11.1、关联规则实例
2016-02-11 17:27
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关联规则
junjun
2016年2月11日
实例一：通过arules包中的Aprior()函数求关联规则、eclat()函数求频繁项集
#1、加载数据并查看 library(arules)
## Loading required package: Matrix
## ## Attaching package: 'arules'
## The following objects are masked from 'package:base': ## ## %in%, abbreviate, write
data("Groceries")
str(Groceries)## Formal class 'transactions' [package "arules"] with 4 slots ## ..@ transactionInfo:'data.frame': 9835 obs. of 0 variables ## ..@ data :Formal class 'ngCMatrix' [package "Matrix"] with 5 slots ## .. .. ..@ i : int [1:43367] 13 60 69 78 14 29 98 24 15 29 ... ## .. .. ..@ p : int [1:9836] 0 4 7 8 12 16 21 22 27 28 ... ## .. .. ..@ Dim : int [1:2] 169 9835 ## .. .. ..@ Dimnames:List of 2 ## .. .. .. ..$ : NULL ## .. .. .. ..$ : NULL ## .. .. ..@ factors : list() ## ..@ itemInfo :'data.frame': 169 obs. of 3 variables: ## .. ..$ labels: chr [1:169] "frankfurter" "sausage" "liver loaf" "ham" ... ## .. ..$ level2: Factor w/ 55 levels "baby food","bags",..: 44 44 44 44 44 44 44 42 42 41 ... ## .. ..$ level1: Factor w/ 10 levels "canned food",..: 6 6 6 6 6 6 6 6 6 6 ... ## ..@ itemsetInfo :'data.frame': 9835 obs. of 1 variable: ## .. ..$ itemsetID: chr [1:9835] "1" "2" "3" "4" ...
summary(Groceries)
## transactions as itemMatrix in sparse format with ## 9835 rows (elements/itemsets/transactions) and ## 169 columns (items) and a density of 0.02609146 ## ## most frequent items: ## whole milk other vegetables rolls/buns soda ## 2513 1903 1809 1715 ## yogurt (Other) ## 1372 34055 ## ## element (itemset/transaction) length distribution: ## sizes ## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ## 2159 1643 1299 1005 855 645 545 438 350 246 182 117 78 77 55 ## 16 17 18 19 20 21 22 23 24 26 27 28 29 32 ## 46 29 14 14 9 11 4 6 1 1 1 1 3 1 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.000 2.000 3.000 4.409 6.000 32.000 ## ## includes extended item information - examples: ## labels level2 level1 ## 1 frankfurter sausage meet and sausage ## 2 sausage sausage meet and sausage ## 3 liver loaf sausage meet and sausage
dim(Groceries)
## [1] 9835 169
#以Groceries数据为例，超市购物的例子，每一行为一个顾客的购买记录，格式为transactions 也就是以稀疏矩阵储存的物品矩阵数据 inspect(Groceries[1:3])
## items
## 1 {citrus fruit,
## semi-finished bread,
## margarine,
## ready soups}
## 2 {tropical fruit,
## yogurt,
## coffee}
## 3 {whole milk}#2、数据清洗 #1）查看某些数据项出现的频率 itemFrequency(Groceries[, 1:3])
## frankfurter sausage liver loaf ## 0.058973055 0.093950178 0.005083884
#2)数据探索 itemFrequencyPlot(Groceries, support=0.1)
#有8项支持度大于0.1 itemFrequencyPlot(Groceries, topN=20)
# 画出前20个频率最大的项 #3)稀疏矩阵可视化 image(Groceries[1:5])
image(sample(Groceries, 100))
#4)对稀疏矩阵进行转换，把transaction类型转化为data.frame类型 df_Gro <- as(Groceries, "data.frame") dim(df_Gro)
## [1] 9835 1
head(df_Gro, 3)
## items
## 1 {citrus fruit,semi-finished bread,margarine,ready soups}
## 2 {tropical fruit,yogurt,coffee}
## 3 {whole milk}#对transactions类型的Groceries数据做处理：aprior()函数求关联规则，eclat()函数求频繁项集 #3、创建关联规则：aprior()函数求关联规则 rules <- apriori(Groceries, parameter = list(support=0.01, confidence=0.2))
## Apriori ## ## Parameter specification: ## confidence minval smax arem aval originalSupport support minlen maxlen ## 0.2 0.1 1 none FALSE TRUE 0.01 1 10 ## target ext ## rules FALSE ## ## Algorithmic control: ## filter tree heap memopt load sort verbose ## 0.1 TRUE TRUE FALSE TRUE 2 TRUE ## ## Absolute minimum support count: 98 ## ## set item appearances ...[0 item(s)] done [0.00s]. ## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s]. ## sorting and recoding items ... [88 item(s)] done [0.00s]. ## creating transaction tree ... done [0.00s]. ## checking subsets of size 1 2 3 4 done [0.00s]. ## writing ... [232 rule(s)] done [0.00s]. ## creating S4 object ... done [0.00s].
summary(rules)
## set of 232 rules ## ## rule length distribution (lhs + rhs):sizes ## 1 2 3 ## 1 151 80 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.000 2.000 2.000 2.341 3.000 3.000 ## ## summary of quality measures: ## support confidence lift ## Min. :0.01007 Min. :0.2006 Min. :0.8991 ## 1st Qu.:0.01200 1st Qu.:0.2470 1st Qu.:1.4432 ## Median :0.01490 Median :0.3170 Median :1.7277 ## Mean :0.02005 Mean :0.3321 Mean :1.7890 ## 3rd Qu.:0.02227 3rd Qu.:0.4033 3rd Qu.:2.0762 ## Max. :0.25552 Max. :0.5862 Max. :3.2950 ## ## mining info: ## data ntransactions support confidence ## Groceries 9835 0.01 0.2
#保存数据到磁盘 df_rules <- as(rules, "data.frame") write.csv(df_rules, "F:/R/GeroRules.csv") #直接保存 #write(rules, file="F:/R/GeroRules1.csv", sep=",", col.names=NA) #4、按支持度对求得的关联规则子集排序并查看前3条规则 inspect(sort(rules)[1:3]) #默认decreasing=T，按支持度排序
## lhs rhs support confidence
## 1 {} => {whole milk} 0.25551601 0.2555160
## 151 {other vegetables} => {whole milk} 0.07483477 0.3867578
## 152 {whole milk} => {other vegetables} 0.07483477 0.2928770
## lift
## 1 1.000000
## 151 1.513634
## 152 1.513634inspect(sort(rules, decreasing = F)[1:3])
## lhs rhs support confidence lift
## 2 {hard cheese} => {whole milk} 0.01006609 0.4107884 1.607682
## 20 {waffles} => {other vegetables} 0.01006609 0.2619048 1.353565
## 153 {curd,yogurt} => {whole milk} 0.01006609 0.5823529 2.279125inspect(sort(rules, by="lift")[1:3])
## lhs rhs support confidence lift
## 1 {citrus fruit,
## other vegetables} => {root vegetables} 0.01037112 0.3591549 3.295045
## 2 {other vegetables,
## yogurt} => {whipped/sour cream} 0.01016777 0.2341920 3.267062
## 3 {tropical fruit,
## other vegetables} => {root vegetables} 0.01230300 0.3427762 3.144780#5、求所需要的关联规则子集：用subset做规则的筛选,取"右手边"含有whole milk且lift大于1.2的规则 sub_rules <- subset(rules, subset=rhs %in% "whole milk" & lift>1.2) berryrules <- subset(Groceries, items %in% "berries") inspect(berryrules[1:3])
## items
## 1 {pork,
## berries,
## other vegetables,
## whole milk,
## whipped/sour cream,
## artif. sweetener,
## soda,
## abrasive cleaner}
## 2 {berries,
## yogurt}
## 3 {tropical fruit,
## pip fruit,
## berries,
## whole milk,
## frozen potato products,
## rolls/buns,
## pickled vegetables,
## chocolate}class(sub_rules)
## [1] "rules" ## attr(,"package") ## [1] "arules"
head(as(sub_rules, "data.frame"))
## rules support confidence lift
## 2 {hard cheese} => {whole milk} 0.01006609 0.4107884 1.607682
## 4 {butter milk} => {whole milk} 0.01159126 0.4145455 1.622385
## 5 {ham} => {whole milk} 0.01148958 0.4414062 1.727509
## 6 {sliced cheese} => {whole milk} 0.01077783 0.4398340 1.721356
## 7 {oil} => {whole milk} 0.01128622 0.4021739 1.573968
## 9 {onions} => {whole milk} 0.01209964 0.3901639 1.526965#6、eclat()函数求频繁项集 sets <- eclat(Groceries, parameter = list(support=0.05, maxlen=10))
## Eclat ## ## parameter specification: ## tidLists support minlen maxlen target ext ## FALSE 0.05 1 10 frequent itemsets FALSE ## ## algorithmic control: ## sparse sort verbose ## 7 -2 TRUE ## ## Absolute minimum support count: 491 ## ## create itemset ... ## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s]. ## sorting and recoding items ... [28 item(s)] done [0.00s]. ## creating sparse bit matrix ... [28 row(s), 9835 column(s)] done [0.00s]. ## writing ... [31 set(s)] done [0.00s]. ## Creating S4 object ... done [0.00s].
