Homework 10. Market Basket Analysis
Daria Dubovskaia
#chunks
knitr::opts_chunk$set(eval=TRUE, message=FALSE, warning=FALSE, fig.height=5, fig.align='center')
#libraries
library(tidyverse)
library(fpp3)
library(GGally)
library(gridExtra)
library(reshape2)
library(Hmisc)
library(corrplot)
library(e1071)
library(caret)
library(VIM)
library(forecast)
library(urca)
library(earth)
library(kernlab)
library(aTSA)
library(arules)
library(arulesViz)
library(factoextra)Assignment
Imagine 10000 receipts sitting on your table. Each receipt represents a transaction with items that were purchased. The receipt is a representation of stuff that went into a customer’s basket - and therefore ‘Market Basket Analysis’. That is exactly what the Groceries Data Set contains: a collection of receipts with each line representing 1 receipt and the items purchased. Each line is called a transaction and each column in a row represents an item. The data set is attached. Your assignment is to use R to mine the data for association rules. You should report support, confidence and lift and your top 10 rules by lift. Extra credit: do a simple cluster analysis on the data as well. Use whichever packages you like.
1. Market Basket Analysis
The dataset was loaded from Github with read.transactions() function to convert it straight into a transactions object. There are 9,835 transcations in the dataset (each is a customer receipt), and 169 of unique items. The proportion of non-zero items in the transaction matrix is 2.61%. Most popular items are “whole milk,” “other vegetables,” “rolls/buns,” “soda,” and “yogurt.”
The apriori() function was used to generated rules with
parameters:
Support Threshold = 0.01 (the rules apply to at least 1% of
transactions)
The confidence threshold = 0.5 (rules must be accurate at least 50% of
the time)
The table and the plot below show top 10 rules ranked by lift (the strength of the rule as contrasted to random chance). Edges represent rules, thicker edges and larger nodes suggest stronger lift-and-support laws. There is a significant connections between dairy products (e.g., “whole milk,” “yogurt”) and vegetables. The rule {citrus fruit, root vegetables} → {other vegetables} has the maximum lift (3.03), showing that customers who buy “citrus fruit” and “root vegetables” are more likely to buy “other vegetables.” Dairy items, particularly “whole milk,” are commonly used as the consequence in rules. The rule {rolls/buns, root vegetables} → {other vegetables} has a lift of 2.59, “rolls/buns” and “root vegetables” are moderately associated with “other vegetables,” likely for meal preparation. The rule {root vegetables, yogurt} → {other vegetables} has a lift of (2.58) wwhich emphasizes the centrality of “other vegetables” in baskets. For other rules we also see the connection between dairy products, between fruits, vegetables and essential dairy products
Based on the analysis, we can provide recommendations:
- For product Placement: keep “root vegetables” and “other vegetables”
close together to facilitate cross-selling.
- For promotions: use rules with a high lift (for example, yogurt and
curd with whole milk). - Make bundles of frequently linked items
(“yogurt,” “whole milk,” “curd”).
# Load data from Github
data <- read.transactions("https://raw.githubusercontent.com/ex-pr/DATA624/refs/heads/main/market_basket_analysis/GroceryDataSet.csv", sep = ",")
basket_df <- data##Check transcations
set.seed(547)
