It-Be'],
204: ['Led-Zeppelin', 'Black-Dog'],
205: ['Marvin-Gaye', "Let's-Get-It-On"],
206: ['Ozzy-Osbourne', 'Flying-High-Again'],
207: ['Days-Of-The-New', '"Touch,-Peel-&-Stand"'],
208: ['Nirvana', 'In-Bloom'],
209: ['Rise-Against', 'Savior'],
210: ['Kid-Rock', 'Bawitdaba'],
211: ['Finger-Eleven', 'Paralyzer'],
212: ['Godsmack', 'Love-Hate-Sex-Pain'],
213: ['The-Red-Hot-Chili-Peppers', 'Other-Side'],
214: ['Bush', 'Comedown'],
215: ['Three-Days-Grace', 'World-So-Cold'],
216: ['Chevelle', 'The-Red'],
217: ['Metallica', 'Welcome-Home-(Sanitarium)'],
218: ['Shinedown', 'Sound-Of-Madness'],
219: ['Foo-Fighters', 'Learn-To-Fly'],
220: ['Five-Finger-Death-Punch', 'Far-From-Home'],
221: ['Pantera', 'Walk'],
222: ['Disturbed', 'Another-Way-To-Die'],
223: ['Audioslave', 'Like-A-Stone'],
224: ['Saving-Abel', 'The-Sex-Is-Good'],
225: ['Linkin-Park', 'Breaking-The-Habit'],
226: ['Rage-Against-The-Machine', 'Guerrilla-Radio'],
227: ['Theory-Of-A-Deadman', 'Bad-Girlfriend'],
228: ['Staind', "It's-Been-Awhile"],
229: ['The-Offspring', 'Gotta-Get-Away'],
230: ['Stone-Sour', "Say-You'll-Haunt-Me"],
231: ['Tool', 'Stinkfist'],
232: ['Foo-Fighters', 'Everlong'],
233: ['Megadeth', 'Angry-Again'],
234: ['Metallica', 'The-Memory-Remains'],
235: ['Tool', 'H.'],
236: ['Nine-Inch-Nails', 'Head-Like-A-Hole'],
237: ['Alice-In-Chains', 'Your-Decision'],
238: ['Staind', 'For-You'],
239: ['Bush', 'Machinehead'],
240: ['Danzig', 'Mother'],
241: ['Green-Day', 'When-I-Come-Around'],
242: ['Avenged-Sevenfold', 'Nightmare'],
243: ['Blur', 'Song-2'],
244: ['Marilyn-Manson', 'The-Beautiful-People'],
245: ['Mudvayne', 'Scream-With-Me'],
246: ['Beck', 'Loser'],
247: ['Papa-Roach', 'Getting-Away-With-Murder'],
248: ['Everlast', "What-It's-Like"],
249: ['Ozzy-Osbourne', "Mama-I'm-Coming-Home"],
250: ['The-Red-Hot-Chili-Peppers', 'Dani-California'],
251: ['Alice-In-Chains', 'Man-In-The-Box'],
252: ['Drowning-Pool', 'Bodies'],
253: ['The-Jimi-Hendrix-Experience', 'All-Along-The-Watchtower'],
254: ['System-Of-A-Down', 'Chop-Suey!'],
255: ['3-Doors-Down', 'Kryptonite'],
256: ['Rage-Against-The-Machine', 'Bulls-On-Parade'],
257: ['Five-Finger-Death-Punch', 'Bad-Company'],
258: ['The-White-Stripes', 'Seven-Nation-Army'],
259: ['Powerman-5000', 'When-Worlds-Collide'],
260: ['Skid-Row', '18-And-Life'],
261: ['The-Red-Hot-Chili-Peppers', 'Under-The-Bridge'],
262: ['Sick-Puppies', "You're-Going-Down"],
263: ['Motley-Crue', 'Kickstart-My-Heart'],
264: ['Fuel', 'Hemorrhage-(In-My-Hands)'],
265: ['Breaking-Benjamin', 'I-Will-Not-Bow'],
266: ['Rush', 'Tom-Sawyer'],
267: ['Incubus', 'Pardon-Me'],
268: ['Queen', 'Bohemian-Rhapsody'],
269: ['Bush', 'Little-Things'],
270: ['Pearl-Jam', 'Daughter'],
271: ['AC\\/DC', 'Dirty-Deeds-Done-Dirt-Cheap'],
272: ['Nirvana', 'Smells-Like-Teen-Spirit'],
273: ['Metallica', 'The-Unforgiven-II'],
274: ['Skillet', 'Monster'],
275: ['Pink-Floyd', 'Hey-You'],
276: ['The-Offspring', "The-Kids-Aren't-Alright"],
277: ['Korn', 'Make-Me-Bad'],
278: ['System-Of-A-Down', 'Toxicity'],
279: ['Green-Day', 'Longview'],
280: ['Three-Days-Grace', 'Break'],
281: ['Tool', 'Forty-Six-&-2'],
282: ['Stone-Temple-Pilots', 'Interstate-Love-Song'],
283: ['P.O.D.', 'Alive'],
284: ['Black-Sabbath', 'Paranoid'],
285: ['My-Darkest-Days', 'Porn-Star-Dancing'],
286: ['Nine-Inch-Nails', 'Closer'],
287: ['AC\\/DC', 'You-Shook-Me-All-Night-Long'],
288: ['Alice-In-Chains', 'Them-Bones'],
289: ['Rage-Against-The-Machine', 'People-Of-The-Sun'],
290: ['Seether', 'Fine-Again'],
291: ['Pearl-Jam', 'Black'],
292: ['Scorpions', 'No-One-Like-You'],
293: ['The-Red-Hot-Chili-Peppers', 'By-The-Way'],
294: ['Disturbed', 'Down-With-The-Sickness'],
295: ['Nirvana', 'Rape-Me'],
296: ['Metallica', 'One'],
297: ['Marilyn-Manson', 'Sweet-Dreams-(Are-Made-Of-This)'],
298: ['Rage-Against-The-Machine', 'Killing-In-The-Name'],
299: ['Bush', 'Glycerine'],
300: ['Queen', 'Another-One-Bites-The-Dust'],
301: ['Pearl-Jam', 'Alive'],
302: ['Staind', 'Mudshovel'],
303: ['Soundgarden', 'Fell-On-Black-Days'],
304: ['The-Beastie-Boys', "So-What'Cha-Want"],
305: ['Bon-Jovi', "Livin'-On-A-Prayer"],
306: ['Sublime', 'What-I-Got'],
307: ['The-Beastie-Boys', 'Brass-Monkey'],
308: ['Van-Halen', 'Eruption'],
309: ['Van-Halen', 'You-Really-Got-Me'],
310: ['Bush', 'Everything-Zen'],
311: ['10-Years', 'Wasteland'],
312: ['Toadies', 'Possum-Kingdom'],
313: ['AC\\/DC', "Hell's-Bells"],
314: ['Nirvana', 'Lithium'],
315: ['A-Perfect-Circle', 'Judith'],
316: ['Bon-Jovi', 'Wanted-Dead-Or-Alive'],
317: ['Metallica', 'Fuel'],
318: ["Guns-N'-Roses", 'Welcome-To-The-Jungle'],
319: ['Soundgarden', 'Black-Hole-Sun'],
320: ['The-Offspring', 'Gone-Away'],
321: ['Puddle-Of-Mudd', 'Control'],
322: ['Iron-Maiden', 'The-Number-Of-The-Beast'],
323: ['3-Doors-Down', "When-I'm-Gone"],
324: ['AC\\/DC', 'T.N.T.'],
325: ['Hoobastank', 'Crawling-In-The-Dark'],
326: ['311', 'Down'],
327: ['Pink-Floyd', 'Comfortably-Numb'],
328: ['Chevelle', 'Send-The-Pain-Below'],
329: ['AC\\/DC', "Rock-And-Roll-Ain't-Noise-Pollution"],
330: ['The-Red-Hot-Chili-Peppers', 'Scar-Tissue'],
331: ['White-Zombie', "Thunder-Kiss-'65"],
332: ['Puddle-Of-Mudd', 'Blurry'],
333: ['Led-Zeppelin', 'Stairway-To-Heaven'],
334: ['Trapt', 'Headstrong'],
335: ['AC\\/DC', 'Thunderstruck'],
336: ['Metallica', 'Harvester-Of-Sorrow'],
337: ['Ram-Jam', 'Black-Betty'],
338: ['Rob-Zombie', 'Living-Dead-Girl'],
339: ['The-Red-Hot-Chili-Peppers', "Can't-Stop"],
340: ['The-Beastie-Boys', 'No-Sleep-Till-Brooklyn'],
341: ['Def-Leppard', 'Pour-Some-Sugar-On-Me'],
342: ['Candlebox', 'Far-Behind'],
343: ['Filter', 'Hey-Man-Nice-Shot'],
344: ['P.O.D.', 'Youth-Of-The-Nation'],
345: ['Stone-Temple-Pilots', 'Vasoline'],
346: ['Rage-Against-The-Machine', 'Testify'],
347: ['Cold', 'Stupid-Girl'],
348: ['Ted-Nugent', 'Stranglehold'],
349: ['Tool', 'Aenema'],
350: ['The-Red-Hot-Chili-Peppers', 'Soul-To-Squeeze'],
351: ['AC\\/DC', 'Back-In-Black'],
352: ['The-Beastie-Boys', 'Sabotage'],
353: ['Rob-Zombie', 'Dragula'],
354: ['Stabbing-Westward', 'Save-Yourself'],
355: ['Nirvana', 'Dumb'],
356: ['Stone-Temple-Pilots', 'Big-Empty'],
357: ['Korn', 'Falling-Away-From-Me'],
358: ['Nickelback', 'How-You-Remind-Me'],
359: ['System-Of-A-Down', 'Aerials'],
360: ["Guns-N'-Roses", 'Civil-War'],
361: ['Sublime', 'Wrong-Way'],
362: ['The-Red-Hot-Chili-Peppers', 'Californication'],
363: ['Deftones', 'Change-(In-The-House-Of-Flies)'],
364: ['Nirvana', 'Heart-Shaped-Box'],
365: ['AC\\/DC', 'For-Those-About-To-Rock'],
366: ['Metallica', 'Nothing-Else-Matters'],
367: ['Green-Day', 'Basket-Case'],
368: ['Linkin-Park', 'Lying-From-You'],
369: ['Incubus', 'Wish-You-Were-Here'],
370: ['The-Dirty-Edge', 'Lay-Me-Down'],
371: ['Skid-Row', 'Youth-Gone-Wild'],
372: ['The-Black-Crowes', 'Hard-To-Handle'],
373: ['Stone-Temple-Pilots', 'Creep'],
374: ["Guns-N'-Roses", "Knockin'-On-Heaven's-Door"],
375: ['Rage-Against-The-Machine', 'Renegades-Of-Funk'],
376: ['Slipknot', 'Snuff'],
377: ['Butthole-Surfers', 'Pepper'],
378: ['Soundgarden', 'Spoonman'],
379: ['Stone-Temple-Pilots', 'Dead-And-Bloated'],
380: ['Metallica', 'Until-It-Sleeps'],
381: ['Alice-In-Chains', 'Would?'],
382: ['Stone-Temple-Pilots', 'Plush'],
383: ['Korn', 'Got-The-Life'],
384: ['Live', 'Lightning-Crashes'],
385: ['Smashing-Pumpkins', 'Cherub-Rock'],
386: ['Cake', 'The-Distance'],
387: ['Tool', 'Sober'],
388: ['Blink-182', 'All-The-Small-Things'],
389: ['Soundgarden', 'Outshined'],
390: ['Pantera', 'Cemetery-Gates'],
391: ['Green-Day', 'Brain-Stew'],
392: ['Godsmack', 'Whatever'],
393: ['Pearl-Jam', 'Better-Man'],
394: ['Metallica', 'Master-Of-Puppets'],
395: ['Metallica', 'Wherever-I-May-Roam'],
396: ['Megadeth', 'Symphony-Of-Destruction'],
397: ['Nirvana', 'All-Apologies'],
398: ['Pink-Floyd', 'Money'],
399: ['Sixx-A.M.', 'Life-Is-Beautiful'],
400: ['Stone-Temple-Pilots', 'Sex-Type-Thing'],
401: ['The-Beastie-Boys', '(You-Gotta)-Fight-For-Your-Right'],
402: ['Three-Days-Grace', 'Just-Like-You'],
403: ['Scorpions', 'Rock-You-Like-A-Hurricane'],
404: ['Linkin-Park', 'Given-Up'],
405: ['Sublime', 'Santeria'],
406: ['Metallica', 'King-Nothing'],
407: ['The-Beastie-Boys', 'Intergalactic'],
408: ['AC\\/DC', 'Highway-To-Hell'],
409: ['System-Of-A-Down', 'BYOB'],
410: ['Motley-Crue', 'Dr.-Feelgood'],
411: ['Stone-Temple-Pilots', 'Wicked-Garden'],
412: ['Pink-Floyd', 'Wish-You-Were-Here'],
413: ['Linkin-Park', 'Numb'],
414: ['Primus', 'N.I.B.'],
415: ['White-Zombie', 'More-Human-Than-Human'],
416: ['Faith-No-More', 'Epic'],
417: ['Foo-Fighters', 'All-My-Life'],
418: ['The-Offspring', 'Come-Out-And-Play'],
419: ['Alice-In-Chains', 'Down-In-A-Hole'],
420: ['Stone-Temple-Pilots', "Trippin'-On-A-Hole-In-A-Paper-Heart"],
421: ['Drowning-Pool', 'Turn-So-Cold'],
422: ['A-Day-To-Remember', 'All-I-Want'],
423: ['Ozzy-Osbourne', "Life-Won't-Wait"],
424: ['Sick-Puppies', 'Maybe'],
425: ['Breaking-Benjamin', 'Lights-Out'],
426: ['Finger-Eleven', 'Living-In-A-Dream'],
427: ['Alice-In-Chains', 'Lesson-Learned'],
428: ['Linkin-Park', 'New-Divide'],
429: ['Alice-In-Chains', 'Angry-Chair'],
430: ['Mudvayne', 'Happy?'],
431: ['Nine-Inch-Nails', 'The-Hand-That-Feeds'],
432: ['Metallica', 'Sad-But-True'],
433: ['Mudvayne', 'Not-Falling'],
434: ['Linkin-Park', 'Faint'],
435: ['Korn', 'Freak-On-A-Leash'],
436: ['Smashing-Pumpkins', 'Bullet-With-Butterfly-Wings'],
437: ['Three-Days-Grace', 'Never-Too-Late'],
438: ['Nirvana', 'Come-As-You-Are'],
439: ['Pearl-Jam', 'Jeremy'],
440: ['Incubus', 'Drive'],
441: ['Black-Sabbath', 'War-Pigs'],
442: ['The-Offspring', 'Self-Esteem'],
443: ['Papa-Roach', 'Last-Resort'],
444: ['Tool', 'Schism'],
445: ['Aerosmith', 'Dream-On'],
446: ['Led-Zeppelin', 'Immigrant-Song'],
447: ['Pearl-Jam', 'Even-Flow'],
448: ['Godsmack', 'I-Stand-Alone'],
449: ['Limp-Bizkit', 'Break-Stuff'],
450: ['Saliva', 'Click-Click-Boom'],
451: ['Tool', 'Prison-Sex'],
452: ['Alice-In-Chains', 'Rooster'],
453: ['Metallica', 'Enter-Sandman'],
454: ['Linkin-Park', 'In-The-End'],
455: ['Ozzy-Osbourne', 'Crazy-Train'],
456: ['Foo-Fighters', 'My-Hero'],
457: ['The-Red-Hot-Chili-Peppers', 'Give-It-Away'],
458: ['Linkin-Park', 'Crawling'],
459: ['Rage-Against-The-Machine', 'Sleep-Now-In-The-Fire'],
460: ['Ozzy-Osbourne', 'No-More-Tears'],
461: ['Puddle-Of-Mudd', 'She-Hates-Me'],
462: ['Metallica', 'Turn-The-Page'],
463: ['Linkin-Park', 'One-Step-Closer'],
464: ['Godsmack', 'Voodoo'],
465: ['Queen', 'We-Will-Rock-You'],
466: ['Disturbed', 'Stupify'],
467: ['Green-Day', 'Boulevard-Of-Broken-Dreams'],
468: ['Metallica', 'Fade-To-Black'],
469: ['Disturbed', 'Indestructible'],
470: ['Breaking-Benjamin', 'So-Cold'],
471: ["Guns-N'-Roses", "Sweet-Child-O'-Mine"],
472: ['Audioslave', 'I-Am-The-Highway'],
473: ['Foo-Fighters', 'Best-Of-You'],
474: ['Keith-Urban', 'Sweet-Thing'],
475: ['Darius-Rucker', 'Come-Back-Song'],
476: ['Gretchen-Wilson', 'Redneck-Woman'],
477: ['Tim-McGraw', 'Felt-Good-On-My-Lips'],
478: ['Toby-Keith', 'God-Love-Her'],
479: ['Dierks-Bentley', 'Free-And-Easy-(Down-The-Road-I-Go)'],
480: ['Taylor-Swift', 'Mine'],
481: ['Montgomery-Gentry', 'Something-To-Be-Proud-Of'],
482: ['Easton-Corbin', 'Roll-With-It'],
483: ['Rascal-Flatts', 'Why-Wait'],
484: ['Miranda-Lambert', 'Gunpowder-&-Lead'],
485: ['Brad-Paisley', 'Anything-Like-Me'],
486: ['Alan-Jackson', "Who's-Cheatin'-Who"],
487: ['Chris-Young', 'Voices'],
488: ['Carrie-Underwood', 'Cowboy-Casanova'],
489: ['Justin-Moore', 'How-I-Got-To-Be-This-Way'],
490: ['Rodney-Atkins', "Farmer's-Daughter"],
491: ['Billy-Currington', 'People-Are-Crazy'],
492: ['Sugarland', 'Stuck-Like-Glue'],
493: ['Kenny-Chesney', 'The-Boys-Of-Fall'],
494: ['Rascal-Flatts', 'These-Days'],
495: ['Josh-Thompson', 'Way-Out-Here'],
496: ['Big-&-Rich', 'Save-A-Horse-(Ride-A-Cowboy)'],
497: ['Zac-Brown-Band', "As-She's-Walking-Away"],
498: ['Toby-Keith', 'As-Good-As-I-Once-Was'],
499: ['The-Band-Perry', 'If-I-Die-Young'],
500: ['Luke-Bryan', 'Rain-Is-A-Good-Thing'],
501: ['Lady-Antebellum', 'Hello-World'],
502: ['Little-Big-Town', 'Boondocks'],
503: ['Kenny-Chesney', "Don't-Happen-Twice"],
504: ['Carrie-Underwood', "Mama's-Song"],
505: ['Blake-Shelton', 'All-About-Tonight'],
506: ['Toby-Keith', 'How-Do-You-Like-Me-Now?!'],
507: ['Montgomery-Gentry', 'One-In-Every-Crowd'],
508: ['Dierks-Bentley', 'Come-A-Little-Closer'],
509: ['Jason-Aldean', 'My-Kind-Of-Party'],
510: ['Tim-McGraw', 'Down-On-The-Farm'],
511: ['Carrie-Underwood', 'Undo-It'],
512: ['Billy-Currington', 'Good-Directions'],
513: ['Steve-Holy', 'Good-Morning-Beautiful'],
514: ['Kenny-Chesney', 'Beer-In-Mexico'],
515: ['Tim-McGraw', 'Southern-Voice'],
516: ['Darius-Rucker', 'Alright'],
517: ['George-Strait', 'The-Breath-You-Take'],
518: ['Tim-McGraw', 'Just-To-See-You-Smile'],
519: ['Keith-Urban', 'Put-You-In-A-Song'],
520: ['Lady-Antebellum', 'Need-You-Now'],
521: ['Gary-Allan', 'Nothing-On-But-The-Radio'],
522: ['Sugarland', 'Something-More'],
523: ['George-Strait', 'Write-This-Down'],
524: ['Keith-Urban', 'Somebody-Like-You'],
525: ['Luke-Bryan', 'Someone-Else-Calling-You-Baby'],
526: ['Rodney-Atkins',
"If-You're-Going-Through-Hell-(Before-The-Devil-Even-Knows)"],
527: ['Josh-Turner', 'All-Over-Me'],
528: ['Craig-Morgan', 'Redneck-Yacht-Club'],
529: ['Rascal-Flatts', 'Stand'],
530: ['Tim-McGraw', 'Where-The-Green-Grass-Grows'],
531: ['Carrie-Underwood', 'Before-He-Cheats'],
532: ['Toby-Keith', 'Beer-For-My-Horses'],
533: ['Emerson-Drive', 'Fall-Into-Me'],
534: ['Keith-Urban', "I'm-In"],
535: ['Brad-Paisley', "Waitin'-On-A-Woman"],
536: ['Tim-McGraw', '"I-Like-It,-I-Love-It"'],
537: ['Luke-Bryan', 'Do-I'],
538: ['Trace-Adkins', "This-Ain't-No-Love-Song"],
539: ['Lady-Antebellum', "Love-Don't-Live-Here"],
540: ['Montgomery-Gentry', 'Back-When-I-Knew-It-All'],
541: ['Keith-Urban', 'Better-Life'],
542: ['Toby-Keith', 'Bullets-In-The-Gun'],
543: ['Randy-Houser', 'Boots-On'],
544: ['Darius-Rucker', "It-Won't-Be-Like-This-For-Long"],
545: ['Luke-Bryan', 'All-My-Friends-Say'],
546: ['Miranda-Lambert', 'Only-Prettier'],
547: ['Lonestar', 'My-Front-Porch-Looking-In'],
548: ['Taylor-Swift', 'Love-Story'],
549: ['Lee-Brice', 'Love-Like-Crazy'],
550: ['Trace-Adkins', 'Ladies-Love-Country-Boys'],
551: ['Reba', 'Turn-On-The-Radio'],
552: ['Jason-Aldean', 'Big-Green-Tractor'],
553: ['Toby-Keith', 'Get-Drunk-And-Be-Somebody'],
554: ['Kid-Rock', 'Picture'],
555: ['Josh-Gracin', "Nothin'-To-Lose"],
556: ['Martina-McBride', "This-One's-For-The-Girls"],
557: ['Curb-Records', "She-Won't-Be-Lonely-Long"],
558: ['Alan-Jackson', "It's-Five-O'Clock-Somewhere"],
559: ['Lady-Antebellum', 'Our-Kind-Of-Love'],
560: ['Rodney-Atkins', 'These-Are-My-People'],
561: ['Bon-Jovi', "Who-Says-You-Can't-Go-Home"],
562: ['Rascal-Flatts', 'Fast-Cars-And-Freedom'],
563: ['Trisha-Yearwood', "She's-In-Love-With-The-Boy"],
564: ['Toby-Keith', "Should've-Been-A-Cowboy"],
565: ['Jerrod-Niemann', '"Lover,-Lover"'],
566: ['Martina-McBride', 'My-Baby-Loves-Me'],
567: ['Alan-Jackson', 'Where-I-Come-From'],
568: ['Brad-Paisley', 'The-World'],
569: ['Keith-Urban', 'Days-Go-By'],
570: ['Little-Big-Town', 'Little-White-Church'],
571: ['Luke-Bryan', 'Country-Man'],
572: ['Montgomery-Gentry', 'Gone'],
573: ['Diamond-Rio', 'Meet-In-The-Middle'],
574: ['Kenny-Chesney', 'Never-Wanted-Nothing-More'],
575: ['Dierks-Bentley', 'Sideways'],
576: ['Garth-Brooks', 'Friends-In-Low-Places'],
577: ['Jason-Aldean', 'Crazy-Town'],
578: ['Brad-Paisley', "She's-Everything"],
579: ['Rascal-Flatts', 'Mayberry'],
580: ['Keith-Urban', 'You-Look-Good-In-My-Shirt'],
581: ['Chris-Cagle', 'What-Kinda-Gone'],
582: ['Kenny-Chesney', "She-Thinks-My-Tractor's-Sexy"],
583: ['Brad-Paisley', 'Water'],
584: ['Toby-Keith', "Who's-Your-Daddy"],
585: ['Sugarland', 'Already-Gone'],
586: ['Jo-Dee-Messina', "Lesson-In-Leavin'"],
587: ['Kenny-Chesney', 'The-Good-Stuff-'],
588: ['Montgomery-Gentry', 'Hell-Yeah'],
589: ['Keith-Urban', "Who-Wouldn't-Wanna-Be-Me"],
590: ['Lady-Antebellum', "Lookin'-For-A-Good-Time"],
591: ['Josh-Turner', "Why-Don't-We-Just-Dance"],
592: ['Alan-Jackson', 'Summertime-Blues'],
593: ['Miranda-Lambert', 'The-House-That-Built-Me'],