summary(sets)
## set of 31 itemsets ## ## most frequent items: ## whole milk other vegetables yogurt rolls/buns ## 4 2 2 2 ## frankfurter (Other) ## 1 23 ## ## element (itemset/transaction) length distribution:sizes ## 1 2 ## 28 3 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.000 1.000 1.000 1.097 1.000 2.000 ## ## summary of quality measures: ## support ## Min. :0.05236 ## 1st Qu.:0.05831 ## Median :0.07565 ## Mean :0.09212 ## 3rd Qu.:0.10173 ## Max. :0.25552 ## ## includes transaction ID lists: FALSE ## ## mining info: ## data ntransactions support ## Groceries 9835 0.05
#7、按支持度对求得的频繁项集排序并查看前6条频繁项集： inspect(sort(sets, by="support")[1:6])
## items support
## 4 {whole milk} 0.2555160
## 5 {other vegetables} 0.1934926
## 6 {rolls/buns} 0.1839349
## 8 {soda} 0.1743772
## 7 {yogurt} 0.1395018
## 11 {bottled water} 0.1105236#8、针对transcation数据画频繁项的图 itemFrequencyPlot(Groceries, support=0.05, cex.names=0.8)
#9、简单介绍一下关联规则的可视化包： #每个画图包背后都有一堆包，像ggplot2 library(arulesViz) #载入需要的程辑包：scatterplot3d #载入需要的程辑包：vcd #载入需要的程辑包：MASS #载入需要的程辑包：grid #载入需要的程辑包：colorspace #载入需要的程辑包：seriation #载入需要的程辑包：cluster #载入需要的程辑包：TSP #载入需要的程辑包：gclus #arulesViz中有很多图形，介绍几个好看的，画图的对象都是rules library(arulesViz)
## Loading required package: grid
## ## Attaching package: 'arulesViz'
## The following object is masked from 'package:arules': ## ## abbreviate
## The following object is masked from 'package:base': ## ## abbreviate
plot(rules, shading="order", control=list(main="Two-key plot"))
plot(rules, method="grouped")
plot(rules, method="graph")
实例二、
购物篮数据，每行表示一个篮子，篮子里用逗号分隔出一个个品牌。 现在采用频繁模式挖掘出品牌关联，主要是频繁二项集。将关联看成一条边，出现次数看作边的权重，这样就得到了一张图，对图进行社区发现，可以看到品牌间是否有关联。 原始数据下载：http://pan.baidu.com/s/1jGHr8iy#1、加载数据并查看
x <- readLines("F:\\R\\Rworkspace\\实验数据/user2items.csv")
str(x)## chr [1:475] "6805" "4750,19394,25651,6395,5592" ...
#2、数据预处理
data <- list()
for(n in 1:length(x)) {
data[n] <- strsplit(x[n], ",")
}
data[1]## [[1]] ## [1] "6805"
data[2]
## [[1]] ## [1] "4750" "19394" "25651" "6395" "5592"
trans <- as(data, "transactions") #3、建模 library(arules) frequentsets <- eclat(trans, parameter = list(support=0.004, maxlen=10))
## Eclat ## ## parameter specification: ## tidLists support minlen maxlen target ext ## FALSE 0.004 1 10 frequent itemsets FALSE ## ## algorithmic control: ## sparse sort verbose ## 7 -2 TRUE ## ## Absolute minimum support count: 1
## Warning in eclat(trans, parameter = list(support = 0.004, maxlen = 10)): You chose a very low absolute support count of 1. You might run out of memory! Increase minimum support.
## create itemset ... ## set transactions ...[1642 item(s), 475 transaction(s)] done [0.00s]. ## sorting and recoding items ... [520 item(s)] done [0.00s]. ## creating sparse bit matrix ... [520 row(s), 475 column(s)] done [0.00s]. ## writing ... [753 set(s)] done [0.00s]. ## Creating S4 object ... done [0.00s].
#查看频繁项集 inspect(frequentsets[1:10])
## items support
## 1 {13471,7868} 0.004210526
## 2 {12688,15217} 0.004210526
## 3 {15921,7105} 0.004210526
## 4 {18712,26737} 0.004210526
## 5 {1282,18180} 0.004210526
## 6 {11196,14048} 0.004210526
## 7 {26576,6571} 0.004210526
## 8 {29078,5598} 0.004210526
## 9 {11330,26614} 0.004210526
## 10 {7868,9899} 0.004210526inspect(sort(frequentsets, by="support")[1:3])
## items support
## 234 {7868} 0.05052632
## 237 {27791} 0.04421053
## 235 {29099} 0.03789474inspect(sort(frequentsets, by="support", decreasing=F)[1:3])
## items support
## 1 {13471,7868} 0.004210526
## 2 {12688,15217} 0.004210526
## 3 {15921,7105} 0.004210526#4、求关联规则 rules <- apriori(trans, parameter = list(support=0.004, confidence=0.001))
## Apriori ## ## Parameter specification: ## confidence minval smax arem aval originalSupport support minlen maxlen ## 0.001 0.1 1 none FALSE TRUE 0.004 1 10 ## target ext ## rules FALSE ## ## Algorithmic control: ## filter tree heap memopt load sort verbose ## 0.1 TRUE TRUE FALSE TRUE 2 TRUE ## ## Absolute minimum support count: 1
## Warning in apriori(trans, parameter = list(support = 0.004, confidence = 0.001)): You chose a very low absolute support count of 1. You might run out of memory! Increase minimum support.
## set item appearances ...[0 item(s)] done [0.00s]. ## set transactions ...[1642 item(s), 475 transaction(s)] done [0.00s]. ## sorting and recoding items ... [520 item(s)] done [0.00s]. ## creating transaction tree ... done [0.00s]. ## checking subsets of size 1 2 3 4 done [0.00s]. ## writing ... [1026 rule(s)] done [0.00s]. ## creating S4 object ... done [0.00s].
summary(rules)
## set of 1026 rules ## ## rule length distribution (lhs + rhs):sizes ## 1 2 3 4 ## 520 396 90 20 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.00 1.00 1.00 1.62 2.00 4.00 ## ## summary of quality measures: ## support confidence lift ## Min. :0.004211 Min. :0.00421 Min. : 1.00 ## 1st Qu.:0.004211 1st Qu.:0.00421 1st Qu.: 1.00 ## Median :0.004211 Median :0.02947 Median : 1.00 ## Mean :0.005836 Mean :0.25990 Mean : 24.92 ## 3rd Qu.:0.006316 3rd Qu.:0.40000 3rd Qu.: 31.67 ## Max. :0.050526 Max. :1.00000 Max. :237.50 ## ## mining info: ## data ntransactions support confidence ## trans 475 0.004 0.001
inspect(rules)
## lhs rhs support confidence lift
## 1 {} => {3658} 0.004210526 0.004210526 1.000000
## 2 {} => {14294} 0.004210526 0.004210526 1.000000
## 3 {} => {7963} 0.004210526 0.004210526 1.000000
## 4 {} => {7150} 0.004210526 0.004210526 1.000000
## 5 {} => {28438} 0.004210526 0.004210526 1.000000
## 6 {} => {5094} 0.004210526 0.004210526 1.000000
## 7 {} => {11790} 0.004210526 0.004210526 1.000000
## 8 {} => {21899} 0.004210526 0.004210526 1.000000
## 9 {} => {11280} 0.004210526 0.004210526 1.000000
## 10 {} => {9829} 0.004210526 0.004210526 1.000000
## 11 {} => {26722} 0.004210526 0.004210526 1.000000
## 12 {} => {4039} 0.004210526 0.004210526 1.000000
## 13 {} => {25193} 0.004210526 0.004210526 1.000000
## 14 {} => {17237} 0.004210526 0.004210526 1.000000
## 15 {} => {9301} 0.004210526 0.004210526 1.000000
## 16 {} => {25596} 0.004210526 0.004210526 1.000000
## 17 {} => {20902} 0.006315789 0.006315789 1.000000
## 18 {} => {13975} 0.004210526 0.004210526 1.000000
## 19 {} => {24193} 0.004210526 0.004210526 1.000000
## 20 {} => {4808} 0.004210526 0.004210526 1.000000
## 21 {} => {22240} 0.004210526 0.004210526 1.000000
## 22 {} => {12055} 0.004210526 0.004210526 1.000000
## 23 {} => {4960} 0.004210526 0.004210526 1.000000
## 24 {} => {14360} 0.004210526 0.004210526 1.000000
## 25 {} => {15831} 0.004210526 0.004210526 1.000000
## 26 {} => {1481} 0.006315789 0.006315789 1.000000
## 27 {} => {3185} 0.004210526 0.004210526 1.000000
## 28 {} => {9193} 0.004210526 0.004210526 1.000000
## 29 {} => {12453} 0.004210526 0.004210526 1.000000
## 30 {} => {12647} 0.004210526 0.004210526 1.000000
## 31 {} => {20506} 0.004210526 