str(basket_df)## Formal class 'transactions' [package "arules"] with 3 slots
## ..@ data :Formal class 'ngCMatrix' [package "Matrix"] with 5 slots
## .. .. ..@ i : int [1:43367] 29 88 118 132 33 157 167 166 38 91 ...
## .. .. ..@ 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 1 variable:
## .. ..$ labels: chr [1:169] "abrasive cleaner" "artif. sweetener" "baby cosmetics" "baby food" ...
## ..@ itemsetInfo:'data.frame': 0 obs. of 0 variablessummary(basket_df)## 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 16
## 2159 1643 1299 1005 855 645 545 438 350 246 182 117 78 77 55 46
## 17 18 19 20 21 22 23 24 26 27 28 29 32
## 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
## 1 abrasive cleaner
## 2 artif. sweetener
## 3 baby cosmeticsinspect(head(basket_df))## items
## [1] {citrus fruit,
## margarine,
## ready soups,
## semi-finished bread}
## [2] {coffee,
## tropical fruit,
## yogurt}
## [3] {whole milk}
## [4] {cream cheese,
## meat spreads,
## pip fruit,
## yogurt}
## [5] {condensed milk,
## long life bakery product,
## other vegetables,
## whole milk}
## [6] {abrasive cleaner,
## butter,
## rice,
## whole milk,
## yogurt}# Mine association rules
rules <- apriori(basket_df, parameter = list(supp = 0.01, conf = 0.5))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.5 0.1 1 none FALSE TRUE 5 0.01 1
## maxlen target ext
## 10 rules TRUE
##
## 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 ... [15 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].# Inspect summary of the rules
summary(rules)## set of 15 rules
##
## rule length distribution (lhs + rhs):sizes
## 3
## 15
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3 3 3 3 3 3
##
## summary of quality measures:
## support confidence coverage lift
## Min. :0.01007 Min. :0.5000 Min. :0.01729 Min. :1.984
## 1st Qu.:0.01174 1st Qu.:0.5151 1st Qu.:0.02089 1st Qu.:2.036
## Median :0.01230 Median :0.5245 Median :0.02430 Median :2.203
## Mean :0.01316 Mean :0.5411 Mean :0.02454 Mean :2.299
## 3rd Qu.:0.01403 3rd Qu.:0.5718 3rd Qu.:0.02598 3rd Qu.:2.432
## Max. :0.02227 Max. :0.5862 Max. :0.04342 Max. :3.030
## count
## Min. : 99.0
## 1st Qu.:115.5
## Median :121.0
## Mean :129.4
## 3rd Qu.:138.0
## Max. :219.0
##
## mining info:
## data ntransactions support confidence
## basket_df 9835 0.01 0.5
## call
## apriori(data = basket_df, parameter = list(supp = 0.01, conf = 0.5))# Sort and extract the top 10 rules by lift
top_rules <- sort(rules, by = "lift")[1:10]
# Display the top rules in an interactive table
DT::datatable(
inspect(top_rules),
options = list(scrollX = TRUE,
dom = 'lBfrtip',
paging = FALSE,
searching = FALSE),
rownames = FALSE,
caption = htmltools::tags$caption(
style = 'caption-side: top; text-align: left; font-size: 16px; font-weight: bold;',
'Top 10 Rules (by Lift)'
)
)## lhs rhs support
## [1] {citrus fruit, root vegetables} => {other vegetables} 0.01037112
## [2] {root vegetables, tropical fruit} => {other vegetables} 0.01230300
## [3] {rolls/buns, root vegetables} => {other vegetables} 0.01220132
## [4] {root vegetables, yogurt} => {other vegetables} 0.01291307
## [5] {curd, yogurt} => {whole milk} 0.01006609
## [6] {butter, other vegetables} => {whole milk} 0.01148958
## [7] {root vegetables, tropical fruit} => {whole milk} 0.01199797
## [8] {root vegetables, yogurt} => {whole milk} 0.01453991
## [9] {domestic eggs, other vegetables} => {whole milk} 0.01230300
## [10] {whipped/sour cream, yogurt} => {whole milk} 0.01087951
## confidence coverage lift count
## [1] 0.5862069 0.01769192 3.029608 102
## [2] 0.5845411 0.02104728 3.020999 121
## [3] 0.5020921 0.02430097 2.594890 120
## [4] 0.5000000 0.02582613 2.584078 127
## [5] 0.5823529 0.01728521 2.279125 99
## [6] 0.5736041 0.02003050 2.244885 113
## [7] 0.5700483 0.02104728 2.230969 118
## [8] 0.5629921 0.02582613 2.203354 143
## [9] 0.5525114 0.02226741 2.162336 121
## [10] 0.5245098 0.02074225 2.052747 107# Visualize the top rules as a graph
plot(top_rules, method = "graph", engine = "htmlwidget")2. Cluster analysis
For the cluster analysis, we had to transform dataset to a binary
matrix with rows as transactions, columns as items, each cell was 1
(purchased) or 0 (not purchased). We used 5 clusters (centers=5) and 20
random initializations (nstart=20):
Cluster 1: 1,349 transactions
Cluster 2: 780 transactions
Cluster 3: 4,952 transactions
Cluster 4: 1,373 transactions
Cluster 5: 1,381 transactions
The top five items for each cluster:
Cluster 1: soda, rolls/buns, bottled water, whole milk, shopping bags
(quick purchases for daily needs)
Cluster 2: whole milk, yogurt, other vegetables, root vegetables,
tropical fruit (health-conscious buying)
Cluster 3: rolls/buns, canned beer, yogurt, bottled water, shopping bags
(beverages and snacks)
Cluster 4: whole milk, rolls/buns, root vegetables, yogurt, bottled
water (dairy goods, fresh produce)
Cluster 5: other vegetables, whole milk, rolls/buns, root vegetables,
soda (fresh produce with beverages)
The clusters were visualized with the fviz_cluster(), clusters overlap, as they supposed to for high-dimensional data. Cluster 1 (red) indicates a strong desire for necessary commodities such as soda and rolls/buns. Cluster 2 (green) focuses on health-conscious purchases including fresh veggies and dairy. Cluster 3 (blue) represents clients who prefer beverages and quick food. Cluster 4 (purple) identifies shoppers who prioritize staple foods and fresh produce. Cluster 5 (pink) attracts customers interested in premium produce and occasional indulgences such as soda.