594: ['Zac-Brown-Band', 'Chicken-Fried'],
595: ['Carrie-Underwood', 'Wasted'],
596: ['Rascal-Flatts', 'Life-Is-A-Highway'],
597: ['Brad-Paisley', 'Online'],
598: ['Dierks-Bentley', "What-Was-I-Thinkin'"],
599: ['Kenny-Chesney', "Don't-Blink"],
600: ['LeAnn-Rimes', 'I-Need-You'],
601: ['Lonestar', 'Mr.-Mom'],
602: ['Eric-Church', 'Smoke-A-Little-Smoke'],
603: ['Brad-Paisley', 'Mud-On-The-Tires'],
604: ['Zac-Brown-Band', 'Toes'],
605: ['Rodney-Atkins', "It's-America"],
606: ['Craig-Morgan', "This-Ain't-Nothin'"],
607: ['Tim-McGraw', 'Something-Like-That'],
608: ['Sugarland', "Settlin'"],
609: ['Kenny-Chesney', 'How-Forever-Feels'],
610: ['Darryl-Worley', 'Sounds-Like-Life-To-Me'],
611: ['Craig-Morgan', "That's-What-I-Love-About-Sunday"],
612: ['Toby-Keith', 'I-Wanna-Talk-About-Me-'],
613: ['Brooks-&-Dunn', 'Red-Dirt-Road'],
614: ['Carrie-Underwood', '"Jesus,-Take-The-Wheel"'],
615: ['Josh-Kelley', 'Georgia-Clay'],
616: ['Billy-Currington', "Pretty-Good-At-Drinkin'-Beer"],
617: ['Tim-McGraw', 'Real-Good-Man'],
618: ['Lady-Antebellum', 'I-Run-To-You'],
619: ['Kenny-Chesney', 'When-The-Sun-Goes-Down'],
620: ['Zac-Brown-Band', 'Free'],
621: ['Toby-Keith', 'American-Soldier'],
622: ['Emerson-Drive', 'Moments'],
623: ['Jason-Aldean', "She's-Country"],
624: ['Garth-Brooks', "Ain't-Goin'-Down-Till-The-Sun-Comes-Up"],
625: ['Rodney-Atkins', 'Watching-You'],
626: ['Brad-Paisley', 'Start-A-Band'],
627: ['Trace-Adkins', "You're-Gonna-Miss-This"],
628: ['Toby-Keith', 'My-List-'],
629: ['Sugarland', 'Stay'],
630: ['Kenny-Chesney', 'Big-Star'],
631: ['Faith-Hill', 'Wild-One'],
632: ['Jerrod-Niemann', 'What-Do-You-Want'],
633: ['Clay-Walker', 'Where-Do-I-Go-From-You'],
634: ['Blake-Shelton', "Who-Are-You-When-I'm-Not-Looking"],
635: ['Thompson-Square', 'Are-You-Gonna-Kiss-Me-Or-Not?'],
636: ['Craig-Campbell', 'Family-Man'],
637: ['James-Wesley', 'Real'],
638: ['The-JaneDear-Girls', 'Wildflower'],
639: ['Sunny-Sweeney', 'From-A-Table-Away'],
640: ['Joe-Nichols', "The-Shape-I'm-In"],
641: ['Toby-Keith', 'American-Ride'],
642: ['Kenny-Chesney', '"No-Shoes,-No-Shirt,-No-Problems"'],
643: ['Darius-Rucker', "Don't-Think-I-Don't-Think-About-It"],
644: ['Rodney-Atkins', 'Cleaning-This-Gun-(Come-On-In-Boy)'],
645: ['Carrie-Underwood', 'All-American-Girl'],
646: ['Toby-Keith', 'A-Little-Less-Talk-And-A-Lot-More-Action'],
647: ['Steel-Magnolia', 'Keep-On-Loving-You'],
648: ['Lonestar', 'What-About-Now'],
649: ['Shania-Twain', 'Forever-and-For-Always'],
650: ['Kenny-Chesney', 'There-Goes-My-Life'],
651: ['Taylor-Swift', 'Picture-to-Burn'],
652: ['George-Strait', 'Check-Yes-Or-No'],
653: ['Faith-Hill', 'The-Way-You-Love-Me'],
654: ['Kenny-Chesney', 'Living-In-Fast-Forward'],
655: ['Taylor-Swift', "Should've-Said-No"],
656: ['David-Lee-Murphy', 'Dust-On-The-Bottle'],
657: ['Carrie-Underwood', 'Last-Name'],
658: ['Toby-Keith', 'I-Love-This-Bar'],
659: ['Brad-Paisley', "He-Didn't-Have-To-Be"],
660: ['Jason-Aldean', 'Amarillo-Sky'],
661: ['Brad-Paisley', 'Ticks'],
662: ['Alan-Jackson', 'Gone-Country'],
663: ['Josh-Turner', 'Would-You-Go-With-Me'],
664: ['Blake-Shelton', 'Hillbilly-Bone'],
665: ['Uncle-Kracker', 'Smile'],
666: ['Sara-Evans', 'Suds-In-The-Bucket'],
667: ['Rascal-Flatts', "Prayin'-For-Daylight"],
668: ['Tim-McGraw', 'My-Next-Thirty-Years'],
669: ['Blake-Shelton', 'Some-Beach'],
670: ['Sugarland', 'All-I-Want-To-Do'],
671: ['Sugarland', 'Baby-Girl'],
672: ['Brad-Paisley', 'Letter-To-Me'],
673: ['Zac-Brown-Band', 'Whatever-It-Is'],
674: ['Alan-Jackson', 'Little-Bitty'],
675: ['Kid-Rock', 'All-Summer-Long'],
676: ['Miranda-Lambert', 'White-Liar'],
677: ['Brooks-&-Dunn', 'My-Maria'],
678: ['Sugarland', 'It-Happens'],
679: ['Alan-Jackson', "Livin'-On-Love"],
680: ['Tim-McGraw', 'Live-Like-You-Were-Dying'],
681: ['Taylor-Swift', 'You-Belong-With-Me'],
682: ['Kenny-Chesney', 'I-Go-Back'],
683: ['Travis-Tritt', "It's-A-Great-Day-To-Be-Alive"],
684: ['Brad-Paisley', 'Welcome-To-The-Future'],
685: ['Darius-Rucker', 'History-In-The-Making'],
686: ['Taylor-Swift', 'Our-Song'],
687: ['Kenny-Chesney', 'Young'],
688: ['George-Strait', 'Give-It-Away'],
689: ['Alan-Jackson', 'Chattahoochee'],
690: ['Zac-Brown', 'Highway-20-Ride'],
691: ['Kenny-Chesney', 'Out-Last-Night'],
692: ['Martina-McBride', 'Independence-Day'],
693: ['Brad-Paisley', "I'm-Still-A-Guy"],
694: ['Craig-Morgan', 'Bonfire'],
695: ['Lonestar', "I'm-Already-There"],
696: ['George-Jones', 'Finally-Friday'],
697: ['Garth-Brooks', 'Two-Pina-Coladas'],
698: ['Kenny-Chesney', "She's-Got-It-All"],
699: ['Alan-Jackson', 'Drive-(For-Daddy-Gene)'],
700: ['Steve-Holy', 'Brand-New-Girlfriend'],
701: ['Joe-Nichols', 'Gimmie-That-Girl'],
702: ['Garth-Brooks', 'Rodeo'],
703: ['Guster', 'Do-You-Love-Me'],
704: ['Brad-Paisley', "I'm-Gonna-Miss-Her-(Fishin'-Song)"],
705: ['Lady-Antebellum', 'American-Honey'],
706: ['Kenny-Chesney', 'Summertime'],
707: ['Rascal-Flatts', 'Bless-The-Broken-Road'],
708: ['Toby-Keith',
'"Courtesy-Of-The-Red,-White-And-Blue-(The-Angry-American)"'],
709: ['Blake-Shelton', 'Home'],
710: ['Tim-McGraw', 'Last-Dollar-(Fly-Away)'],
711: ['Tracy-Byrd', 'Ten-Rounds-With-Jose-Cuervo'],
712: ['Montgomery-Gentry', 'Lucky-Man'],
713: ['Billy-Currington', "Must-Be-Doin'-Somethin'-Right"],
714: ['George-Strait', 'I-Saw-God-Today'],
715: ['Jo-Dee-Messina', '"Bye,-Bye"'],
716: ['Tim-McGraw', 'Back-When'],
717: ['Billy-Currington', "That's-How-Country-Boys-Roll"],
718: ['Trace-Adkins', 'Every-Light-In-The-House'],
719: ['Kellie-Pickler', 'Best-Days-Of-Your-Life'],
720: ['Mark-Wills', "19-Somethin'"],
721: ['Kenny-Chesney', "Ain't-Back-Yet"],
722: ['George-Strait', 'Gotta-Get-To-You'],
723: ['Tracy-Lawrence', 'Find-Out-Who-Your-Friends-Are'],
724: ['Montgomery-Gentry', 'Roll-With-Me'],
725: ['Dierks-Bentley', 'Feel-That-Fire'],
726: ['Alan-Jackson', 'Good-Time'],
727: ['Garth-Brooks', 'Shameless'],
728: ['Trace-Adkins', 'Honky-Tonk-Badonkadonk'],
729: ['Brooks-&-Dunn', "Ain't-Nothing-'Bout-You"],
730: ['Rascal-Flatts', 'My-Wish'],
731: ['Justin-Moore', 'Small-Town-USA'],
732: ['Dierks-Bentley', "Lot-Of-Leavin'-Left-To-Do"],
733: ['Josh-Turner', 'Your-Man'],
734: ['Blake-Shelton', "Ol'-Red"],
735: ['Garth-Brooks', 'The-Dance'],
736: ['Kenny-Chesney-With-The-Wailers', 'Everybody-Wants-To-Go-To-Heaven'],
737: ['Blake-Shelton', 'Austin'],
738: ['Keith-Urban', 'Kiss-A-Girl'],
739: ['Tim-McGraw', "Don't-Take-The-Girl"],
740: ['Jessica-Andrews', 'Who-I-Am'],
741: ['James-Otto', "Just-Got-Started-Lovin'-You"],
742: ['Montgomery-Gentry', 'My-Town'],
743: ['Garth-Brooks', '"Two-Of-A-Kind,-Workin\'-On-A-Full-House"'],
744: ['Reba-McEntire', 'Fancy'],
745: ['Toby-Keith', "You-Ain't-Much-Fun"],
746: ['Keith-Urban', 'But-For-The-Grace-Of-God'],
747: ['Joe-Nichols', 'Tequila-Makes-Her-Clothes-Fall-Off'],
748: ['John-Michael-Montgomery', 'Sold-(The-Grundy-County-Auction-Incident)'],
749: ['Blake-Shelton', "She-Wouldn't-Be-Gone"],
750: ['Easton-Corbin', 'A-Little-More-Country-Than-That'],
751: ['Chris-Young', 'The-Man-I-Want-To-Be'],
752: ['Tracy-Byrd', "I'm-From-The-Country"],
753: ['Brad-Paisley', 'American-Saturday-Night'],
754: ['Garth-Brooks', 'The-Thunder-Rolls'],
755: ['Rascal-Flatts', 'What-Hurts-The-Most'],
756: ['David-Nail', 'Red-Light'],
757: ['Pink-Floyd', 'Have-A-Cigar'],
758: ['Van-Halen', "Jamie's-Cryin'"],
759: ['Cheap-Trick', 'I-Want-You-To-Want-Me'],
760: ['The-Eagles', 'Hotel-California'],
761: ['Great-White', 'Once-Bitten-Twice-Shy'],
762: ['Fleetwood-Mac', 'Rhiannon'],
763: ['Jackson-Browne', 'Running-On-Empty'],
764: ['The-Who', 'Behind-Blue-Eyes'],
765: ['Golden-Earring', 'Radar-Love'],
766: ['.38-Special', 'Hold-On-Loosely'],
767: ['The-Jimi-Hendrix-Experience', 'Fire'],
768: ['Tom-Petty', "Free-Fallin'"],
769: ['Journey', '"Lovin\',-Touchin\',-Squeezin\'"'],
770: ['The-Steve-Miller-Band', 'Take-The-Money-And-Run'],
771: ['Blue-Oyster-Cult', "(Don't-Fear)-The-Reaper"],
772: ['The-Doobie-Brothers', 'Black-Water'],
773: ['Aerosmith', 'Back-In-The-Saddle'],
774: ['Boston', 'More-Than-A-Feeling'],
775: ['Judas-Priest', "You've-Got-Another-Thing-Comin'"],
776: ['Led-Zeppelin', 'Hey-Hey-What-Can-I-Do'],
777: ['The-Cars', 'You-Might-Think'],
778: ['Queen', 'Killer-Queen'],
779: ['The-Who', "Won't-Get-Fooled-Again"],
780: ['Jackson-Browne', "Somebody's-Baby"],
781: ['Thin-Lizzy', 'The-Boys-Are-Back-In-Town'],
782: ['The-Steve-Miller-Band', 'Swingtown'],
783: ['Eddie-Money', 'Take-Me-Home-Tonight'],
784: ['Led-Zeppelin', 'Rock-And-Roll'],
785: ['Journey', 'Wheel-In-The-Sky'],
786: ['Aerosmith', 'Sweet-Emotion'],
787: ['Lynyrd-Skynyrd', 'Sweet-Home-Alabama'],
788: ['Deep-Purple', 'Smoke-On-The-Water'],
789: ['Foreigner', 'Double-Vision'],
790: ['The-Who', "Baba-O'Riley"],
791: ['Tom-Petty-&-The-Heartbreakers', "Don't-Do-Me-Like-That"],
792: ['Rush', 'Red-Barchetta'],
793: ['Van-Halen', 'Jump'],
794: ['Boston', 'Rock-And-Roll-Band'],
795: ['Bad-Company', 'Bad-Company'],
796: ['Aerosmith', 'Rag-Doll'],
797: ['The-Rolling-Stones', "It's-Only-Rock-'N-Roll-(But-I-Like-It)"],
798: ['Foo-Fighters', 'The-Pretender'],
799: ['Creedence-Clearwater-Revival', 'Fortunate-Son'],
800: ['AC\\/DC', "It's-A-Long-Way-To-The-Top-(If-You-Wanna-Rock-'N'-Roll)"],
801: ['The-Beatles', 'Come-Together'],
802: ['Journey', 'Lights'],
803: ['Heart', 'Magic-Man'],
804: ['AC\\/DC', 'Have-A-Drink-On-Me'],
805: ['The-Doors', 'Love-Her-Madly'],
806: ['The-Guess-Who', 'American-Woman'],
807: ['The-Police', 'Every-Little-Thing-She-Does-Is-Magic'],
808: ['Creedence-Clearwater-Revival', "Lookin'-Out-My-Back-Door"],
809: ['Lynyrd-Skynyrd', 'Free-Bird'],
810: ['Pink-Floyd', 'Young-Lust'],
811: ['Paul-McCartney', "Maybe-I'm-Amazed"],
812: ['Eric-Clapton', 'Cocaine'],
813: ['Georgia-Satellites', 'Keep-Your-Hands-To-Yourself'],
814: ['Dio', 'Holy-Diver'],
815: ['Queen', 'Under-Pressure'],
816: ['Rush', 'Freewill'],
817: ['Bachman-Turner-Overdrive', 'Let-It-Ride'],
818: ['Def-Leppard', "Foolin'"],
819: ['Tom-Petty-&-The-Heartbreakers', 'Breakdown'],
820: ['Pink-Floyd', 'Learning-To-Fly'],
821: ['Ozzy-Osbourne', 'Over-The-Mountain'],
822: ['Van-Halen', "Why-Can't-This-Be-Love"],
823: ['Red-Rider', 'Lunatic-Fringe'],
824: ['Led-Zeppelin', 'Kashmir'],
825: ['Kansas', 'Dust-In-The-Wind'],
826: ['Dio', 'Rainbow-In-The-Dark'],
827: ['Steely-Dan', 'Do-It-Again'],
828: ['T.-Rex', 'Bang-A-Gong-(Get-It-On)'],
829: ['Boston', 'Foreplay\\/Longtime'],
830: ['U2', 'Beautiful-Day'],
831: ['Van-Halen', "I'll-Wait"],
832: ['The-Steve-Miller-Band', 'Fly-Like-An-Eagle'],
833: ['Molly-Hatchet', "Flirtin'-With-Disaster"],
834: ['The-Rolling-Stones', 'Sympathy-For-The-Devil'],
835: ['Jefferson-Airplane', 'Somebody-To-Love'],
836: ['Pink-Floyd', 'Mother'],
837: ['Steely-Dan', 'Reeling-In-The-Years'],
838: ['Stevie-Ray-Vaughan-&-Double-Trouble', 'Crossfire'],
839: ['Ted-Nugent', 'Cat-Scratch-Fever'],
840: ['Lynyrd-Skynyrd', 'Gimme-Three-Steps'],
841: ['Tom-Petty', "Runnin'-Down-A-Dream"],
842: ['Stevie-Nicks', 'Edge-Of-Seventeen'],
843: ['Def-Leppard', 'Rock-Of-Ages'],
844: ['ZZ-Top', 'Sharp-Dressed-Man'],
845: ['Norman-Greenbaum', 'Spirit-In-The-Sky'],
846: ['Rush', 'Limelight'],
847: ['Stevie-Ray-Vaughan-&-Double-Trouble', 'Pride-And-Joy'],
848: ['Cheap-Trick', 'Surrender'],
849: ['Bob-Seger-&-The-Silver-Bullet-Band', 'Old-Time-Rock-&-Roll'],
850: ['Paul-McCartney-&-Wings', 'Band-On-The-Run'],
851: ['Queensryche', 'Silent-Lucidity'],
852: ['Pink-Floyd', 'Another-Brick-In-The-Wall-(Part-2)'],
853: ['The-Doobie-Brothers', "Long-Train-Runnin'"],
854: ['Tommy-Tutone', '867-5309\\/Jenny'],
855: ["Guns-N'-Roses", 'Patience'],
856: ['Night-Ranger', 'Sister-Christian'],
857: ['Motley-Crue', 'Looks-That-Kill'],
858: ['Foreigner', 'Cold-As-Ice'],
859: ['The-Cars', 'Just-What-I-Needed'],
860: ['The-Doors', 'People-Are-Strange'],
861: ['Def-Leppard', 'Too-Late-For-Love'],
862: ['Steve-Winwood', 'While-You-See-A-Chance'],
863: ['The-Rolling-Stones', 'Start-Me-Up'],
864: ['Eric-Clapton', 'Run-Back-To-Your-Side'],
865: ['Toto', 'Hold-The-Line'],
866: ['Foreigner', 'Hot-Blooded'],
867: ['Queen', 'Somebody-To-Love'],
868: ["Manfred-Mann's-Earth-Band", 'Blinded-By-The-Light'],
869: ['Led-Zeppelin', 'The-Ocean'],
870: ['Stevie-Ray-Vaughan-&-Double-Trouble', 'Cold-Shot'],
871: ['The-Edgar-Winter-Group', 'Free-Ride'],
872: ['Billy-Squier', 'Lonely-Is-The-Night'],
873: ['Pink-Floyd', 'Run-Like-Hell'],
874: ['AC\\/DC', 'Moneytalks'],
875: ['Steppenwolf', 'Magic-Carpet-Ride'],
876: ['Bob-Seger-&-The-Silver-Bullet-Band', 'Hollywood-Nights'],
877: ['Def-Leppard', 'Hysteria'],
878: ['Bad-Company', "Rock-'N'-Roll-Fantasy"],
879: ['Black-Sabbath', 'Iron-Man'],
880: ['Tom-Petty', "I-Won't-Back-Down"],
881: ['The-Jimi-Hendrix-Experience', 'Foxey-Lady'],
882: ['Pink-Floyd', 'Time'],
883: ['The-Eagles', 'Life-In-The-Fast-Lane'],
884: ['Metallica', 'For-Whom-The-Bell-Tolls'],
885: ['The-Who', 'Pinball-Wizard'],
886: ['Warren-Zevon', 'Werewolves-Of-London'],
887: ['The-Beatles', 'Get-Back'],
888: ['The-Jimi-Hendrix-Experience', 'Purple-Haze'],
889: ['Iron-Maiden', 'Run-To-The-Hills'],
890: ['The-Allman-Brothers-Band', "Ramblin'-Man"],
891: ['Boston', "Don't-Look-Back"],
892: ['Bob-Seger', 'Turn-The-Page'],
893: ['Pink-Floyd', 'Welcome-To-The-Machine'],
894: ['Creedence-Clearwater-Revival', 'Down-On-The-Corner'],
895: ['Led-Zeppelin', 'Over-The-Hills-And-Far-Away'],
896: ['Bob-Seger-&-The-Silver-Bullet-Band', 'Night-Moves'],
897: ['AC\\/DC', 'Shoot-To-Thrill'],
898: ['David-Bowie', 'Space-Oddity'],
899: ['Pat-Benatar', 'Hit-Me-With-Your-Best-Shot'],
900: ['Dire-Straits', 'Money-For-Nothing'],
901: ['The-Eagles', 'Already-Gone'],
902: ['Santana', 'Evil-Ways'],
903: ['Led-Zeppelin', 'When-The-Levee-Breaks'],
904: ['Elton-John', "Saturday-Night's-Alright-(For-Fighting)"],
905: ['Van-Halen', 'Hot-For-Teacher'],
906: ['Journey', 'Separate-Ways'],
907: ['Led-Zeppelin', "D'yer-Ma'ker"],
908: ['The-Black-Crowes', 'She-Talks-To-Angels'],
909: ['Scorpions', 'The-Zoo'],
910: ["Guns-N'-Roses", 'Paradise-City'],
911: ['Buffalo-Springfield', "For-What-It's-Worth"],
912: ['Rush', 'Closer-To-The-Heart'],
913: ['Autograph', 'Turn-Up-The-Radio'],
914: ['Phil-Collins', 'In-The-Air-Tonight'],
915: ['Van-Halen', 'Right-Now'],
916: ['Grand-Funk-Railroad', "We're-An-American-Band"],
917: ['ZZ-Top', 'Cheap-Sunglasses'],
918: ['Tom-Petty-&-The-Heartbreakers', "Mary-Jane's-Last-Dance"],
919: ['Ozzy-Osbourne', 'Bark-At-The-Moon'],
920: ['Motley-Crue', 'Home-Sweet-Home'],
921: ['Heart', 'Crazy-On-You'],
922: ['Tom-Petty-&-The-Heartbreakers', 'I-Should-Have-Known-It'],
923: ['The-Doobie-Brothers', 'Listen-To-The-Music'],
924: ['Dire-Straits', 'Sultans-Of-Swing'],
925: ['Journey', 'Any-Way-You-Want-It'],
926: ['Grand-Funk-Railroad', 'Some-Kind-Of-Wonderful'],
927: ['The-Beatles', 'Revolution'],
928: ['The-Edgar-Winter-Group', 'Frankenstein'],
929: ['Ratt', 'Round-And-Round'],
930: ['Led-Zeppelin', 'Whole-Lotta-Love'],
931: ['Aerosmith', 'Come-Together'],
932: ['Van-Halen', "Ain't-Talkin'-'Bout-Love"],
933: ['Tom-Petty-&-The-Heartbreakers', 'Refugee'],
934: ['ZZ-Top', "Gimme-All-Your-Lovin'"],
935: ['Led-Zeppelin', 'Ramble-On'],
936: ['Rush', 'The-Spirit-Of-Radio'],
937: ['AC\\/DC', 'Girls-Got-Rhythm'],
938: ['Van-Halen', 'Panama'],
939: ['John-Cafferty-&-The-Beaver-Brown-Band', 'On-The-Dark-Side'],
940: ['Queen', 'Fat-Bottomed-Girls'],
941: ['Kansas', 'Carry-On-Wayward-Son'],
942: ['The-Rolling-Stones', 'Miss-You'],
943: ['R.E.M.', "It's-The-End-Of-The-World-As-We-Know-It-(And-I-Feel-Fine)"],
944: ['AC\\/DC', 'Who-Made-Who'],
945: ['Steppenwolf', 'Born-To-Be-Wild'],
946: ['Motley-Crue', '"Girls,-Girls,-Girls"'],
947: ['Bad-Company', "Feel-Like-Makin'-Love"],
948: ['Pink-Floyd', 'Speak-To-Me\\/Breathe'],
949: ['Billy-Idol', 'White-Wedding-(Part-I)'],
950: ['Heart', 'Barracuda'],
951: ['The-Rolling-Stones', 'Paint-It-Black'],
952: ['Styx', 'Renegade'],
953: ['Ozzy-Osbourne', "I-Don't-Know"],
954: ['Don-Henley', 'The-Boys-Of-Summer'],
955: ['Jethro-Tull', 'Locomotive-Breath'],
956: ['ZZ-Top', 'La-Grange'],
957: ['George-Thorogood-&-The-Destroyers',