0.004210526 1.000000
## 32 {} => {11857} 0.006315789 0.006315789 1.000000
## 33 {} => {5015} 0.004210526 0.004210526 1.000000
## 34 {} => {9195} 0.004210526 0.004210526 1.000000
## 35 {} => {13390} 0.004210526 0.004210526 1.000000
## 36 {} => {24274} 0.004210526 0.004210526 1.000000
## 37 {} => {15672} 0.004210526 0.004210526 1.000000
## 38 {} => {20578} 0.004210526 0.004210526 1.000000
## 39 {} => {11159} 0.004210526 0.004210526 1.000000
## 40 {} => {19814} 0.004210526 0.004210526 1.000000
## 41 {} => {22094} 0.004210526 0.004210526 1.000000
## 42 {} => {12586} 0.004210526 0.004210526 1.000000
## 43 {} => {15911} 0.004210526 0.004210526 1.000000
## 44 {} => {13998} 0.004210526 0.004210526 1.000000
## 45 {} => {24788} 0.004210526 0.004210526 1.000000
## 46 {} => {5403} 0.004210526 0.004210526 1.000000
## 47 {} => {14159} 0.004210526 0.004210526 1.000000
## 48 {} => {13093} 0.004210526 0.004210526 1.000000
## 49 {} => {16243} 0.004210526 0.004210526 1.000000
## 50 {} => {18575} 0.006315789 0.006315789 1.000000
## 51 {} => {17153} 0.006315789 0.006315789 1.000000
## 52 {} => {6096} 0.004210526 0.004210526 1.000000
## 53 {} => {2891} 0.004210526 0.004210526 1.000000
## 54 {} => {8816} 0.004210526 0.004210526 1.000000
## 55 {} => {20548} 0.004210526 0.004210526 1.000000
## 56 {} => {4691} 0.004210526 0.004210526 1.000000
## 57 {} => {16009} 0.004210526 0.004210526 1.000000
## 58 {} => {14795} 0.004210526 0.004210526 1.000000
## 59 {} => {9220} 0.004210526 0.004210526 1.000000
## 60 {} => {20701} 0.004210526 0.004210526 1.000000
## 61 {} => {4300} 0.004210526 0.004210526 1.000000
## 62 {} => {12063} 0.004210526 0.004210526 1.000000
## 63 {} => {13471} 0.004210526 0.004210526 1.000000
## 64 {} => {3555} 0.004210526 0.004210526 1.000000
## 65 {} => {24459} 0.004210526 0.004210526 1.000000
## 66 {} => {25960} 0.004210526 0.004210526 1.000000
## 67 {} => {5845} 0.004210526 0.004210526 1.000000
## 68 {} => {1533} 0.004210526 0.004210526 1.000000
## 69 {} => {1831} 0.004210526 0.004210526 1.000000
## 70 {} => {26972} 0.004210526 0.004210526 1.000000
## 71 {} => {7936} 0.004210526 0.004210526 1.000000
## 72 {} => {2610} 0.004210526 0.004210526 1.000000
## 73 {} => {10908} 0.004210526 0.004210526 1.000000
## 74 {} => {21392} 0.004210526 0.004210526 1.000000
## 75 {} => {11357} 0.004210526 0.004210526 1.000000
## 76 {} => {178} 0.004210526 0.004210526 1.000000
## 77 {} => {16302} 0.004210526 0.004210526 1.000000
## 78 {} => {18281} 0.004210526 0.004210526 1.000000
## 79 {} => {614} 0.004210526 0.004210526 1.000000
## 80 {} => {28391} 0.004210526 0.004210526 1.000000
## 81 {} => {23214} 0.004210526 0.004210526 1.000000
## 82 {} => {11578} 0.006315789 0.006315789 1.000000
## 83 {} => {8693} 0.004210526 0.004210526 1.000000
## 84 {} => {5620} 0.004210526 0.004210526 1.000000
## 85 {} => {15217} 0.004210526 0.004210526 1.000000
## 86 {} => {11018} 0.004210526 0.004210526 1.000000
## 87 {} => {28694} 0.004210526 0.004210526 1.000000
## 88 {} => {3135} 0.004210526 0.004210526 1.000000
## 89 {} => {8313} 0.004210526 0.004210526 1.000000
## 90 {} => {25086} 0.004210526 0.004210526 1.000000
## 91 {} => {15089} 0.004210526 0.004210526 1.000000
## 92 {} => {23622} 0.004210526 0.004210526 1.000000
## 93 {} => {14821} 0.004210526 0.004210526 1.000000
## 94 {} => {6447} 0.004210526 0.004210526 1.000000
## 95 {} => {21995} 0.004210526 0.004210526 1.000000
## 96 {} => {23143} 0.004210526 0.004210526 1.000000
## 97 {} => {16500} 0.004210526 0.004210526 1.000000
## 98 {} => {599} 0.004210526 0.004210526 1.000000
## 99 {} => {28411} 0.004210526 0.004210526 1.000000
## 100 {} => {5067} 0.006315789 0.006315789 1.000000
## 101 {} => {19540} 0.004210526 0.004210526 1.000000
## 102 {} => {22342} 0.004210526 0.004210526 1.000000
## 103 {} => {15921} 0.004210526 0.004210526 1.000000
## 104 {} => {4172} 0.006315789 0.006315789 1.000000
## 105 {} => {28370} 0.004210526 0.004210526 1.000000
## 106 {} => {27117} 0.004210526 0.004210526 1.000000
## 107 {} => {12790} 0.004210526 0.004210526 1.000000
## 108 {} => {26121} 0.004210526 0.004210526 1.000000
## 109 {} => {21593} 0.004210526 0.004210526 1.000000
## 110 {} => {14446} 0.004210526 0.004210526 1.000000
## 111 {} => {360} 0.004210526 0.004210526 1.000000
## 112 {} => {19993} 0.006315789 0.006315789 1.000000
## 113 {} => {11776} 0.004210526 0.004210526 1.000000
## 114 {} => {20154} 0.004210526 0.004210526 1.000000
## 115 {} => {24929} 0.004210526 0.004210526 1.000000
## 116 {} => {8630} 0.004210526 0.004210526 1.000000
## 117 {} => {21372} 0.004210526 0.004210526 1.000000
## 118 {} => {5848} 0.004210526 0.004210526 1.000000
## 119 {} => {1392} 0.006315789 0.006315789 1.000000
## 120 {} => {4819} 0.004210526 0.004210526 1.000000
## 121 {} => {1950} 0.004210526 0.004210526 1.000000
## 122 {} => {15018} 0.004210526 0.004210526 1.000000
## 123 {} => {1966} 0.004210526 0.004210526 1.000000
## 124 {} => {4731} 0.004210526 0.004210526 1.000000
## 125 {} => {10866} 0.004210526 0.004210526 1.000000
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## 453 {} => {7230} 0.010526316 0.010526316 1.000000
## 454 {} => {26614} 0.014736842 0.014736842 1.000000
## 455 {} => {18515} 0.004210526 0.004210526 1.000000
## 456 {} => {14415} 0.006315789 0.006315789 1.000000
## 457 {} => {26288} 0.012631579 0.012631579 1.000000
## 458 {} => {22749} 0.012631579 0.012631579 1.000000
## 459 {} => {15534} 0.006315789 0.006315789 1.000000
## 460 {} => {21071} 0.006315789 0.006315789 1.000000
## 461 {} => {29224} 0.006315789 0.006315789 1.000000
## 462 {} => {7037} 0.004210526 0.004210526 1.000000
## 463 {} => {17061} 0.004210526 0.004210526 1.000000
## 464 {} => {11022} 0.006315789 0.006315789 1.000000
## 465 {} => {22126} 0.012631579 0.012631579 1.000000
## 466 {} => {24669} 0.012631579 0.012631579 1.000000
## 467 {} => {8842} 0.006315789 0.006315789 1.000000
## 468 {} => {17214} 0.006315789 0.006315789 1.000000
## 469 {} => {21092} 0.008421053 0.008421053 1.000000
## 470 {} => {16540} 0.018947368 0.018947368 1.000000
## 471 {} => {10325} 0.004210526 0.004210526 1.000000
## 472 {} => {2128} 0.006315789 0.006315789 1.000000
## 473 {} => {29203} 0.018947368 0.018947368 1.000000
## 474 {} => {19421} 0.006315789 0.006315789 1.000000
## 475 {} => {22313} 0.006315789 0.006315789 1.000000
## 476 {} => {11196} 0.031578947 0.031578947 1.000000
## 477 {} => {18730} 0.018947368 0.018947368 1.000000
## 478 {} => {9563} 0.014736842 0.014736842 1.000000
## 479 {} => {1000} 0.006315789 0.006315789 1.000000
## 480 {} => {21919} 0.010526316 0.010526316 1.000000
## 481 {} => {3151} 0.014736842 0.014736842 1.000000
## 482 {} => {26523} 0.010526316 0.010526316 1.000000
## 483 {} => {10014} 0.010526316 0.010526316 1.000000
## 484 {} => {21336} 0.006315789 0.006315789 1.000000
## 