Based on the analysis, we can tailor promotions to target certain
groups:
For Cluster 1, provide discounts for soda and bottled water, bundle
deals with rolls/buns, shopping bags.
For Cluster 2, promote healthy foods such as yogurt and tropical fruit,
bundle fresh root veggies with dairy goods.
For Cluster 3, offer discounts on canned beer, complement advertising
with bottled drinks, rolls/buns.
For Cluster 4, bundles dairy products (whole milk and yogurt) with fresh
root vegetables.
For Cluster 5, combine vegetables and fruits with occasional beverages
such as soda.
set.seed(547)
#Binary matrix items vs. transactions
cluster_matrix <- as(basket_df, "matrix")
#k-means clustering
k_means <- kmeans(cluster_matrix, centers = 5, nstart = 20)
print(k_means)## K-means clustering with 5 clusters of sizes 1349, 780, 4952, 1373, 1381
##
## Cluster means:
## abrasive cleaner artif. sweetener baby cosmetics baby food bags
## 1 0.001482580 0.002223870 0.0014825797 0.000000000 0.0000000000
## 2 0.015384615 0.005128205 0.0012820513 0.001282051 0.0000000000
## 3 0.001615509 0.003029079 0.0004038772 0.000000000 0.0006058158
## 4 0.003641661 0.002184996 0.0000000000 0.000000000 0.0007283321
## 5 0.005792904 0.005068791 0.0007241130 0.000000000 0.0000000000
## baking powder bathroom cleaner beef berries beverages bottled beer
## 1 0.008895478 0.0044477391 0.02742772 0.03335804 0.02446256 0.09266123
## 2 0.069230769 0.0102564103 0.16538462 0.10897436 0.02948718 0.10512821
## 3 0.008885299 0.0018174475 0.03210824 0.02241519 0.02584814 0.07915994
## 4 0.023306628 0.0007283321 0.05899490 0.02694829 0.02767662 0.06482156
## 5 0.023171615 0.0021723389 0.07965243 0.03548154 0.02461984 0.07530775
## bottled water brandy brown bread butter butter milk cake bar
## 1 0.16382506 0.004447739 0.05337287 0.03558191 0.02075612 0.025203855
## 2 0.21025641 0.001282051 0.16153846 0.22692308 0.08717949 0.032051282
## 3 0.08400646 0.005048465 0.04563813 0.02827141 0.01696284 0.006260097
## 4 0.10997815 0.002913328 0.08157320 0.07428988 0.02986162 0.014566642
## 5 0.09775525 0.003620565 0.07385952 0.05648081 0.03910210 0.014482259
## candles candy canned beer canned fish canned fruit canned vegetables
## 1 0.005930319 0.03928836 0.08376575 0.01482580 0.001482580 0.011860638
## 2 0.015384615 0.06153846 0.03717949 0.02948718 0.008974359 0.038461538
## 3 0.008077544 0.02504039 0.10601777 0.01090468 0.002019386 0.005048465
## 4 0.009468318 0.02330663 0.02403496 0.01238165 0.004369993 0.005826657
## 5 0.010861694 0.02679218 0.04634323 0.02461984 0.005068791 0.019551050
## cat food cereals chewing gum chicken chocolate
## 1 0.02520385 0.002223870 0.03558191 0.03113417 0.06375093
## 2 0.06794872 0.028205128 0.02179487 0.13589744 0.12692308
## 3 0.01635703 0.002221325 0.01817447 0.02403069 0.03634895
## 4 0.02476329 0.007283321 0.01456664 0.04078660 0.04151493
## 5 0.01955105 0.007241130 0.02317161 0.07168718 0.04779146
## chocolate marshmallow citrus fruit cleaner cling film/bags cocoa drinks
## 1 0.009636768 0.05485545 0.004447739 0.011860638 0.001482580
## 2 0.020512821 0.26282051 0.020512821 0.017948718 0.007692308
## 3 0.006462036 0.05492730 0.003432956 0.008279483 0.001009693
## 4 0.013109978 0.08230153 0.005098325 0.012381646 0.005826657
## 5 0.007241130 0.10861694 0.002896452 0.017378711 0.000724113
## coffee condensed milk cooking chocolate cookware