'"One-Bourbon,-One-Scotch,-One-Beer"'],
958: ['Def-Leppard', 'Love-Bites'],
959: ['Tom-Petty-&-The-Heartbreakers', 'American-Girl'],
960: ['The-Rolling-Stones', 'Brown-Sugar'],
961: ['Sammy-Hagar', "I-Can't-Drive-55"],
962: ['Living-Colour', 'Cult-Of-Personality'],
963: ['The-Doobie-Brothers', 'China-Grove'],
964: ['Kiss', 'Rock-And-Roll-All-Nite'],
965: ['Journey', "Don't-Stop-Believin'"],
966: ['Metallica', 'The-Unforgiven'],
967: ['Quiet-Riot', 'Cum-On-Feel-The-Noize'],
968: ['Boston', "Smokin'"],
969: ['Bachman-Turner-Overdrive', "Takin'-Care-Of-Business"],
970: ['Supertramp', 'Give-A-Little-Bit'],
971: ['Boston', 'Peace-Of-Mind'],
972: ['Lynyrd-Skynyrd', 'Simple-Man'],
973: ['Joan-Jett-&-The-Blackhearts', 'I-Love-Rock-And-Roll'],
974: ['Foghat', 'Slow-Ride'],
975: ['The-Black-Crowes', 'Twice-As-Hard'],
976: ['Pat-Benatar', 'Heartbreaker'],
977: ['Whitesnake', 'Here-I-Go-Again'],
978: ['Billy-Squier', 'The-Stroke'],
979: ['Led-Zeppelin', 'Heartbreaker'],
980: ['Led-Zeppelin', "Living-Loving-Maid-(She's-Just-A-Woman)"],
981: ['ZZ-Top', 'Tush'],
982: ['Santana', 'Black-Magic-Woman'],
983: ['Def-Leppard', 'Armageddon-It'],
984: ['Joe-Walsh', 'Rocky-Mountain-Way'],
985: ['John-Cougar-Mellencamp', 'Pink-Houses'],
986: ['The-Rolling-Stones', 'Honky-Tonk-Women'],
987: ['The-Steve-Miller-Band', 'The-Joker'],
988: ['Fleetwood-Mac', 'The-Chain'],
989: ['John-Fogerty', 'Centerfield'],
990: ['Judas-Priest', 'Living-After-Midnight'],
991: ['Queen', "You're-My-Best-Friend"],
992: ['Mountain', 'Mississippi-Queen'],
993: ['The-Steve-Miller-Band', "Rock-'N-Me"],
994: ['Derek-&-The-Dominos', 'Layla'],
995: ['Joe-Walsh', "Life's-Been-Good"],
996: ['George-Thorogood-&-The-Destroyers', 'Bad-To-The-Bone'],
997: ['Cream', 'White-Room'],
998: ['Blue-Oyster-Cult', "Burnin'-For-You"],
999: ['Judas-Priest', 'Breaking-The-Law'],
...}
Apriori¶
In [30]:
#b) Apriori on the playlist data using a min-support value of 0.002.
L, support = apriori(playlist,.002)
In [32]:
rules_confident = generateRules(L,support,metric='confidence',minMetric=0.5)
frozenset([2840]) --> frozenset([2839]) conf: 0.511727078891 lift: 29.1571967478 frozenset([2883]) --> frozenset([2878]) conf: 0.528138528139 lift: 49.9024741394 frozenset([2826]) --> frozenset([2839]) conf: 0.617511520737 lift: 35.1845850003 frozenset([2774]) --> frozenset([2018]) conf: 0.514925373134 lift: 34.843563585 frozenset([2878]) --> frozenset([2839]) conf: 0.507972665148 lift: 28.943277679 frozenset([2878]) --> frozenset([5]) conf: 0.535307517084 lift: 32.7018494973 frozenset([44]) --> frozenset([2018]) conf: 0.502538071066 lift: 34.0053494092 frozenset([2871]) --> frozenset([5]) conf: 0.535294117647 lift: 32.7010309278 frozenset([5]) --> frozenset([2839]) conf: 0.511045655376 lift: 29.1183705838 frozenset([2871]) --> frozenset([2839]) conf: 0.505882352941 lift: 28.8241758242 frozenset([2883]) --> frozenset([5]) conf: 0.510822510823 lift: 31.2060644314 frozenset([2512]) --> frozenset([20]) conf: 0.524038461538 lift: 33.2371794872 frozenset([3018]) --> frozenset([3016]) conf: 0.693548387097 lift: 243.799890651 frozenset([3016]) --> frozenset([3018]) conf: 0.728813559322 lift: 243.799890651 frozenset([2832]) --> frozenset([5]) conf: 0.604651162791 lift: 36.9380415796 frozenset([2781]) --> frozenset([2839]) conf: 0.505494505495 lift: 28.8020770438 frozenset([2826]) --> frozenset([5]) conf: 0.585253456221 lift: 35.7530388278 frozenset([2832]) --> frozenset([2839]) conf: 0.622093023256 lift: 35.4456299514 frozenset([80, 2781]) --> frozenset([5, 2839]) conf: 0.60824742268 lift: 72.7092308149 frozenset([80, 2839]) --> frozenset([5, 2781]) conf: 0.533936651584 lift: 85.1834319527 frozenset([2840, 2878]) --> frozenset([5, 2839]) conf: 0.567010309278 lift: 67.7797914377 frozenset([2781, 2878]) --> frozenset([5, 2839]) conf: 0.597765363128 lift: 71.456216895 frozenset([80, 2840]) --> frozenset([5, 2839]) conf: 0.597122302158 lift: 71.3793460909 frozenset([89, 2781]) --> frozenset([5, 2839]) conf: 0.567073170732 lift: 67.7873058269 frozenset([89, 2839]) --> frozenset([5, 2781]) conf: 0.508196721311 lift: 81.0769230769 frozenset([2781, 6]) --> frozenset([5, 2839]) conf: 0.537037037037 lift: 64.1968192977 frozenset([2018, 2839]) --> frozenset([80, 5]) conf: 0.542857142857 lift: 94.612244898 frozenset([2018, 5]) --> frozenset([80, 2839]) conf: 0.524861878453 lift: 98.5125371866 frozenset([80, 2018]) --> frozenset([5, 2839]) conf: 0.521978021978 lift: 62.3966811287 frozenset([2840, 2781]) --> frozenset([5, 2839]) conf: 0.544973544974 lift: 65.1455407651 frozenset([20, 2781]) --> frozenset([5, 2839]) conf: 0.502857142857 lift: 60.1109921779 frozenset([2018, 2781]) --> frozenset([5, 2839]) conf: 0.61744966443 lift: 73.8092567162 frozenset([2018, 2839]) --> frozenset([5, 2781]) conf: 0.525714285714 lift: 83.8716483516 frozenset([2018, 5]) --> frozenset([2781, 2839]) conf: 0.508287292818 lift: 76.3904235727 frozenset([6, 2839]) --> frozenset([80, 5]) conf: 0.5 lift: 87.1428571429 frozenset([89, 2878]) --> frozenset([5, 2839]) conf: 0.612244897959 lift: 73.1870846321 frozenset([80, 2878]) --> frozenset([5, 2839]) conf: 0.666666666667 lift: 79.6926032661 frozenset([89, 2878]) --> frozenset([5, 2781]) conf: 0.578231292517 lift: 92.2501308216 frozenset([89, 2781]) --> frozenset([5, 2878]) conf: 0.518292682927 lift: 91.4841722885 frozenset([2018, 2781]) --> frozenset([80, 2839]) conf: 0.624161073826 lift: 117.150232318 frozenset([2018, 2839]) --> frozenset([80, 2781]) conf: 0.531428571429 lift: 113.627098675 frozenset([80, 2018]) --> frozenset([2781, 2839]) conf: 0.510989010989 lift: 76.7964644052 frozenset([2018, 2781]) --> frozenset([80, 5]) conf: 0.597315436242 lift: 104.103547459
In [33]:
rules_lift = generateRules(L,support,metric='lift',minMetric=20.0)
frozenset([2839]) --> frozenset([2883]) conf: 0.120879120879 lift: 21.7059131345 frozenset([2883]) --> frozenset([2839]) conf: 0.380952380952 lift: 21.7059131345 frozenset([34]) --> frozenset([80]) conf: 0.364985163205 lift: 28.4578657326 frozenset([80]) --> frozenset([34]) conf: 0.231203007519 lift: 28.4578657326 frozenset([2791]) --> frozenset([634]) conf: 0.297935103245 lift: 37.9090431981 frozenset([634]) --> frozenset([2791]) conf: 0.30981595092 lift: 37.9090431981 frozenset([3003]) --> frozenset([635]) conf: 0.404255319149 lift: 47.3686741195 frozenset([635]) --> frozenset([3003]) conf: 0.268361581921 lift: 47.3686741195 frozenset([2774]) --> frozenset([20]) conf: 0.440298507463 lift: 27.9259664978 frozenset([20]) --> frozenset([2774]) conf: 0.180428134557 lift: 27.9259664978 frozenset([20]) --> frozenset([18]) conf: 0.227828746177 lift: 27.0009611184 frozenset([18]) --> frozenset([20]) conf: 0.425714285714 lift: 27.0009611184 frozenset([89]) --> frozenset([2840]) conf: 0.308823529412 lift: 27.3134328358 frozenset([2840]) --> frozenset([89]) conf: 0.268656716418 lift: 27.3134328358 frozenset([20]) --> frozenset([34]) conf: 0.191131498471 lift: 23.5256218296 frozenset([34]) --> frozenset([20]) conf: 0.370919881306 lift: 23.5256218296 frozenset([2781]) --> frozenset([1]) conf: 0.230769230769 lift: 22.6295690125 frozenset([1]) --> frozenset([2781]) conf: 0.297872340426 lift: 22.6295690125 frozenset([34]) --> frozenset([24]) conf: 0.323442136499 lift: 37.3715315375 frozenset([24]) --> frozenset([34]) conf: 0.303621169916 lift: 37.3715315375 frozenset([2838]) --> frozenset([5]) conf: 0.349315068493 lift: 21.3396009442 frozenset([5]) --> frozenset([2838]) conf: 0.150220913108 lift: 21.3396009442 frozenset([75]) --> frozenset([104]) conf: 0.323170731707 lift: 28.7663561185 frozenset([104]) --> frozenset([75]) conf: 0.227467811159 lift: 28.7663561185 frozenset([5]) --> frozenset([44]) conf: 0.213549337261 lift: 22.4823007857 frozenset([44]) --> frozenset([5]) conf: 0.368020304569 lift: 22.4823007857 frozenset([20]) --> frozenset([10]) conf: 0.195718654434 lift: 22.3033235877 frozenset([10]) --> frozenset([20]) conf: 0.351648351648 lift: 22.3033235877 frozenset([2512]) --> frozenset([80]) conf: 0.485576923077 lift: 37.8603961828 frozenset([80]) --> frozenset([2512]) conf: 0.18984962406 lift: 37.8603961828 frozenset([2781]) --> frozenset([2840]) conf: 0.346153846154 lift: 30.6150565852 frozenset([2840]) --> frozenset([2781]) conf: 0.402985074627 lift: 30.6150565852 frozenset([2781]) --> frozenset([75]) conf: 0.164835164835 lift: 20.8456177968 frozenset([75]) --> frozenset([2781]) conf: 0.274390243902 lift: 20.8456177968 frozenset([2924]) --> frozenset([2792]) conf: 0.355648535565 lift: 52.8756317392 frozenset([2792]) --> frozenset([2924]) conf: 0.304659498208 lift: 52.8756317392 frozenset([2793]) --> frozenset([632]) conf: 0.373626373626 lift: 48.8896592367 frozenset([632]) --> frozenset([2793]) conf: 0.321766561514 lift: 48.8896592367 frozenset([2525]) --> frozenset([1892]) conf: 0.339563862928 lift: 37.4603963677 frozenset([1892]) --> frozenset([2525]) conf: 0.289893617021 lift: 37.4603963677 frozenset([2839]) --> frozenset([2512]) conf: 0.116758241758 lift: 23.2842878276 frozenset([2512]) --> frozenset([2839]) conf: 0.408653846154 lift: 23.2842878276 frozenset([2790]) --> frozenset([632]) conf: 0.361823361823 lift: 47.3452146638 frozenset([632]) --> frozenset([2790]) conf: 0.400630914826 lift: 47.3452146638 frozenset([2883]) --> frozenset([3056]) conf: 0.393939393939 lift: 57.5373452838 frozenset([3056]) --> frozenset([2883]) conf: 0.320422535211 lift: 57.5373452838 frozenset([2791]) --> frozenset([632]) conf: 0.353982300885 lift: 46.3191982357 frozenset([632]) --> frozenset([2791]) conf: 0.378548895899 lift: 46.3191982357 frozenset([1891]) --> frozenset([2793]) conf: 0.360869565217 lift: 54.8310240484 frozenset([2793]) --> frozenset([1891]) conf: 0.304029304029 lift: 54.8310240484 frozenset([6]) --> frozenset([20]) conf: 0.39793814433 lift: 25.2392572275 frozenset([20]) --> frozenset([6]) conf: 0.295107033639 lift: 25.2392572275 frozenset([47]) --> frozenset([39]) conf: 0.441176470588 lift: 36.1660079051 frozenset([39]) --> frozenset([47]) conf: 0.177865612648 lift: 36.1660079051 frozenset([2790]) --> frozenset([2866]) conf: 0.253561253561 lift: 45.3350034385 frozenset([2866]) --> frozenset([2790]) conf: 0.383620689655 lift: 45.3350034385 frozenset([2924]) --> frozenset([635]) conf: 0.397489539749 lift: 46.5758929627 frozenset([635]) --> frozenset([2924]) conf: 0.268361581921 lift: 46.5758929627 frozenset([1892]) --> frozenset([2792]) conf: 0.23670212766 lift: 35.1914131015 frozenset([2792]) --> frozenset([1892]) conf: 0.318996415771 lift: 35.1914131015 frozenset([196]) --> frozenset([11]) conf: 0.364806866953 lift: 33.7772072348 frozenset([11]) --> frozenset([196]) conf: 0.189732142857 lift: 33.7772072348 frozenset([2790]) --> frozenset([525]) conf: 0.273504273504 lift: 37.5660836588 frozenset([525]) --> frozenset([2790]) conf: 0.317880794702 lift: 37.5660836588 frozenset([2830]) --> frozenset([3056]) conf: 0.366255144033 lift: 53.4938851214 frozenset([3056]) --> frozenset([2830]) conf: 0.31338028169 lift: 53.4938851214 frozenset([47]) --> frozenset([20]) conf: 0.43137254902 lift: 27.3598369011 frozenset([20]) --> frozenset([47]) conf: 0.134556574924 lift: 27.3598369011 frozenset([10]) --> frozenset([24]) conf: 0.241758241758 lift: 27.933514953 frozenset([24]) --> frozenset([10]) conf: 0.245125348189 lift: 27.933514953 frozenset([80]) --> frozenset([24]) conf: 0.227443609023 lift: 26.2795568308 frozenset([24]) --> frozenset([80]) conf: 0.33704735376 lift: 26.2795568308 frozenset([2839]) --> frozenset([2840]) conf: 0.32967032967 lift: 29.1571967478 frozenset([2840]) --> frozenset([2839]) conf: 0.511727078891 lift: 29.1571967478 frozenset([2830]) --> frozenset([5]) conf: 0.489711934156 lift: 29.9164227228 frozenset([5]) --> frozenset([2830]) conf: 0.175257731959 lift: 29.9164227228 frozenset([75]) --> frozenset([1]) conf: 0.295731707317 lift: 28.9998846797 frozenset([1]) --> frozenset([75]) conf: 0.229314420804 lift: 28.9998846797 frozenset([78]) --> frozenset([2825]) conf: 0.33908045977 lift: 49.3510788465 frozenset([2825]) --> frozenset([78]) conf: 0.414035087719 lift: 49.3510788465 frozenset([525]) --> frozenset([1892]) conf: 0.331125827815 lift: 36.5295195153 frozenset([1892]) --> frozenset([525]) conf: 0.265957446809 lift: 36.5295195153 frozenset([2781]) --> frozenset([3056]) conf: 0.164835164835 lift: 24.0752205541 frozenset([3056]) --> frozenset([2781]) conf: 0.316901408451 lift: 24.0752205541 frozenset([635]) --> frozenset([2793]) conf: 0.299435028249 lift: 45.4965749881 frozenset([2793]) --> frozenset([635]) conf: 0.388278388278 lift: 45.4965749881 frozenset([1]) --> frozenset([2840]) conf: 0.267139479905 lift: 23.6267497366 frozenset([2840]) --> frozenset([1]) conf: 0.240938166311 lift: 23.6267497366 frozenset([487]) --> frozenset([1892]) conf: 0.274390243902 lift: 30.2704981837 frozenset([1892]) --> frozenset([487]) conf: 0.239361702128 lift: 30.2704981837 frozenset([1938]) --> frozenset([2792]) conf: 0.333333333333 lift: 49.5579450418 frozenset([2792]) --> frozenset([1938]) conf: 0.308243727599 lift: 49.5579450418 frozenset([2781]) --> frozenset([5]) conf: 0.47619047619 lift: 29.0903990462 frozenset([5]) --> frozenset([2781]) conf: 0.382916053019 lift: 29.0903990462 frozenset([2878]) --> frozenset([2883]) conf: 0.277904328018 lift: 49.9024741394 frozenset([2883]) --> frozenset([2878]) conf: 0.528138528139 lift: 49.9024741394 frozenset([2791]) --> frozenset([1899]) conf: 0.256637168142 lift: 30.41517067 frozenset([1899]) --> frozenset([2791]) conf: 0.248571428571 lift: 30.41517067 frozenset([2774]) --> frozenset([2508]) conf: 0.473880597015 lift: 34.3646279094 frozenset([2508]) --> frozenset([2774]) conf: 0.222027972028 lift: 34.3646279094 frozenset([18]) --> frozenset([80]) conf: 0.425714285714 lift: 33.1929108485 frozenset([80]) --> frozenset([18]) conf: 0.28007518797 lift: 33.1929108485 frozenset([2791]) --> frozenset([1891]) conf: 0.259587020649 lift: 46.8159548544 frozenset([1891]) --> frozenset([2791]) conf: 0.382608695652 lift: 46.8159548544 frozenset([2839]) --> frozenset([37]) conf: 0.15521978022 lift: 22.2786037492 frozenset([37]) --> frozenset([2839]) conf: 0.391003460208 lift: 22.2786037492 frozenset([37]) --> frozenset([1]) conf: 0.318339100346 lift: 31.2167987762 frozenset([1]) --> frozenset([37]) conf: 0.217494089835 lift: 31.2167987762 frozenset([2790]) --> frozenset([2525]) conf: 0.321937321937 lift: 41.6011218503 frozenset([2525]) --> frozenset([2790]) conf: 0.352024922118 lift: 41.6011218503 frozenset([5]) --> frozenset([1]) conf: 0.217967599411 lift: 21.3742222779 frozenset([1]) --> frozenset([5]) conf: 0.34988179669 lift: 21.3742222779 frozenset([2839]) --> frozenset([2826]) conf: 0.184065934066 lift: 35.1845850003 frozenset([2826]) --> frozenset([2839]) conf: 0.617511520737 lift: 35.1845850003 frozenset([2791]) --> frozenset([3003]) conf: 0.253687315634 lift: 44.7785100107 frozenset([3003]) --> frozenset([2791]) conf: 0.365957446809 lift: 44.7785100107 frozenset([2790]) --> frozenset([2792]) conf: 0.2849002849 lift: 42.3572179845 frozenset([2792]) --> frozenset([2790]) conf: 0.358422939068 lift: 42.3572179845 frozenset([2887]) --> frozenset([2064]) conf: 0.337037037037 lift: 43.2826510721 frozenset([2064]) --> frozenset([2887]) conf: 0.28173374613 lift: 43.2826510721 frozenset([1043]) --> frozenset([1032]) conf: 0.425339366516 lift: 71.429461227 frozenset([1032]) --> frozenset([1043]) conf: 0.380566801619 lift: 71.429461227 frozenset([2839]) --> frozenset([2825]) conf: 0.151098901099 lift: 21.9915172547 frozenset([2825]) --> frozenset([2839]) conf: 0.385964912281 lift: 21.9915172547 frozenset([18]) --> frozenset([24]) conf: 0.248571428571 lift: 28.7207321926 frozenset([24]) --> frozenset([18]) conf: 0.242339832869 lift: 28.7207321926 frozenset([2791]) --> frozenset([1938]) conf: 0.244837758112 lift: 39.3638380096 frozenset([1938]) --> frozenset([2791]) conf: 0.321705426357 lift: 39.3638380096 frozenset([6]) --> frozenset([164]) conf: 0.19793814433 lift: 37.4907498941 frozenset([164]) --> frozenset([6]) conf: 