485 {} => {7096} 0.014736842 0.014736842 1.000000
## 486 {} => {8637} 0.023157895 0.023157895 1.000000
## 487 {} => {25651} 0.008421053 0.008421053 1.000000
## 488 {} => {11176} 0.021052632 0.021052632 1.000000
## 489 {} => {4807} 0.006315789 0.006315789 1.000000
## 490 {} => {14065} 0.006315789 0.006315789 1.000000
## 491 {} => {22556} 0.008421053 0.008421053 1.000000
## 492 {} => {18712} 0.012631579 0.012631579 1.000000
## 493 {} => {14917} 0.008421053 0.008421053 1.000000
## 494 {} => {17959} 0.008421053 0.008421053 1.000000
## 495 {} => {12285} 0.023157895 0.023157895 1.000000
## 496 {} => {4571} 0.025263158 0.025263158 1.000000
## 497 {} => {15315} 0.016842105 0.016842105 1.000000
## 498 {} => {7061} 0.010526316 0.010526316 1.000000
## 499 {} => {20979} 0.016842105 0.016842105 1.000000
## 500 {} => {7105} 0.025263158 0.025263158 1.000000
## 501 {} => {4949} 0.018947368 0.018947368 1.000000
## 502 {} => {3228} 0.029473684 0.029473684 1.000000
## 503 {} => {11080} 0.031578947 0.031578947 1.000000
## 504 {} => {18805} 0.021052632 0.021052632 1.000000
## 505 {} => {3627} 0.023157895 0.023157895 1.000000
## 506 {} => {23628} 0.021052632 0.021052632 1.000000
## 507 {} => {15584} 0.012631579 0.012631579 1.000000
## 508 {} => {18024} 0.029473684 0.029473684 1.000000
## 509 {} => {4411} 0.012631579 0.012631579 1.000000
## 510 {} => {11679} 0.025263158 0.025263158 1.000000
## 511 {} => {8689} 0.029473684 0.029473684 1.000000
## 512 {} => {23928} 0.016842105 0.016842105 1.000000
## 513 {} => {9111} 0.016842105 0.016842105 1.000000
## 514 {} => {155} 0.023157895 0.023157895 1.000000
## 515 {} => {10702} 0.014736842 0.014736842 1.000000
## 516 {} => {14261} 0.023157895 0.023157895 1.000000
## 517 {} => {27791} 0.044210526 0.044210526 1.000000
## 518 {} => {14020} 0.037894737 0.037894737 1.000000
## 519 {} => {29099} 0.037894737 0.037894737 1.000000
## 520 {} => {7868} 0.050526316 0.050526316 1.000000
## 521 {13471} => {7868} 0.004210526 1.000000000 19.791667
## 522 {7868} => {13471} 0.004210526 0.083333333 19.791667
## 523 {15217} => {12688} 0.004210526 1.000000000 118.750000
## 524 {12688} => {15217} 0.004210526 0.500000000 118.750000
## 525 {15921} => {7105} 0.004210526 1.000000000 39.583333
## 526 {7105} => {15921} 0.004210526 0.166666667 39.583333
## 527 {1282} => {18180} 0.004210526 1.000000000 79.166667
## 528 {18180} => {1282} 0.004210526 0.333333333 79.166667
## 529 {26737} => {18712} 0.004210526 1.000000000 79.166667
## 530 {18712} => {26737} 0.004210526 0.333333333 79.166667
## 531 {29078} => {5598} 0.004210526 1.000000000 95.000000
## 532 {5598} => {29078} 0.004210526 0.400000000 95.000000
## 533 {26576} => {6571} 0.004210526 1.000000000 47.500000
## 534 {6571} => {26576} 0.004210526 0.200000000 47.500000
## 535 {14048} => {11196} 0.004210526 1.000000000 31.666667
## 536 {11196} => {14048} 0.004210526 0.133333333 31.666667
## 537 {11330} => {26614} 0.004210526 0.666666667 45.238095
## 538 {26614} => {11330} 0.004210526 0.285714286 45.238095
## 539 {25570} => {11176} 0.004210526 1.000000000 47.500000
## 540 {11176} => {25570} 0.004210526 0.200000000 47.500000
## 541 {9899} => {7868} 0.004210526 0.666666667 13.194444
## 542 {7868} => {9899} 0.004210526 0.083333333 13.194444
## 543 {17087} => {17060} 0.004210526 0.666666667 79.166667
## 544 {17060} => {17087} 0.004210526 0.500000000 79.166667
## 545 {7680} => {21110} 0.004210526 0.666666667 52.777778
## 546 {21110} => {7680} 0.004210526 0.333333333 52.777778
## 547 {7680} => {12754} 0.004210526 0.666666667 52.777778
## 548 {12754} => {7680} 0.004210526 0.333333333 52.777778
## 549 {7680} => {16463} 0.004210526 0.666666667 35.185185
## 550 {16463} => {7680} 0.004210526 0.222222222 35.185185
## 551 {5667} => {19405} 0.004210526 1.000000000 158.333333
## 552 {19405} => {5667} 0.004210526 0.666666667 158.333333
## 553 {14580} => {11080} 0.004210526 0.666666667 21.111111
## 554 {11080} => {14580} 0.004210526 0.133333333 21.111111
## 555 {3438} => {16331} 0.004210526 0.666666667 63.333333
## 556 {16331} => {3438} 0.004210526 0.400000000 63.333333
## 557 {5661} => {18741} 0.004210526 0.666666667 45.238095
## 558 {18741} => {5661} 0.004210526 0.285714286 45.238095
## 559 {25372} => {5598} 0.004210526 0.333333333 31.666667
## 560 {5598} => {25372} 0.004210526 0.400000000 31.666667
## 561 {2729} => {3151} 0.004210526 0.666666667 45.238095
## 562 {3151} => {2729} 0.004210526 0.285714286 45.238095
## 563 {2729} => {14020} 0.004210526 0.666666667 17.592593
## 564 {14020} => {2729} 0.004210526 0.111111111 17.592593
## 565 {12717} => {22043} 0.004210526 1.000000000 118.750000
## 566 {22043} => {12717} 0.004210526 0.500000000 118.750000
## 567 {12717} => {22359} 0.004210526 1.000000000 79.166667
## 568 {22359} => {12717} 0.004210526 0.333333333 79.166667
## 569 {23774} => {8689} 0.004210526 0.666666667 22.619048
## 570 {8689} => {23774} 0.004210526 0.142857143 22.619048
## 571 {19416} => {4571} 0.004210526 0.666666667 26.388889
## 572 {4571} => {19416} 0.004210526 0.166666667 26.388889
## 573 {4220} => {29203} 0.004210526 0.400000000 21.111111
## 574 {29203} => {4220} 0.004210526 0.222222222 21.111111
## 575 {4220} => {10014} 0.004210526 0.400000000 38.000000
## 576 {10014} => {4220} 0.004210526 0.400000000 38.000000
## 577 {12688} => {18741} 0.004210526 0.500000000 33.928571
## 578 {18741} => {12688} 0.004210526 0.285714286 33.928571
## 579 {4931} => {29099} 0.004210526 1.000000000 26.388889
## 580 {29099} => {4931} 0.004210526 0.111111111 26.388889
## 581 {3047} => {4949} 0.004210526 0.500000000 26.388889
## 582 {4949} => {3047} 0.004210526 0.222222222 26.388889
## 583 {24944} => {12068} 0.004210526 0.666666667 63.333333
## 584 {12068} => {24944} 0.004210526 0.400000000 63.333333
## 585 {3032} => {7105} 0.004210526 0.500000000 19.791667
## 586 {7105} => {3032} 0.004210526 0.166666667 19.791667
## 587 {12541} => {15315} 0.004210526 0.500000000 29.687500
## 588 {15315} => {12541} 0.004210526 0.250000000 29.687500
## 589 {2251} => {7868} 0.004210526 1.000000000 19.791667
## 590 {7868} => {2251} 0.004210526 0.083333333 19.791667
## 591 {7692} => {23019} 0.004210526 1.000000000 237.500000
## 592 {23019} => {7692} 0.004210526 1.000000000 237.500000
## 593 {7692} => {27791} 0.004210526 1.000000000 22.619048
## 594 {27791} => {7692} 0.004210526 0.095238095 22.619048
## 595 {24172} => {21838} 0.004210526 0.666666667 79.166667
## 596 {21838} => {24172} 0.004210526 0.500000000 79.166667
## 597 {24172} => {11080} 0.004210526 0.666666667 21.111111
## 598 {11080} => {24172} 0.004210526 0.133333333 21.111111
## 599 {1773} => {29203} 0.004210526 0.666666667 35.185185
## 600 {29203} => {1773} 0.004210526 0.222222222 35.185185
## 601 {4479} => {29099} 0.006315789 0.750000000 19.791667
## 602 {29099} => {4479} 0.006315789 