cream
## 1 0.04966642 0.008154188 0.002223870 0.0029651594 0.000000000
## 2 0.10512821 0.016666667 0.007692308 0.0064102564 0.005128205
## 3 0.05270598 0.009491115 0.001817447 0.0030290792 0.001009693
## 4 0.06336489 0.008739985 0.002913328 0.0007283321 0.000000000
## 5 0.05358436 0.013034033 0.002172339 0.0014482259 0.002896452
## cream cheese curd curd cheese decalcifier dental care dessert
## 1 0.02594514 0.03706449 0.000000000 0.0007412898 0.003706449 0.04373610
## 2 0.14230769 0.20384615 0.017948718 0.0064102564 0.014102564 0.11153846
## 3 0.02382876 0.02907916 0.003634895 0.0012116317 0.004240711 0.02302100
## 4 0.04442826 0.06627822 0.005098325 0.0007283321 0.005098325 0.03714494
## 5 0.04706734 0.05792904 0.007965243 0.0014482259 0.009413469 0.03910210
## detergent dish cleaner dishes dog food domestic eggs
## 1 0.01408451 0.012601927 0.005189029 0.011119348 0.04521868
## 2 0.05000000 0.024358974 0.028205128 0.019230769 0.20769231
## 3 0.01191438 0.008683360 0.015953150 0.006462036 0.03412763
## 4 0.02694829 0.008011653 0.015294975 0.005826657 0.08739985
## 5 0.02534395 0.009413469 0.031860970 0.010137581 0.08110065
## female sanitary products finished products fish flour
## 1 0.008895478 0.006671609 0.001482580 0.011119348
## 2 0.012820513 0.012820513 0.006410256 0.066666667
## 3 0.004846527 0.005856220 0.002625202 0.009693053
## 4 0.005826657 0.002913328 0.002913328 0.021121631
## 5 0.004344678 0.008689356 0.003620565 0.019551050
## flower (seeds) flower soil/fertilizer frankfurter frozen chicken
## 1 0.007412898 0.001482580 0.05040771 0.0007412898
## 2 0.014102564 0.001282051 0.15128205 0.0012820513
## 3 0.006663974 0.002625202 0.04422456 0.0006058158
## 4 0.013838310 0.001456664 0.06190823 0.0007283321
## 5 0.020999276 0.000724113 0.06517017 0.0000000000
## frozen dessert frozen fish frozen fruits frozen meals frozen potato products
## 1 0.010378058 0.002965159 0.0014825797 0.02816901 0.013343217
## 2 0.033333333 0.034615385 0.0051282051 0.07435897 0.020512821
## 3 0.007471729 0.008481422 0.0004038772 0.02261712 0.005048465
## 4 0.008739985 0.010924982 0.0000000000 0.02476329 0.006554989
## 5 0.012309920 0.019551050 0.0028964518 0.02679218 0.010861694
## frozen vegetables fruit/vegetable juice grapes hair spray ham
## 1 0.03335804 0.09117865 0.01927354 0.0007412898 0.02001483
## 2 0.15256410 0.21794872 0.06794872 0.0000000000 0.08589744
## 3 0.02827141 0.04644588 0.01474152 0.0012116317 0.01575121
## 4 0.05389658 0.07137655 0.01747997 0.0014566642 0.02621996
## 5 0.06879073 0.06517017 0.03186097 0.0014482259 0.03475742
## hamburger meat hard cheese herbs honey house keeping products
## 1 0.02742772 0.01630838 0.007412898 0.0007412898 0.006671609
## 2 0.09615385 0.08333333 0.057692308 0.0025641026 0.033333333
## 3 0.01575121 0.01352989 0.007673667 0.0004038772 0.005048465
## 4 0.03932993 0.02767662 0.017479971 0.0065549891 0.009468318
## 5 0.06010138 0.03548154 0.031136857 0.0007241130 0.006517017
## hygiene articles ice cream instant coffee Instant food products jam
## 1 0.03706449 0.03261675 0.010378058 0.008895478 0.004447739
## 2 0.09102564 0.03846154 0.023076923 0.021794872 0.019230769
## 3 0.02201131 0.02504039 0.005856220 0.005048465 0.003029079
## 4 0.03058995 0.01602331 0.002184996 0.005826657 0.007283321
## 5 0.03765387 0.01882694 0.006517017 0.012309920 0.005068791
## ketchup kitchen