0.438356164384 lift: 37.4907498941 frozenset([2774]) --> frozenset([2018]) conf: 0.514925373134 lift: 34.843563585 frozenset([2018]) --> frozenset([2774]) conf: 0.225122349103 lift: 34.843563585 frozenset([6]) --> frozenset([44]) conf: 0.210309278351 lift: 22.1411900152 frozenset([44]) --> frozenset([6]) conf: 0.258883248731 lift: 22.1411900152 frozenset([20]) --> frozenset([2018]) conf: 0.380733944954 lift: 25.763203975 frozenset([2018]) --> frozenset([20]) conf: 0.406199021207 lift: 25.763203975 frozenset([2791]) --> frozenset([2790]) conf: 0.407079646018 lift: 48.1073040365 frozenset([2790]) --> frozenset([2791]) conf: 0.393162393162 lift: 48.1073040365 frozenset([2790]) --> frozenset([1892]) conf: 0.364672364672 lift: 40.2303449112 frozenset([1892]) --> frozenset([2790]) conf: 0.340425531915 lift: 40.2303449112 frozenset([6]) --> frozenset([18]) conf: 0.263917525773 lift: 31.2779970545 frozenset([18]) --> frozenset([6]) conf: 0.365714285714 lift: 31.2779970545 frozenset([10]) --> frozenset([41]) conf: 0.258241758242 lift: 32.1677721678 frozenset([41]) --> frozenset([10]) conf: 0.282282282282 lift: 32.1677721678 frozenset([39]) --> frozenset([196]) conf: 0.175889328063 lift: 31.3128297342 frozenset([196]) --> frozenset([39]) conf: 0.381974248927 lift: 31.3128297342 frozenset([39]) --> frozenset([104]) conf: 0.308300395257 lift: 27.4427047109 frozenset([104]) --> frozenset([39]) conf: 0.334763948498 lift: 27.4427047109 frozenset([39]) --> frozenset([2018]) conf: 0.310276679842 lift: 20.9955573896 frozenset([2018]) --> frozenset([39]) conf: 0.256117455139 lift: 20.9955573896 frozenset([2525]) --> frozenset([632]) conf: 0.373831775701 lift: 48.9165364545 frozenset([632]) --> frozenset([2525]) conf: 0.378548895899 lift: 48.9165364545 frozenset([2839]) --> frozenset([2878]) conf: 0.306318681319 lift: 28.943277679 frozenset([2878]) --> frozenset([2839]) conf: 0.507972665148 lift: 28.943277679 frozenset([78]) --> frozenset([5]) conf: 0.333333333333 lift: 20.3632793324 frozenset([5]) --> frozenset([78]) conf: 0.170839469809 lift: 20.3632793324 frozenset([2878]) --> frozenset([2781]) conf: 0.407744874715 lift: 30.9766619106 frozenset([2781]) --> frozenset([2878]) conf: 0.327838827839 lift: 30.9766619106 frozenset([2525]) --> frozenset([635]) conf: 0.358255451713 lift: 41.9786331556 frozenset([635]) --> frozenset([2525]) conf: 0.324858757062 lift: 41.9786331556 frozenset([11]) --> frozenset([10]) conf: 0.308035714286 lift: 35.1025313972 frozenset([10]) --> frozenset([11]) conf: 0.379120879121 lift: 35.1025313972 frozenset([44]) --> frozenset([80]) conf: 0.329949238579 lift: 25.7261173238 frozenset([80]) --> frozenset([44]) conf: 0.244360902256 lift: 25.7261173238 frozenset([2790]) --> frozenset([1899]) conf: 0.270655270655 lift: 32.0765160765 frozenset([1899]) --> frozenset([2790]) conf: 0.271428571429 lift: 32.0765160765 frozenset([2774]) --> frozenset([104]) conf: 0.335820895522 lift: 29.8923835757 frozenset([104]) --> frozenset([2774]) conf: 0.19313304721 lift: 29.8923835757 frozenset([2830]) --> frozenset([2878]) conf: 0.452674897119 lift: 42.7721064522 frozenset([2878]) --> frozenset([2830]) conf: 0.250569476082 lift: 42.7721064522 frozenset([2788]) --> frozenset([632]) conf: 0.308771929825 lift: 40.4033427417 frozenset([632]) --> frozenset([2788]) conf: 0.277602523659 lift: 40.4033427417 frozenset([75]) --> frozenset([24]) conf: 0.283536585366 lift: 32.76071744 frozenset([24]) --> frozenset([75]) conf: 0.259052924791 lift: 32.76071744 frozenset([6]) --> frozenset([24]) conf: 0.187628865979 lift: 21.6792349884 frozenset([24]) --> frozenset([6]) conf: 0.25348189415 lift: 21.6792349884 frozenset([11]) --> frozenset([24]) conf: 0.225446428571 lift: 26.0487962595 frozenset([24]) --> frozenset([11]) conf: 0.281337047354 lift: 26.0487962595 frozenset([44]) --> frozenset([2825]) conf: 0.327411167513 lift: 47.652685012 frozenset([2825]) --> frozenset([44]) conf: 0.452631578947 lift: 47.652685012 frozenset([1891]) --> frozenset([2792]) conf: 0.404347826087 lift: 60.115942029 frozenset([2792]) --> frozenset([1891]) conf: 0.333333333333 lift: 60.115942029 frozenset([2508]) --> frozenset([2347]) conf: 0.160839160839 lift: 21.8741258741 frozenset([2347]) --> frozenset([2508]) conf: 0.301639344262 lift: 21.8741258741 frozenset([5]) --> frozenset([2825]) conf: 0.172312223859 lift: 25.0789861251 frozenset([2825]) --> frozenset([5]) conf: 0.410526315789 lift: 25.0789861251 frozenset([44]) --> frozenset([89]) conf: 0.213197969543 lift: 21.6751269036 frozenset([89]) --> frozenset([44]) conf: 0.205882352941 lift: 21.6751269036 frozenset([635]) --> frozenset([634]) conf: 0.268361581921 lift: 34.1461301168 frozenset([634]) --> frozenset([635]) conf: 0.291411042945 lift: 34.1461301168 frozenset([2791]) --> frozenset([525]) conf: 0.277286135693 lift: 38.0855261873 frozenset([525]) --> frozenset([2791]) conf: 0.311258278146 lift: 38.0855261873 frozenset([6]) --> frozenset([34]) conf: 0.19587628866 lift: 24.1096393282 frozenset([34]) --> frozenset([6]) conf: 0.281899109792 lift: 24.1096393282 frozenset([2878]) --> frozenset([5]) conf: 0.535307517084 lift: 32.7018494973 frozenset([5]) --> frozenset([2878]) conf: 0.346097201767 lift: 32.7018494973 frozenset([2924]) --> frozenset([2793]) conf: 0.36820083682 lift: 55.9449476604 frozenset([2793]) --> frozenset([2924]) conf: 0.322344322344 lift: 55.9449476604 frozenset([2781]) --> frozenset([89]) conf: 0.300366300366 lift: 30.5372405372 frozenset([89]) --> frozenset([2781]) conf: 0.401960784314 lift: 30.5372405372 frozenset([6]) --> frozenset([2781]) conf: 0.334020618557 lift: 25.3757788603 frozenset([2781]) --> frozenset([6]) conf: 0.296703296703 lift: 25.3757788603 frozenset([44]) --> frozenset([2018]) conf: 0.502538071066 lift: 34.0053494092 frozenset([2018]) --> frozenset([44]) conf: 0.323001631321 lift: 34.0053494092 frozenset([2795]) --> frozenset([635]) conf: 0.355102040816 lift: 41.6091317883 frozenset([635]) --> frozenset([2795]) conf: 0.245762711864 lift: 41.6091317883 frozenset([501]) --> frozenset([1892]) conf: 0.427046263345 lift: 47.1113803286 frozenset([1892]) --> frozenset([501]) conf: 0.31914893617 lift: 47.1113803286 frozenset([78]) --> frozenset([2018]) conf: 0.390804597701 lift: 26.4446569537 frozenset([2018]) --> frozenset([78]) conf: 0.221859706362 lift: 26.4446569537 frozenset([3003]) --> frozenset([2793]) conf: 0.357446808511 lift: 54.3109656301 frozenset([2793]) --> frozenset([3003]) conf: 0.307692307692 lift: 54.3109656301 frozenset([2831]) --> frozenset([44]) conf: 0.238442822384 lift: 25.1030666815 frozenset([44]) --> frozenset([2831]) conf: 0.248730964467 lift: 25.1030666815 frozenset([10]) --> frozenset([104]) conf: 0.346153846154 lift: 30.8121492242 frozenset([104]) --> frozenset([10]) conf: 0.270386266094 lift: 30.8121492242 frozenset([20]) --> frozenset([11]) conf: 0.227828746177 lift: 21.0945008737 frozenset([11]) --> frozenset([20]) conf: 0.332589285714 lift: 21.0945008737 frozenset([2790]) --> frozenset([2793]) conf: 0.273504273504 lift: 41.5566200182 frozenset([2793]) --> frozenset([2790]) conf: 0.351648351648 lift: 41.5566200182 frozenset([2791]) --> frozenset([2525]) conf: 0.342182890855 lift: 44.2172782327 frozenset([2525]) --> frozenset([2791]) conf: 0.361370716511 lift: 44.2172782327 frozenset([18]) --> frozenset([1]) conf: 0.314285714286 lift: 30.819317798 frozenset([1]) --> frozenset([18]) conf: 0.260047281324 lift: 30.819317798 frozenset([1938]) --> frozenset([632]) conf: 0.391472868217 lift: 51.2249040178 frozenset([632]) --> frozenset([1938]) conf: 0.318611987382 lift: 51.2249040178 frozenset([6]) --> frozenset([1]) conf: 0.286597938144 lift: 28.1042138871 frozenset([1]) --> frozenset([6]) conf: 0.328605200946 lift: 28.1042138871 frozenset([2871]) --> frozenset([5]) conf: 0.535294117647 lift: 32.7010309278 frozenset([5]) --> frozenset([2871]) conf: 0.134020618557 lift: 32.7010309278 frozenset([1892]) --> frozenset([2788]) conf: 0.276595744681 lift: 40.2568122434 frozenset([2788]) --> frozenset([1892]) conf: 0.364912280702 lift: 40.2568122434 frozenset([2791]) --> frozenset([1892]) conf: 0.371681415929 lift: 41.0035774807 frozenset([1892]) --> frozenset([2791]) conf: 0.335106382979 lift: 41.0035774807 frozenset([2839]) --> frozenset([5]) conf: 0.476648351648 lift: 29.1183705838 frozenset([5]) --> frozenset([2839]) conf: 0.511045655376 lift: 29.1183705838 frozenset([24]) --> frozenset([104]) conf: 0.311977715877 lift: 27.7700335936 frozenset([104]) --> frozenset([24]) conf: 0.240343347639 lift: 27.7700335936 frozenset([44]) --> frozenset([104]) conf: 0.271573604061 lift: 24.1735474173 frozenset([104]) --> frozenset([44]) conf: 0.229613733906 lift: 24.1735474173 frozenset([2791]) --> frozenset([2924]) conf: 0.247787610619 lift: 43.0051468138 frozenset([2924]) --> frozenset([2791]) conf: 0.351464435146 lift: 43.0051468138 frozenset([89]) --> frozenset([80]) conf: 0.289215686275 lift: 22.5501253133 frozenset([80]) --> frozenset([89]) conf: 0.221804511278 lift: 22.5501253133 frozenset([20]) --> frozenset([2825]) conf: 0.17125382263 lift: 24.9249423252 frozenset([2825]) --> frozenset([20]) conf: 0.39298245614 lift: 24.9249423252 frozenset([47]) --> frozenset([11]) conf: 0.446078431373 lift: 41.3020833333 frozenset([11]) --> frozenset([47]) conf: 0.203125 lift: 41.3020833333 frozenset([78]) --> frozenset([80]) conf: 0.298850574713 lift: 23.3013568404 frozenset([80]) --> frozenset([78]) conf: 0.195488721805 lift: 23.3013568404 frozenset([2508]) --> frozenset([44]) conf: 0.243006993007 lift: 25.5835788577 frozenset([44]) --> frozenset([2508]) conf: 0.352791878173 lift: 25.5835788577 frozenset([78]) --> frozenset([104]) conf: 0.304597701149 lift: 27.1131172611 frozenset([104]) --> frozenset([78]) conf: 0.227467811159 lift: 27.1131172611 frozenset([3055]) --> frozenset([2838]) conf: 0.39336492891 lift: 55.8793741479 frozenset([2838]) --> frozenset([3055]) conf: 0.284246575342 lift: 55.8793741479 frozenset([11]) --> frozenset([41]) conf: 0.296875 lift: 36.9801051051 frozenset([41]) --> frozenset([11]) conf: 0.399399399399 lift: 36.9801051051 frozenset([80]) --> frozenset([2840]) conf: 0.261278195489 lift: 23.1083572471 frozenset([2840]) --> frozenset([80]) conf: 0.296375266525 lift: 23.1083572471 frozenset([2018]) --> frozenset([104]) conf: 0.231647634584 lift: 20.6196220655 frozenset([104]) --> frozenset([2018]) conf: 0.304721030043 lift: 20.6196220655 frozenset([635]) --> frozenset([2866]) conf: 0.268361581921 lift: 47.9812000779 frozenset([2866]) --> frozenset([635]) conf: 0.409482758621 lift: 47.9812000779 frozenset([2508]) --> frozenset([2018]) conf: 0.342657342657 lift: 23.1866665146 frozenset([2018]) --> frozenset([2508]) conf: 0.319738988581 lift: 23.1866665146 frozenset([1892]) --> frozenset([632]) conf: 0.265957446809 lift: 34.8009933553 frozenset([632]) --> frozenset([1892]) conf: 0.315457413249 lift: 34.8009933553 frozenset([1]) --> frozenset([80]) conf: 0.36170212766 lift: 28.201887698 frozenset([80]) --> frozenset([1]) conf: 0.287593984962 lift: 28.201887698 frozenset([20]) --> frozenset([104]) conf: 0.247706422018 lift: 22.0490609127 frozenset([104]) --> frozenset([20]) conf: 0.347639484979 lift: 22.0490609127 frozenset([18]) --> frozenset([104]) conf: 0.257142857143 lift: 22.889025138 frozenset([104]) --> frozenset([18]) conf: 0.19313304721 lift: 22.889025138 frozenset([1899]) --> frozenset([634]) conf: 0.28 lift: 35.626993865 frozenset([634]) --> frozenset([1899]) conf: 0.300613496933 lift: 35.626993865 frozenset([2508]) --> frozenset([41]) conf: 0.162587412587 lift: 20.2526302526 frozenset([41]) --> frozenset([2508]) conf: 0.279279279279 lift: 20.2526302526 frozenset([2525]) --> frozenset([1938]) conf: 0.299065420561 lift: 48.0823009491 frozenset([1938]) --> frozenset([2525]) conf: 0.372093023256 lift: 48.0823009491 frozenset([2791]) --> frozenset([501]) conf: 0.262536873156 lift: 38.7545533755 frozenset([501]) --> frozenset([2791]) conf: 0.316725978648 lift: 38.7545533755 frozenset([34]) --> frozenset([10]) conf: 0.252225519288 lift: 28.7426223628 frozenset([10]) --> frozenset([34]) conf: 0.233516483516 lift: 28.7426223628 frozenset([39]) --> frozenset([44]) conf: 0.231225296443 lift: 24.3432114123 frozenset([44]) --> frozenset([39]) conf: 0.296954314721 lift: 24.3432114123 frozenset([2878]) --> frozenset([2840]) conf: 0.441913439636 lift: 39.084369885 frozenset([2840]) --> frozenset([2878]) conf: 0.413646055437 lift: 39.084369885 frozenset([3003]) --> frozenset([2792]) conf: 0.357446808511 lift: 53.1429878746 frozenset([2792]) --> frozenset([3003]) conf: 0.301075268817 lift: 53.1429878746 frozenset([29]) --> frozenset([104]) conf: 0.243980738363 lift: 21.7174270972 frozenset([104]) --> frozenset([29]) conf: 0.326180257511 lift: 21.7174270972 frozenset([39]) --> frozenset([11]) conf: 0.284584980237 lift: 26.3495200452 frozenset([11]) --> frozenset([39]) conf: 0.321428571429 lift: 26.3495200452 frozenset([2839]) --> frozenset([2871]) conf: 0.118131868132 lift: 28.8241758242 frozenset([2871]) --> frozenset([2839]) conf: 0.505882352941 lift: 28.8241758242 frozenset([501]) --> frozenset([2788]) conf: 0.313167259786 lift: 45.5795717051 frozenset([2788]) --> frozenset([501]) conf: 0.308771929825 lift: 45.5795717051 frozenset([501]) --> frozenset([634]) conf: 0.345195729537 lift: 43.9224504945 frozenset([634]) --> frozenset([501]) conf: 0.29754601227 lift: 43.9224504945 frozenset([6]) --> frozenset([2512]) conf: 0.175257731959 lift: 34.9504361618 frozenset([2512]) --> frozenset([6]) conf: 0.408653846154 lift: 34.9504361618 frozenset([5]) --> frozenset([2883]) conf: 0.173784977909 lift: 31.2060644314 frozenset([2883]) 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49.9010853874 frozenset([2878]) --> frozenset([80]) conf: 0.28701594533 lift: 22.3786116773 frozenset([80]) --> frozenset([2878]) conf: 0.236842105263 lift: 22.3786116773 frozenset([1891]) --> frozenset([632]) conf: 0.382608695652 lift: 50.0650116582 frozenset([632]) --> frozenset([1891]) conf: 0.277602523659 lift: 50.0650116582 frozenset([20]) --> frozenset([2512]) conf: 0.166666666667 lift: 33.2371794872 frozenset([2512]) --> frozenset([20]) conf: 0.524038461538 lift: 33.2371794872 frozenset([41]) --> frozenset([104]) conf: 0.345345345345 lift: 30.7401822423 frozenset([104]) --> frozenset([41]) conf: 0.24678111588 lift: 30.7401822423 frozenset([2878]) --> frozenset([2826]) conf: 0.220956719818 lift: 42.2363351983 frozenset([2826]) --> frozenset([2878]) conf: 0.447004608295 lift: 42.2363351983 frozenset([632]) --> frozenset([2792]) conf: 0.321766561514 lift: 47.8382687154 frozenset([2792]) --> frozenset([632]) conf: 0.365591397849 lift: 47.8382687154 frozenset([2790]) --> 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frozenset([2792]) --> frozenset([2525]) conf: 0.36917562724 lift: 47.7053115823 frozenset([5]) --> frozenset([2512]) conf: 0.147275405007 lift: 29.3701144217 frozenset([2512]) --> frozenset([5]) conf: 0.480769230769 lift: 29.3701144217 frozenset([78]) --> frozenset([11]) conf: 0.26724137931 lift: 24.7436884236 frozenset([11]) --> frozenset([78]) conf: 0.207589285714 lift: 24.7436884236 frozenset([6]) --> frozenset([75]) conf: 0.263917525773 lift: 33.3759114911 frozenset([75]) --> frozenset([6]) conf: 0.390243902439 lift: 33.3759114911 frozenset([3018]) --> frozenset([3016]) conf: 0.693548387097 lift: 243.799890651 frozenset([3016]) --> frozenset([3018]) conf: 0.728813559322 lift: 243.799890651 frozenset([2018]) --> frozenset([2825]) conf: 0.225122349103 lift: 32.7651755817 frozenset([2825]) --> frozenset([2018]) conf: 0.484210526316 lift: 32.7651755817 frozenset([5]) --> frozenset([89]) conf: 0.294550810015 lift: 29.9459990182 frozenset([89]) --> frozenset([5]) conf: 0.490196078431 lift: 29.9459990182 frozenset([75]) --> frozenset([18]) conf: 0.274390243902 lift: 32.5191637631 frozenset([18]) --> frozenset([75]) conf: 0.257142857143 lift: 32.5191637631 frozenset([2878]) --> frozenset([3056]) conf: 