0.166666667 19.791667
## 603 {23019} => {27791} 0.004210526 1.000000000 22.619048
## 604 {27791} => {23019} 0.004210526 0.095238095 22.619048
## 605 {12795} => {22126} 0.004210526 1.000000000 79.166667
## 606 {22126} => {12795} 0.004210526 0.333333333 79.166667
## 607 {2999} => {24669} 0.004210526 0.666666667 52.777778
## 608 {24669} => {2999} 0.004210526 0.333333333 52.777778
## 609 {3647} => {18741} 0.004210526 0.666666667 45.238095
## 610 {18741} => {3647} 0.004210526 0.285714286 45.238095
## 611 {10840} => {3151} 0.004210526 0.500000000 33.928571
## 612 {3151} => {10840} 0.004210526 0.285714286 33.928571
## 613 {3913} => {530} 0.004210526 1.000000000 118.750000
## 614 {530} => {3913} 0.004210526 0.500000000 118.750000
## 615 {3913} => {11679} 0.004210526 1.000000000 39.583333
## 616 {11679} => {3913} 0.004210526 0.166666667 39.583333
## 617 {21110} => {15534} 0.004210526 0.333333333 52.777778
## 618 {15534} => {21110} 0.004210526 0.666666667 52.777778
## 619 {21146} => {2963} 0.006315789 0.750000000 44.531250
## 620 {2963} => {21146} 0.006315789 0.375000000 44.531250
## 621 {21146} => {7096} 0.004210526 0.500000000 33.928571
## 622 {7096} => {21146} 0.004210526 0.285714286 33.928571
## 623 {24601} => {18024} 0.004210526 0.285714286 9.693878
## 624 {18024} => {24601} 0.004210526 0.142857143 9.693878
## 625 {2367} => {11679} 0.004210526 0.250000000 9.895833
## 626 {11679} => {2367} 0.004210526 0.166666667 9.895833
## 627 {12352} => {3627} 0.004210526 0.400000000 17.272727
## 628 {3627} => {12352} 0.004210526 0.181818182 17.272727
## 629 {8278} => {16331} 0.004210526 0.666666667 63.333333
## 630 {16331} => {8278} 0.004210526 0.400000000 63.333333
## 631 {8278} => {18024} 0.004210526 0.666666667 22.619048
## 632 {18024} => {8278} 0.004210526 0.142857143 22.619048
## 633 {8628} => {16463} 0.006315789 0.500000000 26.388889
## 634 {16463} => {8628} 0.006315789 0.333333333 26.388889
## 635 {8628} => {22359} 0.004210526 0.333333333 26.388889
## 636 {22359} => {8628} 0.004210526 0.333333333 26.388889
## 637 {1739} => {7096} 0.004210526 0.666666667 45.238095
## 638 {7096} => {1739} 0.004210526 0.285714286 45.238095
## 639 {14942} => {5043} 0.004210526 0.333333333 26.388889
## 640 {5043} => {14942} 0.004210526 0.333333333 26.388889
## 641 {14942} => {8637} 0.004210526 0.333333333 14.393939
## 642 {8637} => {14942} 0.004210526 0.181818182 14.393939
## 643 {13592} => {4949} 0.004210526 0.666666667 35.185185
## 644 {4949} => {13592} 0.004210526 0.222222222 35.185185
## 645 {21838} => {4571} 0.004210526 0.500000000 19.791667
## 646 {4571} => {21838} 0.004210526 0.166666667 19.791667
## 647 {21838} => {7105} 0.004210526 0.500000000 19.791667
## 648 {7105} => {21838} 0.004210526 0.166666667 19.791667
## 649 {21838} => {11080} 0.004210526 0.500000000 15.833333
## 650 {11080} => {21838} 0.004210526 0.133333333 15.833333
## 651 {21838} => {7868} 0.004210526 0.500000000 9.895833
## 652 {7868} => {21838} 0.004210526 0.083333333 9.895833
## 653 {28985} => {16463} 0.004210526 0.500000000 26.388889
## 654 {16463} => {28985} 0.004210526 0.222222222 26.388889
## 655 {28985} => {29203} 0.004210526 0.500000000 26.388889
## 656 {29203} => {28985} 0.004210526 0.222222222 26.388889
## 657 {7248} => {3151} 0.004210526 0.400000000 27.142857
## 658 {3151} => {7248} 0.004210526 0.285714286 27.142857
## 659 {16331} => {14261} 0.004210526 0.400000000 17.272727
## 660 {14261} => {16331} 0.004210526 0.181818182 17.272727
## 661 {16331} => {27791} 0.004210526 0.400000000 9.047619
## 662 {27791} => {16331} 0.004210526 0.095238095 9.047619
## 663 {12220} => {11080} 0.004210526 0.285714286 9.047619
## 664 {11080} => {12220} 0.004210526 0.133333333 9.047619
## 665 {21657} => {23628} 0.004210526 0.666666667 31.666667
## 666 {23628} => {21657} 0.004210526 0.200000000 31.666667
## 667 {24869} => {3228} 0.004210526 0.285714286 9.693878
## 668 {3228} => {24869} 0.004210526 0.142857143 9.693878
## 669 {23896} => {14261} 0.004210526 0.666666667 28.787879
## 670 {14261} => {23896} 0.004210526 0.181818182 28.787879
## 671 {12977} => {14020} 0.004210526 0.333333333 8.796296
## 672 {14020} => {12977} 0.004210526 0.111111111 8.796296
## 673 {18180} => {26614} 0.004210526 0.333333333 22.619048
## 674 {26614} => {18180} 0.004210526 0.285714286 22.619048
## 675 {18180} => {10014} 0.004210526 0.333333333 31.666667
## 676 {10014} => {18180} 0.004210526 0.400000000 31.666667
## 677 {18180} => {4411} 0.004210526 0.333333333 26.388889
## 678 {4411} => {18180} 0.004210526 0.333333333 26.388889
## 679 {25169} => {8637} 0.004210526 0.500000000 21.590909
## 680 {8637} => {25169} 0.004210526 0.181818182 21.590909
## 681 {18075} => {26523} 0.004210526 0.250000000 23.750000
## 682 {26523} => {18075} 0.004210526 0.400000000 23.750000
## 683 {18075} => {8689} 0.004210526 0.250000000 8.482143
## 684 {8689} => {18075} 0.004210526 0.142857143 8.482143
## 685 {19973} => {4571} 0.004210526 0.400000000 15.833333
## 686 {4571} => {19973} 0.004210526 0.166666667 15.833333
## 687 {12068} => {18024} 0.004210526 0.400000000 13.571429
## 688 {18024} => {12068} 0.004210526 0.142857143 13.571429
## 689 {16944} => {27791} 0.004210526 0.666666667 15.079365
## 690 {27791} => {16944} 0.004210526 0.095238095 15.079365
## 691 {5053} => {11679} 0.004210526 0.500000000 19.791667
## 692 {11679} => {5053} 0.004210526 0.166666667 19.791667
## 693 {21865} => {7105} 0.004210526 0.285714286 11.309524
## 694 {7105} => {21865} 0.004210526 0.166666667 11.309524
## 695 {10999} => {16110} 0.004210526 0.333333333 26.388889
## 696 {16110} => {10999} 0.004210526 0.333333333 26.388889
## 697 {10999} => {16540} 0.004210526 0.333333333 17.592593
## 698 {16540} => {10999} 0.004210526 0.222222222 17.592593
## 699 {10999} => {11679} 0.004210526 0.333333333 13.194444
## 700 {11679} => {10999} 0.004210526 0.166666667 13.194444
## 701 {530} => {22749} 0.006315789 0.750000000 59.375000
## 702 {22749} => {530} 0.006315789 0.500000000 59.375000
## 703 {530} => {12285} 0.004210526 0.500000000 21.590909
## 704 {12285} => {530} 0.004210526 0.181818182 21.590909
## 705 {530} => {23628} 0.004210526 0.500000000 23.750000
## 706 {23628} => {530} 0.004210526 0.200000000 23.750000
## 707 {530} => {11679} 0.004210526 0.500000000 19.791667
## 708 {11679} => {530} 0.004210526 0.166666667 19.791667
## 709 {27625} => {18805} 0.004210526 0.400000000 19.000000
## 710 {18805} => {27625} 0.004210526 0.200000000 19.000000
## 711 {22043} => {22359} 0.004210526 0.500000000 39.583333
## 712 {22359} => {22043} 0.004210526 0.333333333 39.583333
## 713 {18741} => {14020} 0.004210526 0.285714286 7.539683
## 714 {14020} => {18741} 0.004210526 0.111111111 7.539683
## 715 {16110} => {16540} 0.004210526 0.333333333 17.592593
## 716 {16540} => {16110} 0.004210526 0.222222222 17.592593