towels kitchen utensil light bulbs liqueur
## 1 0.004447739 0.005930319 0.0000000000 0.002965159 0.0007412898
## 2 0.017948718 0.017948718 0.0038461538 0.006410256 0.0012820513
## 3 0.002423263 0.003029079 0.0002019386 0.004240711 0.0010096931
## 4 0.003641661 0.005826657 0.0000000000 0.002184996 0.0007283321
## 5 0.003620565 0.010137581 0.0000000000 0.005792904 0.0007241130
## liquor liquor (appetizer) liver loaf long life bakery product
## 1 0.013343217 0.014084507 0.005189029 0.03706449
## 2 0.005128205 0.008974359 0.011538462 0.11282051
## 3 0.015145396 0.007471729 0.002625202 0.02806947
## 4 0.001456664 0.005098325 0.007283321 0.03058995
## 5 0.007241130 0.005792904 0.007965243 0.03548154
## make up remover male cosmetics margarine mayonnaise meat meat spreads
## 1 0.0022238695 0.005930319 0.04892513 0.011860638 0.02446256 0.006671609
## 2 0.0012820513 0.002564103 0.15000000 0.028205128 0.06666667 0.010256410
## 3 0.0006058158 0.005048465 0.03554120 0.005048465 0.01433764 0.003634895
## 4 0.0007283321 0.002184996 0.07064822 0.007283321 0.02694829 0.002913328
## 5 0.0000000000 0.005068791 0.08689356 0.012309920 0.04417089 0.002172339
## misc. beverages mustard napkins newspapers nut snack nuts/prunes
## 1 0.04002965 0.014084507 0.05707932 0.06671609 0.0059303188 0.003706449
## 2 0.03846154 0.026923077 0.15512821 0.13974359 0.0051282051 0.006410256
## 3 0.02746365 0.007471729 0.03513732 0.06502423 0.0026252019 0.002625202
## 4 0.01820830 0.016751639 0.05025492 0.10560816 0.0007283321 0.002184996
## 5 0.02461984 0.013034033 0.05358436 0.08616944 0.0036205648 0.005068791
## oil onions organic products organic sausage other vegetables
## 1 0.02149741 0.01779096 0.001482580 0.002965159 0.004447739
## 2 0.07564103 0.10769231 0.003846154 0.006410256 0.661538462
## 3 0.01797254 0.01817447 0.001009693 0.001211632 0.000000000
## 4 0.03423161 0.02476329 0.002184996 0.003641661 0.000000000
## 5 0.03765387 0.05286025 0.002172339 0.001448226 1.000000000
## packaged fruit/vegetables pasta pastry pet care photo/film
## 1 0.008895478 0.019273536 0.10378058 0.011860638 0.005930319
## 2 0.024358974 0.043589744 0.19871795 0.016666667 0.008974359
## 3 0.011712439 0.008885299 0.06381260 0.008077544 0.011510501
## 4 0.011653314 0.016751639 0.10050983 0.008739985 0.010196650
## 5 0.016654598 0.015206372 0.09123823 0.008689356 0.003620565
## pickled vegetables pip fruit popcorn pork pot plants
## 1 0.014825797 0.05263158 0.010378058 0.05337287 0.01482580
## 2 0.041025641 0.28333333 0.015384615 0.14230769 0.03717949
## 3 0.009693053 0.04826333 0.005048465 0.03432956 0.01413570
## 4 0.021849964 0.07210488 0.009468318 0.05535324 0.01893664
## 5 0.033309196 0.08254888 0.005068791 0.09992759 0.01810282
## potato products preservation products processed cheese prosecco
## 1 0.002223870 0.000000000 0.022979985 0.002223870
## 2 0.012820513 0.001282051 0.051282051 0.001282051
## 3 0.001817447 0.000000000 0.008279483 0.002019386
## 4 0.002913328 0.000000000 0.016023307 0.002184996
## 5 0.001448226 0.000724113 0.020999276 0.002172339
## pudding powder ready soups red/blush wine rice roll products
## 1 0.002223870 0.0029651594 0.023721275 0.001482580 0.005930319
## 2 0.008974359 0.0064102564 0.025641026 0.038461538 0.039743590
## 3 0.001009693 0.0008077544 0.018578352 0.003029079 0.004846527
## 4 0.003641661 0.0021849964 0.008739985 