0.29840546697 lift: 43.5840097533 frozenset([3056]) --> frozenset([2878]) conf: 0.461267605634 lift: 43.5840097533 frozenset([2839]) --> frozenset([80]) conf: 0.303571428571 lift: 23.6694414608 frozenset([80]) --> frozenset([2839]) conf: 0.415413533835 lift: 23.6694414608 frozenset([2029]) --> frozenset([2034]) conf: 0.29702970297 lift: 34.7064565611 frozenset([2034]) --> frozenset([2029]) conf: 0.253521126761 lift: 34.7064565611 frozenset([39]) --> frozenset([2774]) conf: 0.209486166008 lift: 32.4234558433 frozenset([2774]) --> frozenset([39]) conf: 0.39552238806 lift: 32.4234558433 frozenset([5]) --> frozenset([2832]) conf: 0.153166421208 lift: 36.9380415796 frozenset([2832]) --> frozenset([5]) conf: 0.604651162791 lift: 36.9380415796 frozenset([34]) --> 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36.5474481138 frozenset([634]) --> frozenset([1892]) conf: 0.331288343558 lift: 36.5474481138 frozenset([10]) --> frozenset([2018]) conf: 0.313186813187 lift: 21.1924779951 frozenset([2018]) --> frozenset([10]) conf: 0.185970636215 lift: 21.1924779951 frozenset([2830]) --> frozenset([2840]) conf: 0.38683127572 lift: 34.212710697 frozenset([2840]) --> frozenset([2830]) conf: 0.200426439232 lift: 34.212710697 frozenset([2774]) --> frozenset([44]) conf: 0.421641791045 lift: 44.390105311 frozenset([44]) --> frozenset([2774]) conf: 0.286802030457 lift: 44.390105311 frozenset([5]) --> frozenset([75]) conf: 0.160530191458 lift: 20.3011961637 frozenset([75]) --> frozenset([5]) conf: 0.332317073171 lift: 20.3011961637 frozenset([1892]) --> frozenset([635]) conf: 0.316489361702 lift: 37.0846856593 frozenset([635]) --> frozenset([1892]) conf: 0.33615819209 lift: 37.0846856593 frozenset([2018]) --> frozenset([80]) conf: 0.296900489396 lift: 23.1493088349 frozenset([80]) --> frozenset([2018]) conf: 0.342105263158 lift: 23.1493088349 frozenset([6]) --> frozenset([5]) conf: 0.40618556701 lift: 24.8138104854 frozenset([5]) --> frozenset([6]) conf: 0.290132547865 lift: 24.8138104854 frozenset([635]) --> frozenset([1891]) conf: 0.251412429379 lift: 45.3416850897 frozenset([1891]) --> frozenset([635]) conf: 0.386956521739 lift: 45.3416850897 frozenset([5]) --> frozenset([3056]) conf: 0.187039764359 lift: 27.318343048 frozenset([3056]) --> frozenset([5]) conf: 0.447183098592 lift: 27.318343048 frozenset([2839]) --> frozenset([6]) conf: 0.241758241758 lift: 20.6765605528 frozenset([6]) --> frozenset([2839]) conf: 0.362886597938 lift: 20.6765605528 frozenset([2790]) --> frozenset([2788]) conf: 0.296296296296 lift: 43.1241065627 frozenset([2788]) --> frozenset([2790]) conf: 0.364912280702 lift: 43.1241065627 frozenset([44]) --> frozenset([10]) conf: 0.210659898477 lift: 24.0059686506 frozenset([10]) --> frozenset([44]) conf: 0.228021978022 lift: 24.0059686506 frozenset([78]) --> 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30.549764322 frozenset([11]) --> frozenset([44]) conf: 0.290178571429 lift: 30.549764322 frozenset([2831]) --> frozenset([2825]) conf: 0.209245742092 lift: 30.4544329193 frozenset([2825]) --> frozenset([2831]) conf: 0.301754385965 lift: 30.4544329193 frozenset([634]) --> frozenset([632]) conf: 0.29754601227 lift: 38.9344119525 frozenset([632]) --> frozenset([634]) conf: 0.305993690852 lift: 38.9344119525 frozenset([2878]) --> frozenset([89]) conf: 0.334851936219 lift: 34.0432801822 frozenset([89]) --> frozenset([2878]) conf: 0.360294117647 lift: 34.0432801822 frozenset([2781]) --> frozenset([20]) conf: 0.320512820513 lift: 20.3285501451 frozenset([20]) --> frozenset([2781]) conf: 0.267584097859 lift: 20.3285501451 frozenset([2791]) --> frozenset([2788]) conf: 0.271386430678 lift: 39.4986285773 frozenset([2788]) --> frozenset([2791]) conf: 0.322807017544 lift: 39.4986285773 frozenset([1891]) --> frozenset([1938]) conf: 0.386956521739 lift: 62.2130097742 frozenset([1938]) --> 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42.9587490519 frozenset([2791]) --> frozenset([635]) conf: 0.410029498525 lift: 48.0452644034 frozenset([635]) --> frozenset([2791]) conf: 0.392655367232 lift: 48.0452644034 frozenset([5]) --> frozenset([2826]) conf: 0.187039764359 lift: 35.7530388278 frozenset([2826]) --> frozenset([5]) conf: 0.585253456221 lift: 35.7530388278 frozenset([2018]) --> frozenset([41]) conf: 0.181076672104 lift: 22.5557368135 frozenset([41]) --> frozenset([2018]) conf: 0.333333333333 lift: 22.5557368135 frozenset([2034]) --> frozenset([2064]) conf: 0.281690140845 lift: 36.1749444033 frozenset([2064]) --> frozenset([2034]) conf: 0.30959752322 lift: 36.1749444033 frozenset([2791]) --> frozenset([2792]) conf: 0.321533923304 lift: 47.8036815005 frozenset([2792]) --> frozenset([2791]) conf: 0.390681003584 lift: 47.8036815005 frozenset([2525]) --> frozenset([2788]) conf: 0.271028037383 lift: 39.4464666339 frozenset([2788]) --> frozenset([2525]) conf: 0.305263157895 lift: 39.4464666339 frozenset([5]) --> 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30.2900956882 frozenset([196]) --> frozenset([29]) conf: 0.454935622318 lift: 30.2900956882 frozenset([39]) --> frozenset([10]) conf: 0.274703557312 lift: 31.304130652 frozenset([10]) --> frozenset([39]) conf: 0.381868131868 lift: 31.304130652 frozenset([2839]) --> frozenset([3056]) conf: 0.173076923077 lift: 25.2789815818 frozenset([3056]) --> frozenset([2839]) conf: 0.443661971831 lift: 25.2789815818 frozenset([635]) --> frozenset([1938]) conf: 0.290960451977 lift: 46.7792230544 frozenset([1938]) --> frozenset([635]) conf: 0.399224806202 lift: 46.7792230544 frozenset([44]) --> frozenset([41]) conf: 0.230964467005 lift: 28.7699882624 frozenset([41]) --> frozenset([44]) conf: 0.273273273273 lift: 28.7699882624 frozenset([20]) --> frozenset([75]) conf: 0.214067278287 lift: 27.0716789737 frozenset([75]) --> frozenset([20]) conf: 0.426829268293 lift: 27.0716789737 frozenset([2866]) --> frozenset([632]) conf: 0.370689655172 lift: 48.5053845317 frozenset([632]) --> frozenset([2866]) conf: 0.271293375394 lift: 48.5053845317 frozenset([477]) --> frozenset([2525]) conf: 0.281879194631 lift: 36.424763219 frozenset([2525]) --> frozenset([477]) conf: 0.261682242991 lift: 36.424763219 frozenset([20]) --> frozenset([41]) conf: 0.162079510703 lift: 20.1893636756 frozenset([41]) --> frozenset([20]) conf: 0.318318318318 lift: 20.1893636756 frozenset([75]) --> frozenset([80]) conf: 0.44512195122 lift: 34.7061250688 frozenset([80]) --> frozenset([75]) conf: 0.274436090226 lift: 34.7061250688 frozenset([164]) --> frozenset([80]) conf: 0.470319634703 lift: 36.6707865554 frozenset([80]) --> frozenset([164]) conf: 0.193609022556 lift: 36.6707865554 frozenset([2788]) --> frozenset([635]) conf: 0.301754385965 lift: 35.3581127961 frozenset([635]) --> frozenset([2788]) conf: 0.242937853107 lift: 35.3581127961 frozenset([11]) --> frozenset([104]) conf: 0.350446428571 lift: 31.1942443286 frozenset([104]) --> frozenset([11]) conf: 0.336909871245 lift: 31.1942443286 frozenset([2791]) --> frozenset([2795]) conf: 0.262536873156 lift: 44.449099994 frozenset([2795]) --> frozenset([2791]) conf: 0.363265306122 lift: 44.449099994 frozenset([29]) --> frozenset([11]) conf: 0.23113964687 lift: 21.4010548039 frozenset([11]) --> frozenset([29]) conf: 0.321428571429 lift: 21.4010548039 frozenset([2830]) --> frozenset([89]) conf: 0.349794238683 lift: 35.5624142661 frozenset([89]) --> frozenset([2830]) conf: 0.208333333333 lift: 35.5624142661 frozenset([11]) --> frozenset([34]) conf: 0.209821428571 lift: 25.8260915642 frozenset([34]) --> frozenset([11]) conf: 0.278931750742 lift: 25.8260915642 frozenset([5]) --> frozenset([164]) conf: 0.148748159057 lift: 28.173852227 frozenset([164]) --> frozenset([5]) conf: 0.461187214612 lift: 28.173852227 frozenset([1735]) --> frozenset([39]) conf: 0.376569037657 lift: 30.8697305969 frozenset([39]) --> frozenset([1735]) conf: 0.177865612648 lift: 30.8697305969 frozenset([525]) --> frozenset([1899]) conf: 0.298013245033 lift: 35.3188268685 frozenset([1899]) --> frozenset([525]) conf: 0.257142857143 lift: 35.3188268685 frozenset([2839]) --> frozenset([164]) conf: 0.135989010989 lift: 25.7571880175 frozenset([164]) --> frozenset([2839]) conf: 0.452054794521 lift: 25.7571880175 frozenset([2831]) --> frozenset([2774]) conf: 0.248175182482 lift: 38.4115916767 frozenset([2774]) --> frozenset([2831]) conf: 0.380597014925 lift: 38.4115916767 frozenset([2791]) --> frozenset([2789]) conf: 0.244837758112 lift: 54.0205862047 frozenset([2789]) --> frozenset([2791]) conf: 0.441489361702 lift: 54.0205862047 frozenset([2790]) --> frozenset([635]) conf: 0.376068376068 lift: 44.0658650828 frozenset([635]) --> frozenset([2790]) conf: 0.372881355932 lift: 44.0658650828 frozenset([44]) --> frozenset([2018, 11]) conf: 0.223350253807 lift: 61.7637901861 frozenset([11]) --> frozenset([2018, 44]) conf: 0.196428571429 lift: 41.1507936508 frozenset([2018]) --> frozenset([11, 44]) conf: 0.143556280587 lift: 45.8054962982 frozenset([20]) --> frozenset([2018, 44]) conf: 0.203363914373 lift: 42.6037129707 frozenset([2018]) --> frozenset([20, 44]) conf: 0.216965742251 lift: 47.6176666062 frozenset([44]) --> frozenset([2018, 20]) conf: 0.337563451777 lift: 56.2334617658 frozenset([6]) --> frozenset([80, 1]) conf: 0.171134020619 lift: 46.3963344788 frozenset([1]) --> frozenset([80, 6]) conf: 0.19621749409 lift: 39.8975571316 frozenset([80]) --> frozenset([1, 6]) conf: 0.156015037594 lift: 46.5575810029 frozenset([6]) --> frozenset([80, 20]) conf: 0.243298969072 lift: 44.458331441 frozenset([20]) --> frozenset([80, 6]) conf: 0.180428134557 lift: 36.6870540265 frozenset([80]) --> frozenset([20, 6]) conf: 0.221804511278 lift: 47.6707312322 frozenset([2839]) --> frozenset([80, 89]) conf: 0.115384615385 lift: 40.5606258149 frozenset([89]) --> frozenset([80, 2839]) conf: 0.205882352941 lift: 38.6425339367 frozenset([80]) --> frozenset([89, 2839]) conf: 0.157894736842 lift: 35.7894736842 frozenset([2839]) --> frozenset([2018, 5]) conf: 0.179945054945 lift: 41.2382369012 frozenset([5]) --> frozenset([2018, 2839]) conf: 0.19293078056 lift: 45.7301073007 frozenset([2018]) --> frozenset([5, 2839]) conf: 0.213703099511 lift: 25.545834489 frozenset([5]) --> frozenset([80, 2781]) conf: 0.20765832106 lift: 44.4003461731 frozenset([2781]) --> frozenset([80, 5]) conf: 0.258241758242 lift: 45.0078492936 frozenset([80]) --> frozenset([2781, 5]) conf: 0.265037593985 lift: 42.2836899942 frozenset([2878]) --> frozenset([89, 2781]) conf: 0.216400911162 lift: 54.7335963109 frozenset([2781]) --> frozenset([89, 2878]) conf: 0.173992673993 lift: 49.0967082804 frozenset([89]) --> frozenset([2781, 2878]) conf: 0.232843137255 lift: 53.95716946 frozenset([6]) --> frozenset([18, 20]) conf: 0.173195876289 lift: 48.2158721373 frozenset([20]) --> frozenset([18, 6]) conf: 0.128440366972 lift: 41.622706422 frozenset([18]) --> frozenset([20, 6]) conf: 0.24 lift: 51.5813471503 frozenset([2839]) --> frozenset([2781, 6]) conf: 0.14010989011 lift: 35.8750508751 frozenset([6]) --> frozenset([2781, 2839]) conf: 0.210309278351 lift: 31.6073509637 frozenset([2781]) --> frozenset([6, 2839]) conf: 0.186813186813 lift: 44.0284715285 frozenset([78]) --> frozenset([2018, 44]) conf: 0.247126436782 lift: 51.7717403924 frozenset([44]) --> frozenset([2018, 78]) conf: 0.218274111675 lift: 66.5736040609 frozenset([2018]) --> frozenset([44, 78]) conf: 0.140293637847 lift: 40.9815499851 frozenset([2839]) --> frozenset([44, 5]) conf: 0.153846153846 lift: 44.0106100796 frozenset([5]) --> frozenset([44, 2839]) conf: 0.164948453608 lift: 50.6819396716 frozenset([44]) --> frozenset([5, 2839]) conf: 0.284263959391 lift: 33.9806024079 frozenset([44]) --> frozenset([104, 20]) conf: 0.218274111675 lift: 55.8889515573 frozenset([20]) --> frozenset([104, 44]) conf: 0.131498470948 lift: 50.9771642516 frozenset([104]) --> frozenset([44, 20]) conf: 0.184549356223 lift: 40.5032132071 frozenset([2839]) --> frozenset([2825, 5]) conf: 0.127747252747 lift: 45.2902225979 frozenset([5]) --> frozenset([2825, 2839]) conf: 0.136966126657 lift: 51.6486812157 frozenset([2825]) --> frozenset([5, 2839]) conf: 0.326315789474 lift: 39.007432125 frozenset([39]) --> frozenset([2018, 44]) conf: 0.167984189723 lift: 35.191839342 frozenset([44]) --> frozenset([2018, 39]) conf: 0.215736040609 lift: 56.9982863979 frozenset([2018]) --> frozenset([44, 39]) conf: 0.138662316476 lift: 49.1599392089 frozenset([2839]) --> frozenset([2840, 80]) conf: 0.134615384615 lift: 40.1715550636 frozenset([80]) --> frozenset([2840, 2839]) conf: 0.184210526316 lift: 31.8377192982 frozenset([2840]) --> frozenset([80, 2839]) conf: 0.208955223881 lift: 39.2192881745 frozenset([2774]) --> frozenset([2018, 20]) conf: 0.339552238806 lift: 56.5647665288 frozenset([20]) --> frozenset([2018, 2774]) conf: 0.139143730887 lift: 41.8237822985 frozenset([2018]) --> frozenset([20, 2774]) conf: 0.148450244698 lift: 52.1840351702 frozenset([2839]) --> frozenset([89, 2878]) conf: 0.142857142857 lift: 40.3109815355 frozenset([2878]) --> frozenset([89, 2839]) conf: 0.236902050114 lift: 53.6977980258 frozenset([89]) --> frozenset([2878, 2839]) conf: 0.254901960784 lift: 47.4140508221 frozenset([20]) --> frozenset([11, 44]) conf: 0.136085626911 lift: 43.4217831099 frozenset([11]) --> frozenset([20, 44]) conf: 0.198660714286 lift: 43.6002456538 frozenset([44]) --> frozenset([11, 20]) conf: 0.225888324873 lift: 62.8848839982 frozenset([6]) --> frozenset([2018, 20]) conf: 0.181443298969 lift: 30.2259760692 frozenset([20]) --> frozenset([2018, 6]) conf: 0.134556574924 lift: 41.965464119 frozenset([2018]) --> frozenset([20, 6]) conf: 0.143556280587 lift: 30.8534431024 frozenset([2839]) --> frozenset([80, 20]) conf: 0.152472527473 lift: 27.8614997337 frozenset([20]) --> frozenset([80, 2839]) conf: 0.169724770642 lift: 31.8560338744 frozenset([80]) --> frozenset([20, 2839]) conf: 0.208646616541 lift: 43.4907620811 frozenset([2839]) --> frozenset([5, 78]) conf: 0.119505494505 lift: 42.7335164835 frozenset([78]) --> frozenset([5, 2839]) conf: 0.25 lift: 29.8847262248 frozenset([5]) --> frozenset([78, 2839]) conf: 0.128129602356 lift: 49.6711766892 frozenset([2878]) --> frozenset([89, 5]) conf: 0.259681093394 lift: 53.8578587699 frozenset([5]) --> frozenset([89, 2878]) conf: 0.167893961708 lift: 47.3757927324 frozenset([89]) --> frozenset([5, 2878]) conf: 0.279411764706 lift: 49.3191489362 frozenset([5]) --> frozenset([2840, 3056]) conf: 0.134020618557 lift: 45.1965468108 frozenset([3056]) --> frozenset([2840, 5]) conf: 0.320422535211 lift: 57.7875076546 frozenset([2840]) --> frozenset([3056, 5]) conf: 0.194029850746 lift: 63.3728992831 frozenset([6]) --> frozenset([80, 2781]) conf: 0.20206185567 lift: 43.2037410989 frozenset([2781]) --> frozenset([80, 6]) conf: 0.179487179487 lift: 36.4957264957 frozenset([80]) --> frozenset([2781, 6]) conf: 0.184210526316 lift: 47.166991553 frozenset([6]) --> frozenset([80, 18]) conf: 0.181443298969 lift: 50.5118660486 frozenset([18]) --> frozenset([80, 6]) conf: 0.251428571429 lift: 51.1238095238 frozenset([80]) --> frozenset([18, 6]) conf: 0.165413533835 lift: 53.6043233083 frozenset([39]) --> frozenset([2018, 20]) conf: 0.205533596838 lift: 34.2390907504 frozenset([20]) --> frozenset([2018, 39]) conf: 0.159021406728 lift: 42.0140633826 frozenset([2018]) --> frozenset([20, 39]) conf: 0.169657422512 lift: 50.9955788827 frozenset([2839]) --> frozenset([2018, 20]) conf: 0.138736263736 lift: 23.1115671477 frozenset([20]) --> frozenset([2018, 2839]) conf: 0.154434250765 lift: 36.6053298384 frozenset([2018]) --> frozenset([20, 2839]) conf: 0.164763458401 lift: 34.3436595703 frozenset([5]) --> frozenset([2840, 2018]) conf: 0.123711340206 lift: 44.2374688944 frozenset([2018]) --> frozenset([2840, 5]) conf: 0.137030995106 lift: 24.7132420739 frozenset([2840]) --> frozenset([2018, 5]) conf: 0.179104477612 lift: 41.0456007257 frozenset([2781]) --> frozenset([80, 2018]) conf: 0.201465201465 lift: 45.9163547076 frozenset([2018]) --> frozenset([80, 2781]) conf: 