## 717 {16110} => {11679} 0.004210526 0.333333333 13.194444
## 718 {11679} => {16110} 0.004210526 0.166666667 13.194444
## 719 {16110} => {14261} 0.004210526 0.333333333 14.393939
## 720 {14261} => {16110} 0.004210526 0.181818182 14.393939
## 721 {16110} => {14020} 0.004210526 0.333333333 8.796296
## 722 {14020} => {16110} 0.004210526 0.111111111 8.796296
## 723 {22359} => {29203} 0.004210526 0.333333333 17.592593
## 724 {29203} => {22359} 0.004210526 0.222222222 17.592593
## 725 {251} => {11176} 0.004210526 0.285714286 13.571429
## 726 {11176} => {251} 0.004210526 0.200000000 13.571429
## 727 {251} => {4949} 0.004210526 0.285714286 15.079365
## 728 {4949} => {251} 0.004210526 0.222222222 15.079365
## 729 {251} => {3627} 0.004210526 0.285714286 12.337662
## 730 {3627} => {251} 0.004210526 0.181818182 12.337662
## 731 {25329} => {7096} 0.004210526 0.400000000 27.142857
## 732 {7096} => {25329} 0.004210526 0.285714286 27.142857
## 733 {25329} => {27791} 0.004210526 0.400000000 9.047619
## 734 {27791} => {25329} 0.004210526 0.095238095 9.047619
## 735 {7230} => {14415} 0.004210526 0.400000000 63.333333
## 736 {14415} => {7230} 0.004210526 0.666666667 63.333333
## 737 {18515} => {8842} 0.004210526 1.000000000 158.333333
## 738 {8842} => {18515} 0.004210526 0.666666667 158.333333
## 739 {18515} => {10702} 0.004210526 1.000000000 67.857143
## 740 {10702} => {18515} 0.004210526 0.285714286 67.857143
## 741 {14415} => {21919} 0.004210526 0.666666667 63.333333
## 742 {21919} => {14415} 0.004210526 0.400000000 63.333333
## 743 {14415} => {23928} 0.004210526 0.666666667 39.583333
## 744 {23928} => {14415} 0.004210526 0.250000000 39.583333
## 745 {22749} => {12285} 0.004210526 0.333333333 14.393939
## 746 {12285} => {22749} 0.004210526 0.181818182 14.393939
## 747 {22749} => {23628} 0.004210526 0.333333333 15.833333
## 748 {23628} => {22749} 0.004210526 0.200000000 15.833333
## 749 {15534} => {21092} 0.004210526 0.666666667 79.166667
## 750 {21092} => {15534} 0.004210526 0.500000000 79.166667
## 751 {29224} => {15315} 0.004210526 0.666666667 39.583333
## 752 {15315} => {29224} 0.004210526 0.250000000 39.583333
## 753 {7037} => {21092} 0.004210526 1.000000000 118.750000
## 754 {21092} => {7037} 0.004210526 0.500000000 118.750000
## 755 {17061} => {14261} 0.004210526 1.000000000 43.181818
## 756 {14261} => {17061} 0.004210526 0.181818182 43.181818
## 757 {11022} => {20979} 0.004210526 0.666666667 39.583333
## 758 {20979} => {11022} 0.004210526 0.250000000 39.583333
## 759 {11022} => {10702} 0.004210526 0.666666667 45.238095
## 760 {10702} => {11022} 0.004210526 0.285714286 45.238095
## 761 {22126} => {29099} 0.004210526 0.333333333 8.796296
## 762 {29099} => {22126} 0.004210526 0.111111111 8.796296
## 763 {24669} => {10702} 0.004210526 0.333333333 22.619048
## 764 {10702} => {24669} 0.004210526 0.285714286 22.619048
## 765 {8842} => {10702} 0.004210526 0.666666667 45.238095
## 766 {10702} => {8842} 0.004210526 0.285714286 45.238095
## 767 {21092} => {23928} 0.004210526 0.500000000 29.687500
## 768 {23928} => {21092} 0.004210526 0.250000000 29.687500
## 769 {16540} => {11196} 0.004210526 0.222222222 7.037037
## 770 {11196} => {16540} 0.004210526 0.133333333 7.037037
## 771 {16540} => {7105} 0.004210526 0.222222222 8.796296
## 772 {7105} => {16540} 0.004210526 0.166666667 8.796296
## 773 {16540} => {11679} 0.004210526 0.222222222 8.796296
## 774 {11679} => {16540} 0.004210526 0.166666667 8.796296
## 775 {10325} => {21336} 0.004210526 1.000000000 158.333333
## 776 {21336} => {10325} 0.004210526 0.666666667 158.333333
## 777 {10325} => {23928} 0.004210526 1.000000000 59.375000
## 778 {23928} => {10325} 0.004210526 0.250000000 59.375000
## 779 {10325} => {10702} 0.004210526 1.000000000 67.857143
## 780 {10702} => {10325} 0.004210526 0.285714286 67.857143
## 781 {2128} => {9111} 0.004210526 0.666666667 39.583333
## 782 {9111} => {2128} 0.004210526 0.250000000 39.583333
## 783 {29203} => {23628} 0.004210526 0.222222222 10.555556
## 784 {23628} => {29203} 0.004210526 0.200000000 10.555556
## 785 {29203} => {14020} 0.006315789 0.333333333 8.796296
## 786 {14020} => {29203} 0.006315789 0.166666667 8.796296
## 787 {19421} => {22313} 0.004210526 0.666666667 105.555556
## 788 {22313} => {19421} 0.004210526 0.666666667 105.555556
## 789 {19421} => {25651} 0.004210526 0.666666667 79.166667
## 790 {25651} => {19421} 0.004210526 0.500000000 79.166667
## 791 {19421} => {14261} 0.004210526 0.666666667 28.787879
## 792 {14261} => {19421} 0.004210526 0.181818182 28.787879
## 793 {22313} => {25651} 0.004210526 0.666666667 79.166667
## 794 {25651} => {22313} 0.004210526 0.500000000 79.166667
## 795 {22313} => {22556} 0.004210526 0.666666667 79.166667
## 796 {22556} => {22313} 0.004210526 0.500000000 79.166667
## 797 {22313} => {14261} 0.004210526 0.666666667 28.787879
## 798 {14261} => {22313} 0.004210526 0.181818182 28.787879
## 799 {11196} => {4949} 0.004210526 0.133333333 7.037037
## 800 {4949} => {11196} 0.004210526 0.222222222 7.037037
## 801 {9563} => {7105} 0.006315789 0.428571429 16.964286
## 802 {7105} => {9563} 0.006315789 0.250000000 16.964286
## 803 {1000} => {4807} 0.004210526 0.666666667 105.555556
## 804 {4807} => {1000} 0.004210526 0.666666667 105.555556
## 805 {1000} => {7061} 0.004210526 0.666666667 63.333333
## 806 {7061} => {1000} 0.004210526 0.400000000 63.333333
## 807 {1000} => {15584} 0.004210526 0.666666667 52.777778
## 808 {15584} => {1000} 0.004210526 0.333333333 52.777778
## 809 {21919} => {27791} 0.004210526 0.400000000 9.047619
## 810 {27791} => {21919} 0.004210526 0.095238095 9.047619
## 811 {21919} => {29099} 0.004210526 0.400000000 10.555556
## 812 {29099} => {21919} 0.004210526 0.111111111 10.555556
## 813 {3151} => {14020} 0.008421053 0.571428571 15.079365
## 814 {14020} => {3151} 0.008421053 0.222222222 15.079365
## 815 {26523} => {10014} 0.004210526 0.400000000 38.000000
## 816 {10014} => {26523} 0.004210526 0.400000000 38.000000
## 817 {26523} => {4411} 0.004210526 0.400000000 31.666667
## 818 {4411} => {26523} 0.004210526 0.333333333 31.666667
## 819 {26523} => {9111} 0.004210526 0.400000000 23.750000
## 820 {9111} => {26523} 0.004210526 0.250000000 23.750000
## 821 {10014} => {4411} 0.004210526 0.400000000 31.666667
## 822 {4411} => {10014} 0.004210526 0.333333333 31.666667
## 823 {21336} => {7061} 0.004210526 0.666666667 63.333333
## 824 {7061} => {21336} 0.004210526 0.400000000 63.333333
## 825 {21336} => {23928} 0.004210526 0.666666667 39.583333
## 826 {23928} => {21336} 0.004210526 0.250000000 39.583333
## 827 {21336} => {155} 0.004210526 0.666666667 28.787879
## 828 {155} => {21336} 0.004210526 0.181818182 28.787879
## 829 {21336} => {10702} 0.004210526 0.666666667 45.238095
## 830 {10702} => {21336} 0.004210526 0.285714286 45.238095