0.179445350734 lift: 38.3680059198 frozenset([80]) --> frozenset([2018, 2781]) conf: 0.206766917293 lift: 57.5616894585 frozenset([20]) --> frozenset([80, 75]) conf: 0.142201834862 lift: 40.4009048636 frozenset([75]) --> frozenset([80, 20]) conf: 0.283536585366 lift: 51.8110024713 frozenset([80]) --> frozenset([75, 20]) conf: 0.174812030075 lift: 51.7943071966 frozenset([2781]) --> frozenset([5, 6]) conf: 0.201465201465 lift: 42.4201855674 frozenset([6]) --> frozenset([5, 2781]) conf: 0.226804123711 lift: 36.1839809675 frozenset([5]) --> frozenset([2781, 6]) conf: 0.162002945508 lift: 41.4807541955 frozenset([5]) --> frozenset([44, 20]) conf: 0.123711340206 lift: 27.1510391098 frozenset([44]) --> frozenset([20, 5]) conf: 0.213197969543 lift: 46.544483035 frozenset([20]) --> frozenset([44, 5]) conf: 0.128440366972 lift: 36.7428029105 frozenset([5]) --> frozenset([2840, 89]) conf: 0.144329896907 lift: 47.5143184422 frozenset([89]) --> frozenset([2840, 5]) conf: 0.240196078431 lift: 43.3188405797 frozenset([2840]) --> frozenset([89, 5]) conf: 0.208955223881 lift: 43.3373134328 frozenset([5]) --> frozenset([80, 89]) conf: 0.128129602356 lift: 45.0408127605 frozenset([89]) --> frozenset([80, 5]) conf: 0.213235294118 lift: 37.1638655462 frozenset([80]) --> frozenset([89, 5]) conf: 0.163533834586 lift: 33.9169172932 frozenset([2831]) --> frozenset([2018, 20]) conf: 0.228710462287 lift: 38.1000400629 frozenset([20]) --> frozenset([2018, 2831]) conf: 0.14373088685 lift: 41.9856139897 frozenset([2018]) --> frozenset([20, 2831]) conf: 0.153344208809 lift: 55.3105894035 frozenset([2878]) --> frozenset([2840, 3056]) conf: 0.20728929385 lift: 69.9053651129 frozenset([3056]) --> frozenset([2840, 2878]) conf: 0.320422535211 lift: 68.5109626833 frozenset([2840]) --> frozenset([3056, 2878]) conf: 0.194029850746 lift: 61.4378489233 frozenset([2839]) --> frozenset([2840, 3056]) conf: 0.120879120879 lift: 40.7647636916 frozenset([3056]) --> frozenset([2840, 2839]) conf: 0.30985915493 lift: 53.5539906103 frozenset([2840]) --> frozenset([3056, 2839]) conf: 0.18763326226 lift: 61.7700612583 frozenset([2791]) --> frozenset([635, 2790]) conf: 0.247787610619 lift: 77.8653794583 frozenset([2790]) --> frozenset([635, 2791]) conf: 0.239316239316 lift: 71.4160978909 frozenset([635]) --> frozenset([2790, 2791]) conf: 0.237288135593 lift: 71.3239990174 frozenset([2831]) --> frozenset([2018, 2508]) conf: 0.214111922141 lift: 45.3130741348 frozenset([2508]) --> frozenset([2018, 2831]) conf: 0.153846153846 lift: 44.940411701 frozenset([2018]) --> frozenset([2508, 2831]) conf: 0.143556280587 lift: 55.1362455441 frozenset([2839]) --> frozenset([2781, 2878]) conf: 0.178571428571 lift: 41.3806863528 frozenset([2878]) --> frozenset([2781, 2839]) conf: 0.296127562642 lift: 44.5049684725 frozenset([2781]) --> frozenset([2878, 2839]) conf: 0.238095238095 lift: 44.287849669 frozenset([2839]) --> frozenset([80, 5]) conf: 0.212912087912 lift: 37.1075353218 frozenset([5]) --> frozenset([80, 2839]) conf: 0.228276877761 lift: 42.8458139798 frozenset([80]) --> frozenset([5, 2839]) conf: 0.291353383459 lift: 34.8280643973 frozenset([2878]) --> frozenset([2840, 5]) conf: 0.318906605923 lift: 57.5141131029 frozenset([5]) --> frozenset([2840, 2878]) conf: 0.20618556701 lift: 44.085450101 frozenset([2840]) --> frozenset([5, 2878]) conf: 0.298507462687 lift: 52.6897427755 frozenset([2839]) --> frozenset([2840, 89]) conf: 0.122252747253 lift: 40.2463806035 frozenset([89]) --> frozenset([2840, 2839]) conf: 0.218137254902 lift: 37.7013888889 frozenset([2840]) --> frozenset([89, 2839]) conf: 0.189765458422 lift: 43.013503909 frozenset([5]) --> frozenset([2018, 44]) conf: 0.132547864507 lift: 27.7681081805 frozenset([44]) --> frozenset([2018, 5]) conf: 0.228426395939 lift: 52.3487674229 frozenset([2018]) --> frozenset([44, 5]) conf: 0.146818923328 lift: 42.0003375148 frozenset([5]) --> frozenset([2840, 2781]) conf: 0.189985272459 lift: 41.6962386329 frozenset([2781]) --> frozenset([2840, 5]) conf: 0.236263736264 lift: 42.6096512183 frozenset([2840]) --> frozenset([2781, 5]) conf: 0.275053304904 lift: 43.8815811055 frozenset([2839]) --> frozenset([80, 2878]) conf: 0.135989010989 lift: 44.7684458399 frozenset([2878]) --> frozenset([80, 2839]) conf: 0.225512528474 lift: 42.3269668828 frozenset([80]) --> frozenset([2878, 2839]) conf: 0.186090225564 lift: 34.6144509255 frozenset([2839]) --> frozenset([2832, 5]) conf: 0.116758241758 lift: 46.5685756551 frozenset([5]) --> frozenset([2832, 2839]) conf: 0.125184094256 lift: 48.5293105584 frozenset([2832]) --> frozenset([5, 2839]) conf: 0.494186046512 lift: 59.0744588164 frozenset([20]) --> frozenset([2018, 2508]) conf: 0.175840978593 lift: 37.2136928166 frozenset([2018]) --> frozenset([20, 2508]) conf: 0.187601957586 lift: 54.8009098638 frozenset([2508]) --> frozenset([2018, 20]) conf: 0.201048951049 lift: 33.492009998 frozenset([5]) --> frozenset([80, 44]) conf: 0.131075110457 lift: 41.8230429364 frozenset([44]) --> frozenset([80, 5]) conf: 0.225888324873 lift: 39.3691080493 frozenset([80]) --> frozenset([44, 5]) conf: 0.167293233083 lift: 47.857402126 frozenset([20]) --> frozenset([104, 2018]) conf: 0.146788990826 lift: 42.8789249257 frozenset([2018]) --> frozenset([104, 20]) conf: 0.15660685155 lift: 40.0990876684 frozenset([104]) --> frozenset([2018, 20]) conf: 0.206008583691 lift: 34.3182170743 frozenset([2839]) --> frozenset([80, 2781]) conf: 0.197802197802 lift: 42.2929647672 frozenset([2781]) --> frozenset([80, 2839]) conf: 0.263736263736 lift: 49.5012679628 frozenset([80]) --> frozenset([2781, 2839]) conf: 0.270676691729 lift: 40.6799607715 frozenset([2839]) --> frozenset([1, 5]) conf: 0.123626373626 lift: 34.6487971488 frozenset([5]) --> frozenset([1, 2839]) conf: 0.132547864507 lift: 36.4111617201 frozenset([1]) --> frozenset([5, 2839]) conf: 0.212765957447 lift: 25.433809553 frozenset([20]) --> frozenset([80, 2018]) conf: 0.192660550459 lift: 43.9096683133 frozenset([2018]) --> frozenset([80, 20]) conf: 0.205546492659 lift: 37.559773196 frozenset([80]) --> frozenset([2018, 20]) conf: 0.236842105263 lift: 39.4546607483 frozenset([39]) --> frozenset([10, 11]) conf: 0.166007905138 lift: 49.8986080082 frozenset([11]) --> frozenset([10, 39]) conf: 0.1875 lift: 55.9532374101 frozenset([10]) --> frozenset([11, 39]) conf: 0.230769230769 lift: 66.4743589744 frozenset([2781]) --> frozenset([2840, 80]) conf: 0.163003663004 lift: 48.643107492 frozenset([80]) --> frozenset([2840, 2781]) conf: 0.167293233083 lift: 36.7159963401 frozenset([2840]) --> frozenset([80, 2781]) conf: 0.189765458422 lift: 40.5745938936 frozenset([6]) --> frozenset([20, 2781]) conf: 0.177319587629 lift: 42.029808542 frozenset([2781]) --> frozenset([20, 6]) conf: 0.157509157509 lift: 33.8522272201 frozenset([20]) --> frozenset([2781, 6]) conf: 0.131498470948 lift: 33.6701023143 frozenset([2839]) --> frozenset([2840, 5]) conf: 0.215659340659 lift: 38.8936932633 frozenset([5]) --> frozenset([2840, 2839]) conf: 0.231222385862 lift: 39.9629356897 frozenset([2840]) --> frozenset([5, 2839]) conf: 0.334754797441 lift: 40.0162218959 frozenset([29]) --> frozenset([104, 11]) conf: 0.138041733547 lift: 36.4711535512 frozenset([11]) --> frozenset([104, 29]) conf: 0.191964285714 lift: 52.3860432331 frozenset([104]) --> frozenset([11, 29]) conf: 0.184549356223 lift: 53.1604673343 frozenset([2839]) --> frozenset([20, 2781]) conf: 0.157967032967 lift: 37.442700157 frozenset([2781]) --> frozenset([20, 2839]) conf: 0.210622710623 lift: 43.9026635007 frozenset([20]) --> frozenset([2781, 2839]) conf: 0.175840978593 lift: 26.4271151886 frozenset([2839]) --> frozenset([5, 6]) conf: 0.17032967033 lift: 35.864338707 frozenset([6]) --> frozenset([5, 2839]) conf: 0.255670103093 lift: 30.5625241392 frozenset([5]) --> frozenset([6, 2839]) conf: 0.182621502209 lift: 43.0405676797 frozenset([6]) --> frozenset([2018, 5]) conf: 0.171134020619 lift: 39.2190009683 frozenset([5]) --> frozenset([2018, 6]) conf: 0.122238586156 lift: 38.1237334869 frozenset([2018]) --> frozenset([5, 6]) conf: 0.135399673736 lift: 28.5095353632 frozenset([2839]) --> frozenset([2018, 2781]) conf: 0.151098901099 lift: 42.0643115274 frozenset([2781]) --> frozenset([2018, 2839]) conf: 0.201465201465 lift: 47.7530088959 frozenset([2018]) --> frozenset([2781, 2839]) conf: 0.179445350734 lift: 26.9688157553 frozenset([2839]) --> frozenset([89, 5]) conf: 0.181318681319 lift: 37.6054945055 frozenset([5]) --> frozenset([89, 2839]) conf: 0.19440353461 lift: 44.0648011782 frozenset([89]) --> frozenset([5, 2839]) conf: 0.323529411765 lift: 38.674351585 frozenset([6]) --> frozenset([20, 5]) conf: 0.20824742268 lift: 45.4637004883 frozenset([5]) --> frozenset([20, 6]) conf: 0.148748159057 lift: 31.9692934596 frozenset([20]) --> frozenset([5, 6]) conf: 0.154434250765 lift: 32.5174249833 frozenset([2839]) --> frozenset([5, 2878]) conf: 0.225274725275 lift: 39.7633855506 frozenset([2878]) --> frozenset([5, 2839]) conf: 0.373576309795 lift: 44.6569029692 frozenset([5]) --> frozenset([2878, 2839]) conf: 0.241531664212 lift: 44.9270557467 frozenset([5]) --> frozenset([80, 20]) conf: 0.182621502209 lift: 33.3706604037 frozenset([20]) --> frozenset([80, 5]) conf: 0.189602446483 lift: 33.0449978156 frozenset([80]) --> frozenset([20, 5]) conf: 0.233082706767 lift: 50.8856351405 frozenset([2774]) --> frozenset([2018, 2508]) conf: 0.35447761194 lift: 75.0190374657 frozenset([2508]) --> frozenset([2018, 2774]) conf: 0.166083916084 lift: 49.9214553562 frozenset([2018]) --> frozenset([2508, 2774]) conf: 0.154975530179 lift: 50.6172046602 frozenset([2839]) --> frozenset([3056, 5]) conf: 0.133241758242 lift: 43.5186467076 frozenset([5]) --> frozenset([3056, 2839]) conf: 0.142857142857 lift: 47.029478458 frozenset([3056]) --> frozenset([5, 2839]) conf: 0.341549295775 lift: 40.828428786 frozenset([2781]) --> frozenset([2018, 5]) conf: 0.203296703297 lift: 46.5897638273 frozenset([5]) --> frozenset([2018, 2781]) conf: 0.163475699558 lift: 45.5098793132 frozenset([2018]) --> frozenset([5, 2781]) conf: 0.181076672104 lift: 28.888693688 frozenset([44]) --> frozenset([80, 20]) conf: 0.233502538071 lift: 42.6682170889 frozenset([20]) --> frozenset([80, 44]) conf: 0.140672782875 lift: 44.8854387203 frozenset([80]) --> frozenset([44, 20]) conf: 0.172932330827 lift: 37.9536141942 frozenset([2781]) --> frozenset([5, 2878]) conf: 0.245421245421 lift: 43.3194606812 frozenset([2878]) --> frozenset([5, 2781]) conf: 0.305239179954 lift: 48.6973891712 frozenset([5]) --> frozenset([2781, 2878]) conf: 0.19734904271 lift: 45.732057495 frozenset([2839]) --> frozenset([80, 6]) conf: 0.14010989011 lift: 28.489010989 frozenset([6]) --> frozenset([80, 2839]) conf: 0.210309278351 lift: 39.4734337827 frozenset([80]) --> frozenset([6, 2839]) conf: 0.191729323308 lift: 45.1871155161 frozenset([2839]) --> frozenset([2840, 2878]) conf: 0.188186813187 lift: 40.2370567577 frozenset([2878]) --> frozenset([2840, 2839]) conf: 0.312072892938 lift: 53.9365983295 frozenset([2840]) --> frozenset([2878, 2839]) conf: 0.2921108742 lift: 54.3352424297 frozenset([2839]) --> frozenset([2018, 44]) conf: 0.118131868132 lift: 24.748029748 frozenset([44]) --> frozenset([2018, 2839]) conf: 0.218274111675 lift: 51.7372008702 frozenset([2018]) --> frozenset([44, 2839]) conf: 0.140293637847 lift: 43.1065192436 frozenset([39]) --> frozenset([2018, 2774]) conf: 0.166007905138 lift: 49.8986080082 frozenset([2774]) --> frozenset([2018, 39]) conf: 0.313432835821 lift: 82.8101530564 frozenset([2018]) --> frozenset([2774, 39]) conf: 0.137030995106 lift: 53.6230724245 frozenset([20]) --> frozenset([44, 2508]) conf: 0.12996941896 lift: 38.785118694 frozenset([44]) --> frozenset([20, 2508]) conf: 0.215736040609 lift: 63.0192321441 frozenset([2508]) --> frozenset([20, 44]) conf: 0.148601398601 lift: 32.6136826137 frozenset([20]) --> frozenset([2018, 11]) conf: 0.162079510703 lift: 44.8203873598 frozenset([11]) --> frozenset([2018, 20]) conf: 0.236607142857 lift: 39.4155192197 frozenset([2018]) --> frozenset([11, 20]) conf: 0.172920065253 lift: 48.1390893066 frozenset([39]) --> frozenset([2018, 2508]) conf: 0.193675889328 lift: 40.9881422925 frozenset([2508]) --> frozenset([2018, 39]) conf: 0.171328671329 lift: 45.2656897243 frozenset([2018]) --> frozenset([2508, 39]) conf: 0.15986949429 lift: 51.8077079935 frozenset([5]) --> frozenset([80, 2018]) conf: 0.176730486009 lift: 40.279014064 frozenset([2018]) --> frozenset([80, 5]) conf: 0.195758564437 lift: 34.1179212305 frozenset([80]) --> frozenset([2018, 5]) conf: 0.225563909774 lift: 51.6927678312 frozenset([2781]) --> frozenset([80, 20]) conf: 0.201465201465 lift: 36.8139936422 frozenset([20]) --> frozenset([80, 2781]) conf: 0.168195718654 lift: 35.9626722154 frozenset([80]) --> frozenset([20, 2781]) conf: 0.206766917293 lift: 49.0096670247 frozenset([2839]) --> frozenset([89, 2781]) conf: 0.163461538462 lift: 41.3438086304 frozenset([2781]) --> frozenset([89, 2839]) conf: 0.217948717949 lift: 49.4017094017 frozenset([89]) --> frozenset([2781, 2839]) conf: 0.291666666667 lift: 43.8345410628 frozenset([2781]) --> frozenset([5, 2839]) conf: 0.338827838828 lift: 40.5031088028 frozenset([5]) --> frozenset([2781, 2839]) conf: 0.272459499264 lift: 40.9478986574 frozenset([2839]) --> frozenset([5, 2781]) conf: 0.254120879121 lift: 40.5420540997 frozenset([44]) --> frozenset([2825, 2018]) conf: 0.218274111675 lift: 65.6087692195 frozenset([2018]) --> frozenset([2825, 44]) conf: 0.140293637847 lift: 45.111473627 frozenset([2825]) --> frozenset([2018, 44]) conf: 0.301754385965 lift: 63.2160198476 frozenset([2781]) --> frozenset([2018, 20]) conf: 0.179487179487 lift: 29.9001132736 frozenset([20]) --> frozenset([2018, 2781]) conf: 0.149847094801 lift: 41.7158220963 frozenset([2018]) --> frozenset([20, 2781]) conf: 0.15986949429 lift: 37.8936378467 frozenset([2878]) --> frozenset([2018, 5]) conf: 0.189066059226 lift: 43.3285090424 frozenset([5]) --> frozenset([2018, 2878]) conf: 0.122238586156 lift: 48.75438994 frozenset([2018]) --> frozenset([5, 2878]) conf: 0.135399673736 lift: 23.8994828364 frozenset([5]) --> frozenset([89, 2781]) conf: 0.170839469809 lift: 43.2098854126 frozenset([2781]) --> frozenset([89, 5]) conf: 0.212454212454 lift: 44.063003663 frozenset([89]) --> frozenset([2781, 5]) conf: 0.28431372549 lift: 45.358974359 frozenset([2839]) --> frozenset([80, 2018]) conf: 0.159340659341 lift: 36.3156623596 frozenset([2018]) --> frozenset([80, 2839]) conf: 0.189233278956 lift: 35.5176308194 frozenset([80]) --> frozenset([2018, 2839]) conf: 0.218045112782 lift: 51.6829215897 frozenset([44]) --> frozenset([80, 2018]) conf: 0.230964467005 lift: 52.6395939086 frozenset([2018]) --> frozenset([80, 44]) conf: 0.148450244698 lift: 47.3670473083 frozenset([80]) --> frozenset([2018, 44]) conf: 0.171052631579 lift: 35.8346624136 frozenset([2839]) --> frozenset([20, 6]) conf: 0.127747252747 lift: 27.4557307977 frozenset([6]) --> frozenset([20, 2839]) conf: 0.19175257732 lift: 39.969331192 frozenset([20]) --> frozenset([6, 2839]) conf: 0.142201834862 lift: 33.5143869892 frozenset([2878]) --> frozenset([3056, 5]) conf: 0.205011389522 lift: 66.959625491 frozenset([5]) --> frozenset([3056, 2878]) conf: 0.132547864507 lift: 41.9701177079 frozenset([3056]) --> frozenset([5, 2878]) conf: 0.316901408451 lift: 55.9364698831 frozenset([6]) --> frozenset([80, 5]) conf: 0.259793814433 lift: 45.2783505155 frozenset([5]) --> frozenset([80, 6]) conf: 0.185567010309 lift: 37.7319587629 frozenset([80]) --> frozenset([5, 6]) conf: 0.236842105263 lift: 49.8690889661 frozenset([5]) --> frozenset([2018, 20]) conf: 0.153166421208 lift: 25.5154343442 frozenset([20]) --> frozenset([2018, 5]) conf: 0.159021406728 lift: 36.4431378512 frozenset([2018]) --> frozenset([20, 5]) conf: 0.169657422512 lift: 37.0388941358 frozenset([6]) --> frozenset([80, 2018]) conf: 0.183505154639 lift: 41.8230429364 frozenset([2018]) --> frozenset([80, 6]) conf: 0.145187601958 