## 831 {7096} => {23628} 0.004210526 0.285714286 13.571429
## 832 {23628} => {7096} 0.004210526 0.200000000 13.571429
## 833 {7096} => {10702} 0.004210526 0.285714286 19.387755
## 834 {10702} => {7096} 0.004210526 0.285714286 19.387755
## 835 {8637} => {27791} 0.004210526 0.181818182 4.112554
## 836 {27791} => {8637} 0.004210526 0.095238095 4.112554
## 837 {8637} => {7868} 0.006315789 0.272727273 5.397727
## 838 {7868} => {8637} 0.006315789 0.125000000 5.397727
## 839 {25651} => {14261} 0.004210526 0.500000000 21.590909
## 840 {14261} => {25651} 0.004210526 0.181818182 21.590909
## 841 {11176} => {4949} 0.006315789 0.300000000 15.833333
## 842 {4949} => {11176} 0.006315789 0.333333333 15.833333
## 843 {11176} => {3627} 0.006315789 0.300000000 12.954545
## 844 {3627} => {11176} 0.006315789 0.272727273 12.954545
## 845 {11176} => {23628} 0.004210526 0.200000000 9.500000
## 846 {23628} => {11176} 0.004210526 0.200000000 9.500000
## 847 {4807} => {7061} 0.004210526 0.666666667 63.333333
## 848 {7061} => {4807} 0.004210526 0.400000000 63.333333
## 849 {4807} => {15584} 0.004210526 0.666666667 52.777778
## 850 {15584} => {4807} 0.004210526 0.333333333 52.777778
## 851 {14065} => {14917} 0.004210526 0.666666667 79.166667
## 852 {14917} => {14065} 0.004210526 0.500000000 79.166667
## 853 {14065} => {4411} 0.004210526 0.666666667 52.777778
## 854 {4411} => {14065} 0.004210526 0.333333333 52.777778
## 855 {22556} => {155} 0.004210526 0.500000000 21.590909
## 856 {155} => {22556} 0.004210526 0.181818182 21.590909
## 857 {22556} => {14020} 0.004210526 0.500000000 13.194444
## 858 {14020} => {22556} 0.004210526 0.111111111 13.194444
## 859 {14917} => {4411} 0.004210526 0.500000000 39.583333
## 860 {4411} => {14917} 0.004210526 0.333333333 39.583333
## 861 {17959} => {9111} 0.004210526 0.500000000 29.687500
## 862 {9111} => {17959} 0.004210526 0.250000000 29.687500
## 863 {12285} => {23628} 0.004210526 0.181818182 8.636364
## 864 {23628} => {12285} 0.004210526 0.200000000 8.636364
## 865 {12285} => {11679} 0.004210526 0.181818182 7.196970
## 866 {11679} => {12285} 0.004210526 0.166666667 7.196970
## 867 {12285} => {14020} 0.006315789 0.272727273 7.196970
## 868 {14020} => {12285} 0.006315789 0.166666667 7.196970
## 869 {12285} => {7868} 0.004210526 0.181818182 3.598485
## 870 {7868} => {12285} 0.004210526 0.083333333 3.598485
## 871 {4571} => {3228} 0.004210526 0.166666667 5.654762
## 872 {3228} => {4571} 0.004210526 0.142857143 5.654762
## 873 {4571} => {29099} 0.004210526 0.166666667 4.398148
## 874 {29099} => {4571} 0.004210526 0.111111111 4.398148
## 875 {15315} => {9111} 0.004210526 0.250000000 14.843750
## 876 {9111} => {15315} 0.004210526 0.250000000 14.843750
## 877 {15315} => {14020} 0.004210526 0.250000000 6.597222
## 878 {14020} => {15315} 0.004210526 0.111111111 6.597222
## 879 {7061} => {15584} 0.004210526 0.400000000 31.666667
## 880 {15584} => {7061} 0.004210526 0.333333333 31.666667
## 881 {7061} => {155} 0.004210526 0.400000000 17.272727
## 882 {155} => {7061} 0.004210526 0.181818182 17.272727
## 883 {20979} => {14261} 0.004210526 0.250000000 10.795455
## 884 {14261} => {20979} 0.004210526 0.181818182 10.795455
## 885 {7105} => {11080} 0.004210526 0.166666667 5.277778
## 886 {11080} => {7105} 0.004210526 0.133333333 5.277778
## 887 {7105} => {155} 0.004210526 0.166666667 7.196970
## 888 {155} => {7105} 0.004210526 0.181818182 7.196970
## 889 {7105} => {7868} 0.004210526 0.166666667 3.298611
## 890 {7868} => {7105} 0.004210526 0.083333333 3.298611
## 891 {4949} => {3627} 0.004210526 0.222222222 9.595960
## 892 {3627} => {4949} 0.004210526 0.181818182 9.595960
## 893 {4949} => {8689} 0.008421053 0.444444444 15.079365
## 894 {8689} => {4949} 0.008421053 0.285714286 15.079365
## 895 {3228} => {11679} 0.004210526 0.142857143 5.654762
## 896 {11679} => {3228} 0.004210526 0.166666667 5.654762
## 897 {18805} => {18024} 0.006315789 0.300000000 10.178571
## 898 {18024} => {18805} 0.006315789 0.214285714 10.178571
## 899 {18805} => {14261} 0.004210526 0.200000000 8.636364
## 900 {14261} => {18805} 0.004210526 0.181818182 8.636364
## 901 {23628} => {9111} 0.004210526 0.200000000 11.875000
## 902 {9111} => {23628} 0.004210526 0.250000000 11.875000
## 903 {15584} => {4411} 0.004210526 0.333333333 26.388889
## 904 {4411} => {15584} 0.004210526 0.333333333 26.388889
## 905 {15584} => {11679} 0.004210526 0.333333333 13.194444
## 906 {11679} => {15584} 0.004210526 0.166666667 13.194444
## 907 {18024} => {29099} 0.004210526 0.142857143 3.769841
## 908 {29099} => {18024} 0.004210526 0.111111111 3.769841
## 909 {8689} => {155} 0.004210526 0.142857143 6.168831
## 910 {155} => {8689} 0.004210526 0.181818182 6.168831
## 911 {8689} => {14020} 0.006315789 0.214285714 5.654762
## 912 {14020} => {8689} 0.006315789 0.166666667 5.654762
## 913 {23928} => {10702} 0.004210526 0.250000000 16.964286
## 914 {10702} => {23928} 0.004210526 0.285714286 16.964286
## 915 {9111} => {29099} 0.004210526 0.250000000 6.597222
## 916 {29099} => {9111} 0.004210526 0.111111111 6.597222
## 917 {2729,3151} => {14020} 0.004210526 1.000000000 26.388889
## 918 {14020,2729} => {3151} 0.004210526 1.000000000 67.857143
## 919 {14020,3151} => {2729} 0.004210526 0.500000000 79.166667
## 920 {12717,22043} => {22359} 0.004210526 1.000000000 79.166667
## 921 {12717,22359} => {22043} 0.004210526 1.000000000 118.750000
## 922 {22043,22359} => {12717} 0.004210526 1.000000000 237.500000
## 923 {23019,7692} => {27791} 0.004210526 1.000000000 22.619048
## 924 {27791,7692} => {23019} 0.004210526 1.000000000 237.500000
## 925 {23019,27791} => {7692} 0.004210526 1.000000000 237.500000
## 926 {21838,24172} => {11080} 0.004210526 1.000000000 31.666667
## 927 {11080,24172} => {21838} 0.004210526 1.000000000 118.750000
## 928 {11080,21838} => {24172} 0.004210526 1.000000000 158.333333
## 929 {3913,530} => {11679} 0.004210526 1.000000000 39.583333
## 930 {11679,3913} => {530} 0.004210526 1.000000000 118.750000
## 931 {11679,530} => {3913} 0.004210526 1.000000000 237.500000
## 932 {10999,16110} => {16540} 0.004210526 1.000000000 52.777778
## 933 {10999,16540} => {16110} 0.004210526 1.000000000 79.166667
## 934 {16110,16540} => {10999} 0.004210526 1.000000000 79.166667
## 935 {10999,16110} => {11679} 0.004210526 1.000000000 39.583333
## 936 {10999,11679} => {16110} 0.004210526 1.000000000 79.166667
## 937 {11679,16110} => {10999} 0.004210526 1.000000000 79.166667
## 938 {10999,16540} => {11679} 0.004210526 1.000000000 39.583333
## 939 {10999,11679} => {16540} 0.004210526 1.000000000 52.777778
## 940 {11679,16540} => {10999} 0.004210526 1.000000000 79.166667
## 941 {22749,530} => {12285} 0.004210526 0.666666667 28.787879
## 942 {12285,530} => {22749} 0.004210526 1.000000000 79.166667
## 943 {12285,22749} => {530} 