lift: 29.5214790647 frozenset([80]) --> frozenset([2018, 6]) conf: 0.167293233083 lift: 52.1753632201 frozenset([2878]) --> frozenset([2883, 5]) conf: 0.191343963554 lift: 67.2622678661 frozenset([5]) --> frozenset([2883, 2878]) conf: 0.123711340206 lift: 42.0618556701 frozenset([2883]) --> frozenset([5, 2878]) conf: 0.363636363636 lift: 64.1856866538 frozenset([2839]) --> frozenset([2840, 2781]) conf: 0.184065934066 lift: 40.3971161114 frozenset([2781]) --> frozenset([2840, 2839]) conf: 0.245421245421 lift: 42.416971917 frozenset([2840]) --> frozenset([2781, 2839]) conf: 0.285714285714 lift: 42.9399585921 frozenset([5]) --> frozenset([20, 2781]) conf: 0.166421207658 lift: 39.4465811067 frozenset([2781]) --> frozenset([20, 5]) conf: 0.20695970696 lift: 45.1825718142 frozenset([20]) --> frozenset([2781, 5]) conf: 0.172782874618 lift: 27.5655139967 frozenset([29]) --> frozenset([41, 11]) conf: 0.134831460674 lift: 42.0511954042 frozenset([11]) --> frozenset([41, 29]) conf: 0.1875 lift: 59.8269230769 frozenset([41]) --> frozenset([11, 29]) conf: 0.252252252252 lift: 72.6626626627 frozenset([2878]) --> frozenset([2840, 2781]) conf: 0.234624145786 lift: 51.4931723132 frozenset([2781]) --> frozenset([2840, 2878]) conf: 0.188644688645 lift: 40.3349571391 frozenset([2840]) --> frozenset([2781, 2878]) conf: 0.219616204691 lift: 50.892067992 frozenset([5]) --> frozenset([2840, 80]) conf: 0.144329896907 lift: 43.0705332641 frozenset([80]) --> frozenset([2840, 5]) conf: 0.184210526316 lift: 33.2219679634 frozenset([2840]) --> frozenset([80, 5]) conf: 0.208955223881 lift: 36.4179104478 frozenset([2839]) --> frozenset([3056, 2878]) conf: 0.116758241758 lift: 36.9704722758 frozenset([2878]) --> frozenset([3056, 2839]) conf: 0.193621867882 lift: 63.7415482518 frozenset([3056]) --> frozenset([2878, 2839]) conf: 0.299295774648 lift: 55.6716983515 frozenset([20]) --> frozenset([80, 18]) conf: 0.145259938838 lift: 40.4388071342 frozenset([18]) --> frozenset([80, 20]) conf: 0.271428571429 lift: 49.5984896161 frozenset([80]) --> frozenset([18, 20]) conf: 0.178571428571 lift: 49.7123681687 frozenset([44]) --> frozenset([2018, 2508]) conf: 0.263959390863 lift: 55.8624261887 frozenset([2018]) --> frozenset([44, 2508]) conf: 0.169657422512 lift: 50.6287042144 frozenset([2508]) --> frozenset([2018, 44]) conf: 0.181818181818 lift: 38.0899908173 frozenset([2878]) --> frozenset([80, 5]) conf: 0.21867881549 lift: 38.1125935568 frozenset([5]) --> frozenset([80, 2878]) conf: 0.141384388807 lift: 46.5446384739 frozenset([80]) --> frozenset([5, 2878]) conf: 0.18045112782 lift: 31.851543753 frozenset([2839]) --> frozenset([5, 2830]) conf: 0.120879120879 lift: 42.1350078493 frozenset([2830]) --> frozenset([5, 2839]) conf: 0.362139917695 lift: 43.2898091816 frozenset([5]) --> frozenset([2830, 2839]) conf: 0.129602356406 lift: 47.1570679276 frozenset([6]) --> frozenset([80, 75]) conf: 0.185567010309 lift: 52.7213670386 frozenset([75]) --> frozenset([80, 6]) conf: 0.274390243902 lift: 55.7926829268 frozenset([80]) --> frozenset([75, 6]) conf: 0.169172932331 lift: 54.8226033835 frozenset([2839]) --> frozenset([1, 2781]) conf: 0.116758241758 lift: 38.437554509 frozenset([2781]) --> frozenset([1, 2839]) conf: 0.155677655678 lift: 42.764961308 frozenset([1]) --> frozenset([2781, 2839]) conf: 0.200945626478 lift: 30.2000890808 frozenset([2839]) --> frozenset([20, 5]) conf: 0.168956043956 lift: 36.8857721226 frozenset([5]) --> frozenset([20, 2839]) conf: 0.181148748159 lift: 37.7590455962 frozenset([20]) --> frozenset([5, 2839]) conf: 0.188073394495 lift: 22.4820876186 frozenset([2839]) --> frozenset([2826, 5]) conf: 0.138736263736 lift: 45.313230077 frozenset([5]) --> frozenset([2826, 2839]) conf: 0.148748159057 lift: 46.0453256545 frozenset([2826]) --> frozenset([5, 2839]) conf: 0.465437788018 lift: 55.6379234784 frozenset([5, 2781]) --> frozenset([80, 20]) conf: 0.319230769231 lift: 58.3334462894 frozenset([20, 2781]) --> frozenset([80, 5]) conf: 0.474285714286 lift: 82.6612244898 frozenset([20, 5]) --> frozenset([80, 2781]) conf: 0.436842105263 lift: 93.4031470429 frozenset([80, 2781]) --> frozenset([20, 5]) conf: 0.427835051546 lift: 93.4031470429 frozenset([80, 5]) --> frozenset([20, 2781]) conf: 0.348739495798 lift: 82.6612244898 frozenset([80, 20]) --> frozenset([5, 2781]) conf: 0.36563876652 lift: 58.3334462894 frozenset([2781]) --> frozenset([80, 20, 5]) conf: 0.152014652015 lift: 50.8513529481 frozenset([5]) --> frozenset([80, 20, 2781]) conf: 0.122238586156 lift: 46.0950595796 frozenset([20]) --> frozenset([80, 5, 2781]) conf: 0.126911314985 lift: 37.335328692 frozenset([80]) --> frozenset([20, 5, 2781]) conf: 0.156015037594 lift: 57.2699447734 frozenset([2781, 2878]) --> frozenset([2840, 5]) conf: 0.486033519553 lift: 87.6550886568 frozenset([2840, 2878]) --> frozenset([5, 2781]) conf: 0.448453608247 lift: 71.5455987312 frozenset([2840, 2781]) --> frozenset([5, 2878]) conf: 0.460317460317 lift: 81.2509287403 frozenset([5, 2878]) --> frozenset([2840, 2781]) conf: 0.370212765957 lift: 81.2509287403 frozenset([5, 2781]) --> frozenset([2840, 2878]) conf: 0.334615384615 lift: 71.5455987312 frozenset([2840, 5]) --> frozenset([2781, 2878]) conf: 0.378260869565 lift: 87.6550886568 frozenset([2878]) --> frozenset([2840, 5, 2781]) conf: 0.198177676538 lift: 63.7241087037 frozenset([2781]) --> frozenset([2840, 5, 2878]) conf: 0.159340659341 lift: 47.2103610675 frozenset([2840]) --> frozenset([5, 2878, 2781]) conf: 0.185501066098 lift: 57.4222703116 frozenset([5]) --> frozenset([2840, 2781, 2878]) conf: 0.128129602356 lift: 51.6001544247 frozenset([2781, 2839]) --> frozenset([80, 5]) conf: 0.427536231884 lift: 74.5134575569 frozenset([5, 2781]) --> frozenset([80, 2839]) conf: 0.453846153846 lift: 85.1834319527 frozenset([5, 2839]) --> frozenset([80, 2781]) conf: 0.340057636888 lift: 72.7092308149 frozenset([80, 2781]) --> frozenset([5, 2839]) conf: 0.60824742268 lift: 72.7092308149 frozenset([80, 2839]) --> frozenset([5, 2781]) conf: 0.533936651584 lift: 85.1834319527 frozenset([80, 5]) --> frozenset([2781, 2839]) conf: 0.495798319328 lift: 74.5134575569 frozenset([2781]) --> frozenset([80, 5, 2839]) conf: 0.216117216117 lift: 57.8357556422 frozenset([2839]) --> frozenset([80, 5, 2781]) conf: 0.162087912088 lift: 47.683734705 frozenset([5]) --> frozenset([80, 2781, 2839]) conf: 0.173784977909 lift: 50.0597283587 frozenset([80]) --> frozenset([2781, 5, 2839]) conf: 0.221804511278 lift: 49.7321682585 frozenset([2840, 2878]) --> frozenset([5, 2839]) conf: 0.567010309278 lift: 67.7797914377 frozenset([2878, 2839]) --> frozenset([2840, 5]) conf: 0.493273542601 lift: 88.9608110743 frozenset([2840, 2839]) --> frozenset([5, 2878]) conf: 0.458333333333 lift: 80.9007092199 frozenset([5, 2878]) --> frozenset([2840, 2839]) conf: 0.468085106383 lift: 80.9007092199 frozenset([2840, 5]) --> frozenset([2878, 2839]) conf: 0.478260869565 lift: 88.9608110743 frozenset([5, 2839]) --> frozenset([2840, 2878]) conf: 0.317002881844 lift: 67.7797914377 frozenset([2840]) --> frozenset([5, 2878, 2839]) conf: 0.234541577825 lift: 59.3218576109 frozenset([2878]) --> frozenset([2840, 5, 2839]) conf: 0.250569476082 lift: 66.2014131712 frozenset([2839]) --> frozenset([2840, 5, 2878]) conf: 0.151098901099 lift: 44.7684458399 frozenset([5]) --> frozenset([2840, 2878, 2839]) conf: 0.162002945508 lift: 49.0502348881 frozenset([2781, 2878]) --> frozenset([5, 2839]) conf: 0.597765363128 lift: 71.456216895 frozenset([2878, 2839]) --> frozenset([5, 2781]) conf: 0.479820627803 lift: 76.5498447741 frozenset([2781, 2839]) --> frozenset([5, 2878]) conf: 0.38768115942 lift: 68.4298489053 frozenset([5, 2878]) --> frozenset([2781, 2839]) conf: 0.455319148936 lift: 68.4298489053 frozenset([5, 2781]) --> frozenset([2878, 2839]) conf: 0.411538461538 lift: 76.5498447741 frozenset([5, 2839]) --> frozenset([2781, 2878]) conf: 0.308357348703 lift: 71.456216895 frozenset([2878]) --> frozenset([2781, 5, 2839]) conf: 0.243735763098 lift: 54.6495105584 frozenset([2781]) --> frozenset([5, 2878, 2839]) conf: 0.195970695971 lift: 49.5662467614 frozenset([2839]) --> frozenset([5, 2878, 2781]) conf: 0.146978021978 lift: 45.4973757586 frozenset([5]) --> frozenset([2781, 2878, 2839]) conf: 0.157584683358 lift: 50.2816358899 frozenset([2840, 2839]) --> frozenset([80, 5]) conf: 0.345833333333 lift: 60.2738095238 frozenset([2840, 5]) --> frozenset([80, 2839]) conf: 0.360869565217 lift: 67.7324414716 frozenset([5, 2839]) --> frozenset([80, 2840]) conf: 0.239193083573 lift: 71.3793460909 frozenset([80, 2840]) --> frozenset([5, 2839]) conf: 0.597122302158 lift: 71.3793460909 frozenset([80, 2839]) --> frozenset([2840, 5]) conf: 0.37556561086 lift: 67.7324414716 frozenset([80, 5]) --> frozenset([2840, 2839]) conf: 0.348739495798 lift: 60.2738095238 frozenset([2840]) --> frozenset([80, 5, 2839]) conf: 0.17697228145 lift: 47.3600660293 frozenset([2839]) --> frozenset([80, 2840, 5]) conf: 0.114010989011 lift: 48.2568961651 frozenset([5]) --> frozenset([80, 2840, 2839]) conf: 0.122238586156 lift: 51.7393525893 frozenset([80]) --> frozenset([2840, 5, 2839]) conf: 0.156015037594 lift: 41.2197691681 frozenset([5, 2839]) --> frozenset([80, 20]) conf: 0.247838616715 lift: 45.2878670543 frozenset([20, 2839]) --> frozenset([80, 5]) conf: 0.43216080402 lift: 75.3194544149 frozenset([20, 5]) --> frozenset([80, 2839]) conf: 0.452631578947 lift: 84.955465587 frozenset([80, 2839]) --> frozenset([20, 5]) conf: 0.389140271493 lift: 84.955465587 frozenset([80, 5]) --> frozenset([20, 2839]) conf: 0.361344537815 lift: 75.3194544149 frozenset([80, 20]) --> frozenset([5, 2839]) conf: 0.378854625551 lift: 45.2878670543 frozenset([2839]) --> frozenset([80, 20, 5]) conf: 0.118131868132 lift: 39.5170152428 frozenset([5]) --> frozenset([80, 20, 2839]) conf: 0.126656848306 lift: 47.3308654752 frozenset([20]) --> frozenset([80, 5, 2839]) conf: 0.131498470948 lift: 35.1906875802 frozenset([80]) --> frozenset([20, 5, 2839]) conf: 0.161654135338 lift: 54.5155571856 frozenset([89, 2781]) --> frozenset([5, 2839]) conf: 0.567073170732 lift: 67.7873058269 frozenset([2781, 2839]) --> frozenset([89, 5]) conf: 0.336956521739 lift: 69.8847826087 frozenset([89, 2839]) --> frozenset([5, 2781]) conf: 0.508196721311 lift: 81.0769230769 frozenset([5, 2781]) --> frozenset([89, 2839]) conf: 0.357692307692 lift: 81.0769230769 frozenset([89, 5]) --> frozenset([2781, 2839]) conf: 0.465 lift: 69.8847826087 frozenset([5, 2839]) --> frozenset([89, 2781]) conf: 0.268011527378 lift: 67.7873058269 frozenset([89]) --> frozenset([2781, 5, 2839]) conf: 0.227941176471 lift: 51.1081081081 frozenset([2781]) --> frozenset([89, 5, 2839]) conf: 0.17032967033 lift: 53.5248085248 frozenset([2839]) --> frozenset([89, 5, 2781]) conf: 0.127747252747 lift: 45.6806555513 frozenset([5]) --> frozenset([89, 2781, 2839]) conf: 0.136966126657 lift: 47.7424784347 frozenset([2781, 2878]) --> frozenset([2840, 2839]) conf: 0.491620111732 lift: 84.9683426443 frozenset([2840, 2878]) --> frozenset([2781, 2839]) conf: 0.453608247423 lift: 68.1727177648 frozenset([2840, 2781]) --> frozenset([2878, 2839]) conf: 0.465608465608 lift: 86.6073504639 frozenset([2878, 2839]) --> frozenset([2840, 2781]) conf: 0.394618834081 lift: 86.6073504639 frozenset([2781, 2839]) --> frozenset([2840, 2878]) conf: 0.31884057971 lift: 68.1727177648 frozenset([2840, 2839]) --> frozenset([2781, 2878]) conf: 0.366666666667 lift: 84.9683426443 frozenset([2878]) --> frozenset([2840, 2781, 2839]) conf: 0.200455580866 lift: 62.0514738381 frozenset([2781]) --> frozenset([2840, 2878, 2839]) conf: 0.161172161172 lift: 48.7986952221 frozenset([2840]) --> frozenset([2781, 2878, 2839]) conf: 0.18763326226 lift: 59.8694439888 frozenset([2839]) --> frozenset([2840, 2781, 2878]) conf: 0.120879120879 lift: 48.680251787 frozenset([2781, 2839]) --> frozenset([5, 6]) conf: 0.315217391304 lift: 66.3716618848 frozenset([2781, 6]) --> frozenset([5, 2839]) conf: 0.537037037037 lift: 64.1968192977 frozenset([6, 2839]) --> frozenset([5, 2781]) conf: 0.494318181818 lift: 78.8627622378 frozenset([5, 2781]) --> frozenset([6, 2839]) conf: 0.334615384615 lift: 78.8627622378 frozenset([5, 2839]) --> frozenset([2781, 6]) conf: 0.250720461095 lift: 64.1968192977 frozenset([5, 6]) --> frozenset([2781, 2839]) conf: 0.441624365482 lift: 66.3716618848 frozenset([2781]) --> frozenset([5, 6, 2839]) conf: 0.159340659341 lift: 53.3020205601 frozenset([2839]) --> frozenset([5, 6, 2781]) conf: 0.119505494505 lift: 45.0644355644 frozenset([6]) --> frozenset([2781, 5, 2839]) conf: 0.179381443299 lift: 40.2202284759 frozenset([5]) --> frozenset([2781, 6, 2839]) conf: 0.128129602356 lift: 52.1060382916 frozenset([5, 2839]) --> frozenset([80, 2018]) conf: 0.273775216138 lift: 62.3966811287 frozenset([2018, 2839]) --> frozenset([80, 5]) conf: 0.542857142857 lift: 94.612244898 frozenset([2018, 5]) --> frozenset([80, 2839]) conf: 0.524861878453 lift: 98.5125371866 frozenset([80, 2839]) --> frozenset([2018, 5]) conf: 0.429864253394 lift: 98.5125371866 frozenset([80, 5]) --> frozenset([2018, 2839]) conf: 0.399159663866 lift: 94.612244898 frozenset([80, 2018]) --> frozenset([5, 2839]) conf: 0.521978021978 lift: 62.3966811287 frozenset([2839]) --> frozenset([80, 2018, 5]) conf: 0.130494505495 lift: 45.1076007326 frozenset([5]) --> frozenset([80, 2018, 2839]) conf: 0.139911634757 lift: 50.0304707734 frozenset([2018]) --> frozenset([80, 5, 2839]) conf: 0.154975530179 lift: 41.4734515603 frozenset([80]) --> frozenset([2018, 5, 2839]) conf: 0.178571428571 lift: 56.5430752454 frozenset([2840, 2781]) --> frozenset([5, 2839]) conf: 0.544973544974 lift: 65.1455407651 frozenset([2781, 2839]) --> frozenset([2840, 5]) conf: 0.373188405797 lift: 67.3037177064 frozenset([2840, 2839]) --> frozenset([5, 2781]) conf: 0.429166666667 lift: 68.4685897436 frozenset([5, 2781]) --> frozenset([2840, 2839]) conf: 0.396153846154 lift: 68.4685897436 frozenset([2840, 5]) --> frozenset([2781, 2839]) conf: 0.447826086957 lift: 67.3037177064 frozenset([5, 2839]) --> frozenset([2840, 2781]) conf: 0.296829971182 lift: 65.1455407651 frozenset([2840]) --> frozenset([2781, 5, 2839]) conf: 0.219616204691 lift: 49.2415144355 frozenset([2781]) --> frozenset([2840, 5, 2839]) conf: 0.188644688645 lift: 49.840647675 frozenset([2839]) --> frozenset([2840, 5, 2781]) conf: 0.141483516484 lift: 45.4940795638 frozenset([5]) --> frozenset([2840, 2781, 2839]) conf: 0.151693667158 lift: 46.9571142813 frozenset([2781, 2839]) --> frozenset([20, 5]) conf: 0.31884057971 lift: 69.6079328757 frozenset([5, 2781]) --> frozenset([20, 2839]) conf: 0.338461538462 lift: 70.5496714341 frozenset([5, 2839]) --> frozenset([20, 2781]) conf: 0.253602305476 lift: 60.1109921779 frozenset([20, 2781]) --> frozenset([5, 2839]) conf: 0.502857142857 lift: 60.1109921779 frozenset([20, 2839]) --> frozenset([5, 2781]) conf: 0.442211055276 lift: 70.5496714341 frozenset([20, 5]) --> frozenset([2781, 2839]) conf: 0.463157894737 lift: 69.6079328757 frozenset([2781]) --> frozenset([20, 5, 2839]) conf: 0.161172161172 lift: 54.3530182555 frozenset([2839]) --> frozenset([20, 5, 2781]) conf: 0.120879120879 lift: 44.3722649032 frozenset([5]) --> frozenset([20, 2781, 2839]) conf: 0.129602356406 lift: 46.7470064673 frozenset([20]) --> frozenset([2781, 5, 2839]) conf: 0.134556574924 lift: 30.1697660964 frozenset([2781, 2839]) --> frozenset([2018, 5]) conf: 0.333333333333 lift: 76.3904235727 frozenset([5, 2781]) --> frozenset([2018, 2839]) conf: 0.353846153846 lift: 83.8716483516 frozenset([5, 2839]) --> frozenset([2018, 2781]) conf: 0.265129682997 lift: 73.8092567162 frozenset([2018, 2781]) --> frozenset([5, 2839]) conf: 0.61744966443 lift: 73.8092567162 frozenset([2018, 2839]) --> frozenset([5, 2781]) conf: 0.525714285714 lift: 83.8716483516 frozenset([2018, 5]) --> frozenset([2781, 2839]) conf: 0.508287292818 lift: 76.3904235727 frozenset([2781]) --> frozenset([2018, 5, 2839]) conf: 0.168498168498 lift: 53.3534658725 