0.004210526 1.000000000 118.750000
## 944 {22749,530} => {23628} 0.004210526 0.666666667 31.666667
## 945 {23628,530} => {22749} 0.004210526 1.000000000 79.166667
## 946 {22749,23628} => {530} 0.004210526 1.000000000 118.750000
## 947 {12285,530} => {23628} 0.004210526 1.000000000 47.500000
## 948 {23628,530} => {12285} 0.004210526 1.000000000 43.181818
## 949 {12285,23628} => {530} 0.004210526 1.000000000 118.750000
## 950 {16110,16540} => {11679} 0.004210526 1.000000000 39.583333
## 951 {11679,16110} => {16540} 0.004210526 1.000000000 52.777778
## 952 {11679,16540} => {16110} 0.004210526 1.000000000 79.166667
## 953 {18515,8842} => {10702} 0.004210526 1.000000000 67.857143
## 954 {10702,18515} => {8842} 0.004210526 1.000000000 158.333333
## 955 {10702,8842} => {18515} 0.004210526 1.000000000 237.500000
## 956 {12285,22749} => {23628} 0.004210526 1.000000000 47.500000
## 957 {22749,23628} => {12285} 0.004210526 1.000000000 43.181818
## 958 {12285,23628} => {22749} 0.004210526 1.000000000 79.166667
## 959 {10325,21336} => {23928} 0.004210526 1.000000000 59.375000
## 960 {10325,23928} => {21336} 0.004210526 1.000000000 158.333333
## 961 {21336,23928} => {10325} 0.004210526 1.000000000 237.500000
## 962 {10325,21336} => {10702} 0.004210526 1.000000000 67.857143
## 963 {10325,10702} => {21336} 0.004210526 1.000000000 158.333333
## 964 {10702,21336} => {10325} 0.004210526 1.000000000 237.500000
## 965 {10325,23928} => {10702} 0.004210526 1.000000000 67.857143
## 966 {10325,10702} => {23928} 0.004210526 1.000000000 59.375000
## 967 {10702,23928} => {10325} 0.004210526 1.000000000 237.500000
## 968 {19421,22313} => {25651} 0.004210526 1.000000000 118.750000
## 969 {19421,25651} => {22313} 0.004210526 1.000000000 158.333333
## 970 {22313,25651} => {19421} 0.004210526 1.000000000 158.333333
## 971 {19421,22313} => {14261} 0.004210526 1.000000000 43.181818
## 972 {14261,19421} => {22313} 0.004210526 1.000000000 158.333333
## 973 {14261,22313} => {19421} 0.004210526 1.000000000 158.333333
## 974 {19421,25651} => {14261} 0.004210526 1.000000000 43.181818
## 975 {14261,19421} => {25651} 0.004210526 1.000000000 118.750000
## 976 {14261,25651} => {19421} 0.004210526 1.000000000 158.333333
## 977 {22313,25651} => {14261} 0.004210526 1.000000000 43.181818
## 978 {14261,22313} => {25651} 0.004210526 1.000000000 118.750000
## 979 {14261,25651} => {22313} 0.004210526 1.000000000 158.333333
## 980 {1000,4807} => {7061} 0.004210526 1.000000000 95.000000
## 981 {1000,7061} => {4807} 0.004210526 1.000000000 158.333333
## 982 {4807,7061} => {1000} 0.004210526 1.000000000 158.333333
## 983 {1000,4807} => {15584} 0.004210526 1.000000000 79.166667
## 984 {1000,15584} => {4807} 0.004210526 1.000000000 158.333333
## 985 {15584,4807} => {1000} 0.004210526 1.000000000 158.333333
## 986 {1000,7061} => {15584} 0.004210526 1.000000000 79.166667
## 987 {1000,15584} => {7061} 0.004210526 1.000000000 95.000000
## 988 {15584,7061} => {1000} 0.004210526 1.000000000 158.333333
## 989 {10014,26523} => {4411} 0.004210526 1.000000000 79.166667
## 990 {26523,4411} => {10014} 0.004210526 1.000000000 95.000000
## 991 {10014,4411} => {26523} 0.004210526 1.000000000 95.000000
## 992 {21336,7061} => {155} 0.004210526 1.000000000 43.181818
## 993 {155,21336} => {7061} 0.004210526 1.000000000 95.000000
## 994 {155,7061} => {21336} 0.004210526 1.000000000 158.333333
## 995 {21336,23928} => {10702} 0.004210526 1.000000000 67.857143
## 996 {10702,21336} => {23928} 0.004210526 1.000000000 59.375000
## 997 {10702,23928} => {21336} 0.004210526 1.000000000 158.333333
## 998 {11176,4949} => {3627} 0.004210526 0.666666667 28.787879
## 999 {11176,3627} => {4949} 0.004210526 0.666666667 35.185185
## 1000 {3627,4949} => {11176} 0.004210526 1.000000000 47.500000
## 1001 {4807,7061} => {15584} 0.004210526 1.000000000 79.166667
## 1002 {15584,4807} => {7061} 0.004210526 1.000000000 95.000000
## 1003 {15584,7061} => {4807} 0.004210526 1.000000000 158.333333
## 1004 {14065,14917} => {4411} 0.004210526 1.000000000 79.166667
## 1005 {14065,4411} => {14917} 0.004210526 1.000000000 118.750000
## 1006 {14917,4411} => {14065} 0.004210526 1.000000000 158.333333
## 1007 {10999,16110,16540} => {11679} 0.004210526 1.000000000 39.583333
## 1008 {10999,11679,16110} => {16540} 0.004210526 1.000000000 52.777778
## 1009 {10999,11679,16540} => {16110} 0.004210526 1.000000000 79.166667
## 1010 {11679,16110,16540} => {10999} 0.004210526 1.000000000 79.166667
## 1011 {12285,22749,530} => {23628} 0.004210526 1.000000000 47.500000
## 1012 {22749,23628,530} => {12285} 0.004210526 1.000000000 43.181818
## 1013 {12285,23628,530} => {22749} 0.004210526 1.000000000 79.166667
## 1014 {12285,22749,23628} => {530} 0.004210526 1.000000000 118.750000
## 1015 {10325,21336,23928} => {10702} 0.004210526 1.000000000 67.857143
## 1016 {10325,10702,21336} => {23928} 0.004210526 1.000000000 59.375000
## 1017 {10325,10702,23928} => {21336} 0.004210526 1.000000000 158.333333
## 1018 {10702,21336,23928} => {10325} 0.004210526 1.000000000 237.500000
## 1019 {19421,22313,25651} => {14261} 0.004210526 1.000000000 43.181818
## 1020 {14261,19421,22313} => {25651} 0.004210526 1.000000000 118.750000
## 1021 {14261,19421,25651} => {22313} 0.004210526 1.000000000 158.333333
## 1022 {14261,22313,25651} => {19421} 0.004210526 1.000000000 158.333333
## 1023 {1000,4807,7061} => {15584} 0.004210526 1.000000000 79.166667
## 1024 {1000,15584,4807} => {7061} 0.004210526 1.000000000 95.000000
## 1025 {1000,15584,7061} => {4807} 0.004210526 1.000000000 158.333333
## 1026 {15584,4807,7061} => {1000} 0.004210526 1.000000000 158.333333inspect(sort(rules, by="support")[1:3])
## lhs rhs support confidence lift
## 520 {} => {7868} 0.05052632 0.05052632 1
## 517 {} => {27791} 0.04421053 0.04421053 1
## 518 {} => {14020} 0.03789474 0.03789474 1inspect(sort(rules, by="support", decreasing=F)[1:3])
## lhs rhs support confidence lift
## 1 {} => {3658} 0.004210526 0.004210526 1
## 2 {} => {14294} 0.004210526 0.004210526 1
## 3 {} => {7963} 0.004210526 0.004210526 1
实例三、分析Titanic数据，其中不同船舱的生存率
#1、加载数据并查看 str(Titanic)
## table [1:4, 1:2, 1:2, 1:2] 0 0 35 0 0 0 17 0 118 154 ... ## - attr(*, "dimnames")=List of 4 ## ..$ Class : chr [1:4] "1st" "2nd" "3rd" "Crew" ## ..$ Sex : chr [1:2] "Male" "Female" ## ..$ Age : chr [1:2] "Child" "Adult" ## ..$ Survived: chr [1:2] "No" "Yes"
dim(Titanic)
## [1] 4 2 2 2
str(Titanic)
## table [1:4, 1:2, 1:2, 1:2] 0 0 35 0 0 0 17 0 118 154 ... ## - attr(*, "dimnames")=List of 4 ## ..$ Class : chr [1:4] "1st" "2nd" "3rd" "Crew" ## ..$ Sex : chr [1:2] "Male" "Female" ## ..$ Age : chr [1:2] "Child" "Adult" ## ..$ Survived: chr [1:2] "No" "Yes"
str(df)
## function (x, df1, df2, ncp, log = FALSE)
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