frozenset([2839]) --> frozenset([2018, 5, 2781]) conf: 0.126373626374 lift: 47.225027225 frozenset([5]) --> frozenset([2018, 2781, 2839]) conf: 0.135493372607 lift: 51.0933190521 frozenset([2018]) --> frozenset([2781, 5, 2839]) conf: 0.150081566069 lift: 33.6507208677 frozenset([6, 2839]) --> frozenset([80, 5]) conf: 0.5 lift: 87.1428571429 frozenset([5, 2839]) --> frozenset([80, 6]) conf: 0.253602305476 lift: 51.5658021134 frozenset([5, 6]) --> frozenset([80, 2839]) conf: 0.446700507614 lift: 83.8422491214 frozenset([80, 2839]) --> frozenset([5, 6]) conf: 0.398190045249 lift: 83.8422491214 frozenset([80, 6]) --> frozenset([5, 2839]) conf: 0.43137254902 lift: 51.5658021134 frozenset([80, 5]) --> frozenset([6, 2839]) conf: 0.36974789916 lift: 87.1428571429 frozenset([2839]) --> frozenset([80, 5, 6]) conf: 0.120879120879 lift: 39.7941740799 frozenset([6]) --> frozenset([80, 5, 2839]) conf: 0.181443298969 lift: 48.556568008 frozenset([5]) --> frozenset([80, 6, 2839]) conf: 0.129602356406 lift: 52.704958272 frozenset([80]) --> frozenset([5, 6, 2839]) conf: 0.165413533835 lift: 55.3334950279 frozenset([89, 2878]) --> frozenset([5, 2839]) conf: 0.612244897959 lift: 73.1870846321 frozenset([2878, 2839]) --> frozenset([89, 5]) conf: 0.403587443946 lift: 83.7040358744 frozenset([89, 2839]) --> frozenset([5, 2878]) conf: 0.491803278689 lift: 86.8085106383 frozenset([5, 2878]) --> frozenset([89, 2839]) conf: 0.382978723404 lift: 86.8085106383 frozenset([89, 5]) --> frozenset([2878, 2839]) conf: 0.45 lift: 83.7040358744 frozenset([5, 2839]) --> frozenset([89, 2878]) conf: 0.259365994236 lift: 73.1870846321 frozenset([89]) --> frozenset([5, 2878, 2839]) conf: 0.220588235294 lift: 55.7926829268 frozenset([2878]) --> frozenset([89, 5, 2839]) conf: 0.205011389522 lift: 64.4232760406 frozenset([2839]) --> frozenset([89, 5, 2878]) conf: 0.123626373626 lift: 44.98264893 frozenset([5]) --> frozenset([89, 2878, 2839]) conf: 0.132547864507 lift: 52.866205959 frozenset([2878, 2839]) --> frozenset([80, 5]) conf: 0.37668161435 lift: 65.6502242152 frozenset([5, 2878]) --> frozenset([80, 2839]) conf: 0.357446808511 lift: 67.0900163666 frozenset([5, 2839]) --> frozenset([80, 2878]) conf: 0.242074927954 lift: 79.6926032661 frozenset([80, 2878]) --> frozenset([5, 2839]) conf: 0.666666666667 lift: 79.6926032661 frozenset([80, 2839]) --> frozenset([5, 2878]) conf: 0.380090497738 lift: 67.0900163666 frozenset([80, 5]) --> frozenset([2878, 2839]) conf: 0.352941176471 lift: 65.6502242152 frozenset([2878]) --> frozenset([80, 5, 2839]) conf: 0.191343963554 lift: 51.2061136013 frozenset([2839]) --> frozenset([80, 5, 2878]) conf: 0.115384615385 lift: 49.8557692308 frozenset([5]) --> frozenset([80, 2878, 2839]) conf: 0.123711340206 lift: 51.8338019369 frozenset([80]) --> frozenset([5, 2878, 2839]) conf: 0.157894736842 lift: 39.9358151476 frozenset([2781, 2878]) --> frozenset([89, 5]) conf: 0.474860335196 lift: 98.4860335196 frozenset([89, 2878]) --> frozenset([5, 2781]) conf: 0.578231292517 lift: 92.2501308216 frozenset([89, 2781]) --> frozenset([5, 2878]) conf: 0.518292682927 lift: 91.4841722885 frozenset([5, 2878]) --> frozenset([89, 2781]) conf: 0.36170212766 lift: 91.4841722885 frozenset([5, 2781]) --> frozenset([89, 2878]) conf: 0.326923076923 lift: 92.2501308216 frozenset([89, 5]) --> frozenset([2781, 2878]) conf: 0.425 lift: 98.4860335196 frozenset([2878]) --> frozenset([89, 5, 2781]) conf: 0.193621867882 lift: 69.236509308 frozenset([2781]) --> frozenset([89, 5, 2878]) conf: 0.155677655678 lift: 56.6448171711 frozenset([89]) --> frozenset([5, 2878, 2781]) conf: 0.208333333333 lift: 64.4900497512 frozenset([5]) --> frozenset([89, 2781, 2878]) conf: 0.125184094256 lift: 54.6593287342 frozenset([2781, 2839]) --> frozenset([80, 20]) conf: 0.307971014493 lift: 56.2759369214 frozenset([20, 2781]) --> frozenset([80, 2839]) conf: 0.485714285714 lift: 91.1648351648 frozenset([20, 2839]) --> frozenset([80, 2781]) conf: 0.427135678392 lift: 91.327772885 frozenset([80, 2781]) --> frozenset([20, 2839]) conf: 0.438144329897 lift: 91.327772885 frozenset([80, 2839]) --> frozenset([20, 2781]) conf: 0.384615384615 lift: 91.1648351648 frozenset([80, 20]) --> frozenset([2781, 2839]) conf: 0.374449339207 lift: 56.2759369214 frozenset([2781]) --> frozenset([80, 20, 2839]) conf: 0.155677655678 lift: 58.1757581758 frozenset([2839]) --> frozenset([80, 20, 2781]) conf: 0.116758241758 lift: 44.0284715285 frozenset([20]) --> frozenset([80, 2781, 2839]) conf: 0.12996941896 lift: 37.4384131838 frozenset([80]) --> frozenset([20, 2781, 2839]) conf: 0.15977443609 lift: 57.6299444263 frozenset([2781, 2839]) --> frozenset([80, 2018]) conf: 0.336956521739 lift: 76.7964644052 frozenset([2018, 2781]) --> frozenset([80, 2839]) conf: 0.624161073826 lift: 117.150232318 frozenset([2018, 2839]) --> frozenset([80, 2781]) conf: 0.531428571429 lift: 113.627098675 frozenset([80, 2781]) --> frozenset([2018, 2839]) conf: 0.479381443299 lift: 113.627098675 frozenset([80, 2839]) --> frozenset([2018, 2781]) conf: 0.420814479638 lift: 117.150232318 frozenset([80, 2018]) --> frozenset([2781, 2839]) conf: 0.510989010989 lift: 76.7964644052 frozenset([2781]) --> frozenset([80, 2018, 2839]) conf: 0.17032967033 lift: 60.9075407351 frozenset([2839]) --> frozenset([80, 2018, 2781]) conf: 0.127747252747 lift: 48.1723276723 frozenset([2018]) --> frozenset([80, 2781, 2839]) conf: 0.151712887439 lift: 43.7017400761 frozenset([80]) --> frozenset([2018, 2781, 2839]) conf: 0.174812030075 lift: 65.9200273411 frozenset([20, 5]) --> frozenset([80, 2018]) conf: 0.442105263158 lift: 100.761133603 frozenset([2018, 5]) --> frozenset([80, 20]) conf: 0.46408839779 lift: 84.8034658164 frozenset([2018, 20]) --> frozenset([80, 5]) conf: 0.33734939759 lift: 58.7951807229 frozenset([80, 5]) --> frozenset([2018, 20]) conf: 0.352941176471 lift: 58.7951807229 frozenset([80, 20]) --> frozenset([2018, 5]) conf: 0.370044052863 lift: 84.8034658164 frozenset([80, 2018]) --> frozenset([20, 5]) conf: 0.461538461538 lift: 100.761133603 frozenset([5]) --> frozenset([80, 2018, 20]) conf: 0.123711340206 lift: 40.7265586647 frozenset([20]) --> frozenset([80, 2018, 5]) conf: 0.128440366972 lift: 44.3975535168 frozenset([2018]) --> frozenset([80, 20, 5]) conf: 0.137030995106 lift: 45.8390780403 frozenset([80]) --> frozenset([2018, 20, 5]) conf: 0.157894736842 lift: 62.975708502 frozenset([5, 2781]) --> frozenset([80, 2018]) conf: 0.342307692308 lift: 78.0160608622 frozenset([2018, 2781]) --> frozenset([80, 5]) conf: 0.597315436242 lift: 104.103547459 frozenset([2018, 5]) --> frozenset([80, 2781]) conf: 0.491712707182 lift: 105.13527368 frozenset([80, 2781]) --> frozenset([2018, 5]) conf: 0.458762886598 lift: 105.13527368 frozenset([80, 5]) --> frozenset([2018, 2781]) conf: 0.373949579832 lift: 104.103547459 frozenset([80, 2018]) --> frozenset([5, 2781]) conf: 0.489010989011 lift: 78.0160608622 frozenset([2781]) --> frozenset([80, 2018, 5]) conf: 0.163003663004 lift: 56.3449328449 frozenset([5]) --> frozenset([80, 2018, 2781]) conf: 0.131075110457 lift: 49.4272325613 frozenset([2018]) --> frozenset([80, 5, 2781]) conf: 0.145187601958 lift: 42.7119271575 frozenset([80]) --> frozenset([2018, 5, 2781]) conf: 0.167293233083 lift: 62.5164262006
know much about music? ¶
In [ ]:
To get comprenhensive rules do:
pntRules(rules_confident, songs)
pntRules(rules_lift,songs)
The following two rules are extracted from confidence metric:
The rule show below is interesting since the first Artist New Boyz is not as famous as Nicki Minaj. But still the rule says that if a playlist has Back seat implies Moment 4 life would also be in it. Is like referencing one artis to another.
['New-Boyz', 'Back-Seat']
-------->
['Nicki-Minaj', 'Moment-4-Life']
[confidence: 0.617512, lift: 35.184585]
Te second rule has been found by both metircs. Is interesting, I would not imagine that a song from Bruno Mars and Lil Wayne, that are maybe similar Artist would imply a song from Waka Flocka Flame. I do see the relation to Nicki Minaj.
['Bruno-Mars', 'Grenade']
['Lil-Wayne', '6-Foot-7-Foot']
-------->
['Waka-Flocka-Flame', 'No-Hands']
['Nicki-Minaj', 'Moment-4-Life']
[confidence: 0.624161, lift: 117.150232]
The next rule is from lift and is interesting since is in direct relation to the previous one. I think that all these songs are strongly related to eachother.
['Waka-Flocka-Flame', 'No-Hands']
['Lil-Wayne', '6-Foot-7-Foot']
-------->
['Bruno-Mars', 'Grenade']
['Nicki-Minaj', 'Moment-4-Life']
[confidence: 0.479381, lift: 113.627099]
Item-Based Joke Recommendation¶
In [2]:
# item-based recommender algorithm.
from numpy import *
from numpy import linalg as la
import numpy as np
def ecludSim(inA,inB):
return 1.0 / (1.0 + la.norm(inA - inB))
def pearsSim(inA,inB):
if len(inA) < 3 : return 1.0
return 0.5 + 0.5 * corrcoef(inA, inB, rowvar = 0)[0][1]
def cosSim(inA,inB):
num = float(inA.T * inB)
denom = la.norm(inA)*la.norm(inB)
return 0.5 + 0.5 * (num / denom)
def standEst(dataMat, user, simMeas, item):
n = shape(dataMat)[1]
simTotal = 0.0; ratSimTotal = 0.0
for j in range(n):
#j=2
userRating = dataMat[user,j] ; userRating
if userRating == 0:
continue
overLap = nonzero(logical_and(dataMat[:,item]>0, \
dataMat[:,j]>0))[0]
if len(overLap) == 0: similarity = 0
else: similarity = simMeas(dataMat[overLap,item], \
dataMat[overLap,j])
#print 'the %d and %d similarity is: %f' % (item, j, similarity)
simTotal += similarity
ratSimTotal += similarity * userRating
if simTotal == 0:
return 0
else:
return ratSimTotal/simTotal
def svdEst(dataMat, user, simMeas, item):
n = shape(dataMat)[1]
simTotal = 0.0; ratSimTotal = 0.0
data=mat(dataMat)
U,Sigma,VT = la.svd(data)
Sig4 = mat(eye(4)*Sigma[:4]) #arrange Sig4 into a diagonal matrix
xformedItems = data.T * U[:,:4] * Sig4.I #create transformed items
for j in range(n):
userRating = data[user,j]
if userRating == 0 or j==item: continue
similarity = simMeas(xformedItems[item,:].T,\
xformedItems[j,:].T)
#print 'the %d and %d similarity is: %f' % (item, j, similarity)
simTotal += similarity
ratSimTotal += similarity * userRating
if simTotal == 0: return 0
else: return ratSimTotal/simTotal
# This function is not needed for Assignment 4, but may be useful for experimentation
def recommend(dataMat, user, N=3, simMeas=cosSim, estMethod=standEst):
unratedItems = nonzero(dataMat[user,:].A==0)[1] #find unrated items
if len(unratedItems) == 0: return 'you rated everything'
itemScores = []
for item in unratedItems:
estimatedScore = estMethod(dataMat, user, simMeas, item)
itemScores.append((item, estimatedScore))
return sorted(itemScores, key=lambda jj: jj[1], reverse=True)[:N]
# This function performs cross-validation on a single user based on the test_ratio
# For example, with test_ratio = 0.2, 5-fold x-validation is performed where in each fold,
# 20 percent of rated items are withheld and the rest are used to estimate the withheld ratings
def cross_validate_user(dataMat, user, test_ratio, estMethod=standEst, simMeas=pearsSim):
number_of_items = np.shape(dataMat)[1]
rated_items_by_user = np.array([i for i in range(number_of_items) if dataMat[user,i]>0])
test_size = int(test_ratio * len(rated_items_by_user))
test_indices = np.random.randint(0, len(rated_items_by_user), test_size)
withheld_items = rated_items_by_user[test_indices]
original_user_profile = np.copy(dataMat[user])[0] # len(original_user_profile[0])
dataMat[user, withheld_items] = 0 # So that the withheld test items is not used in the rating estimation below
error_u = 0.0
count_u = len(withheld_items)
# Compute absolute error for user u over all test items
for item in withheld_items:
# item = withheld_items[0];item
# Estimate rating on the withheld item
estimatedScore = estMethod(dataMat, user, simMeas, item) #pearsSim()
error_u = error_u + abs(estimatedScore - original_user_profile[item])
# Now restore ratings of the withheld items to the user profile
for item in withheld_items:
dataMat[user, item] = original_user_profile[item]
# Return sum of absolute errors and the count of test cases for this user
# Note that these will have to be accumulated for each user to compute MAE
return error_u, count_u
def load_jokes(file):
jokes = genfromtxt(file, delimiter=',', dtype=str)
jokes = np.array(jokes[:,1])
return jokes
def get_joke_text(jokes, id):
return jokes[id]
Loading data¶
In [3]:
# jokes data
jokes = load_jokes('jokes.csv')
# users ratings data
users = pan.read_csv('modified_jester_data.csv')
dataMat= np.matrix(users)
Impleenting the test function¶
In [5]:
def test(dataMat, test_ratio= 0.2, estMethod='standEst'):
# Write this function to iterate over all users and for each perform cross-validation on items by calling
# the above cross-validation function on each user.
mae = []
for i in range(len(dataMat)):
# user = 0; user ; test_ratio = 0.2 ; estMethod=standEst
mae.append(cross_validate_user(dataMat, i, test_ratio))
# MAE will be the ratio of total error across all test cases to the total number of test cases, for all users
MAE = 0.0
for i in mae:
MAE += i[0] *i[1]
MAE = MAE / sum(mae)
print 'Mean Absoloute Error for ',estMethod,' : ', MAE
test(dataMat, test_ratio= 0.2, estMethod='standEst')
Mean Absoloute Error for standEst : 12.19
Most similar jokes¶
In [8]:
def print_most_similar_jokes(dataMat, queryJoke=1, k=3, metric=pearsSim):
# reading jokes files
jokes = load_jokes('jokes.csv')
# number of jokes
njokes = shape(dataMat)[1]
# distance dict
distances = {}
for i in range(njokes):
# i=0
# computing distances
overLap = nonzero(logical_and(dataMat[:,queryJoke]>0, dataMat[:,i]>0))[0] # len(dataMat[:,queryJoke])
distances[i] = metric(dataMat[overLap,i], dataMat[overLap,i])
# soting distances
sortedD = sorted(distances.items(), key=operator.itemgetter(1))
# printig query
print 'Selected joke:\n' , jokes[queryJoke] , '\n'
# printing k neightbors
for j in range(k):
print 'Joke %i: ' % (j+1), '\n' ,jokes[sortedD[j][0]] , '\n'
# calling function with k = 5
print_most_similar_jokes(dataMat, queryJoke=99, k=5, metric=pearsSim)
Selected joke: Q: What's the difference between greeting a Queen and greeting thePresident of the United States?A: You only have to get on one knee to greet the queen. Joke 1: A man visits the doctor. The doctor says "I have bad news for you.You have cancer and Alzheimer's disease". The man replies "Well thank God I don't have cancer!" Joke 2: This couple had an excellent relationship going until one day he came home from work to find his girlfriend packing. He asked her why she was leaving him and she told him that she had heard awful things about him. "What could they possibly have said to make you move out?" "They told me that you were a pedophile." He replied "That's an awfully big word for a ten year old." Joke 3: Q. What's 200 feet long and has 4 teeth? A. The front row at a Willie Nelson Concert. Joke 4: Q. What's the difference between a man and a toilet? A. A toilet doesn't follow you around after you use it. Joke 5: Q. What's O. J. Simpson's Internet address? A. Slash slash backslash slash slash escape.
In [10]:
# calling function with k = 3
print_most_similar_jokes(dataMat, queryJoke=37, k=3, metric=pearsSim)
Selected joke: "May I take your order?" the waiter asked. "Yes how do you prepare your chickens?" "Nothing special sir" he replied. "We just tell them straight out that they're going to die." Joke 1: A man visits the doctor. The doctor says "I have bad news for you.You have cancer and Alzheimer's disease". The man replies "Well thank God I don't have cancer!" Joke 2: This couple had an excellent relationship going until one day he came home from work to find his girlfriend packing. He asked her why she was leaving him and she told him that she had heard awful things about him. "What could they possibly have said to make you move out?" "They told me that you were a pedophile." He replied "That's an awfully big word for a ten year old." Joke 3: Q. What's 200 feet long and has 4 teeth? A. The front row at a Willie Nelson Concert.