0.010196650 0.010196650
## 5 0.002172339 0.0014482259 0.023895728 0.010137581 0.017378711
## rolls/buns root vegetables rubbing alcohol rum salad dressing
## 1 0.1994070 0.06300964 0.0000000000 0.003706449 0.0007412898
## 2 0.3435897 0.43076923 0.0051282051 0.007692308 0.0025641026
## 3 0.1512520 0.05149435 0.0006058158 0.002827141 0.0004038772
## 4 0.2032047 0.11070648 0.0014566642 0.005826657 0.0000000000
## 5 0.1766836 0.17668356 0.0007241130 0.007965243 0.0021723389
## salt salty snack sauces sausage seasonal products
## 1 0.007412898 0.04595997 0.005189029 0.11415864 0.011860638
## 2 0.024358974 0.07307692 0.010256410 0.24230769 0.034615385
## 3 0.007471729 0.02948304 0.003836834 0.06441842 0.013933764
## 4 0.012381646 0.03058995 0.006554989 0.08230153 0.006554989
## 5 0.016654598 0.04706734 0.007965243 0.10789283 0.013758146
## semi-finished bread shopping bags skin care sliced cheese snack products
## 1 0.01556709 0.13417346 0.003706449 0.02149741 0.005189029
## 2 0.05128205 0.12948718 0.011538462 0.09615385 0.003846154
## 3 0.01352989 0.08400646 0.002019386 0.01312601 0.002221325
## 4 0.01675164 0.07793154 0.002913328 0.02257830 0.002184996
## 5 0.01665460 0.11875453 0.005068791 0.02968863 0.004344678
## soap soda soft cheese softener sound storage medium
## 1 0.005189029 1.0000000 0.006671609 0.006671609 0.0007412898
## 2 0.003846154 0.2102564 0.079487179 0.012820513 0.0000000000
## 3 0.001615509 0.0000000 0.008683360 0.003029079 0.0000000000
## 4 0.003641661 0.0000000 0.018936635 0.007283321 0.0000000000
## 5 0.002172339 0.1462708 0.020275163 0.007241130 0.0000000000
## soups sparkling wine specialty bar specialty cheese specialty chocolate
## 1 0.005189029 0.004447739 0.04002965 0.010378058 0.03335804
## 2 0.025641026 0.006410256 0.03076923 0.033333333 0.04487179
## 3 0.003231018 0.005654281 0.02625202 0.003029079 0.02827141
## 4 0.007283321 0.003641661 0.01675164 0.005098325 0.02694829
## 5 0.010137581 0.007965243 0.02751629 0.015930485 0.03041274
## specialty fat specialty vegetables spices spread cheese sugar
## 1 0.002223870 0.0029651594 0.001482580 0.015567087 0.02742772
## 2 0.008974359 0.0051282051 0.016666667 0.026923077 0.09615385
## 3 0.003432956 0.0008077544 0.003836834 0.008279483 0.02241519
## 4 0.002184996 0.0007283321 0.004369993 0.008739985 0.04005827
## 5 0.004344678 0.0028964518 0.007965243 0.010861694 0.03982621
## sweet spreads syrup tea tidbits toilet cleaner
## 1 0.010378058 0.003706449 0.000000000 0.005930319 0.0007412898
## 2 0.023076923 0.007692308 0.014102564 0.005128205 0.0000000000
## 3 0.005654281 0.002625202 0.002423263 0.001009693 0.0006058158
## 4 0.008011653 0.001456664 0.004369993 0.003641661 0.0007283321
## 5 0.013034033 0.004344678 0.006517017 0.000724113 0.0014482259
## tropical fruit turkey UHT-milk vinegar waffles
## 1 0.08154188 0.003706449 0.04151223 0.002223870 0.04670126
## 2 0.39487179 0.034615385 0.05256410 0.020512821 0.08974359
## 3 0.06381260 0.004240711 0.03251212 0.004644588 0.02806947
## 4 0.10342316 0.005826657 0.01383831 0.007283321 0.03787327
## 5 0.11296162 0.013758146 0.03765387 0.008689356 0.03910210
## whipped/sour cream whisky white bread white wine whole milk yogurt
## 1 0.04002965 0.000000000 0.03558191 0.021497405 0.1564122 0.11415864
## 2 0.31923077 0.001282051 0.12435897 0.008974359 0.7628205 0.66666667
## 3 0.03675283 0.001211632 0.02483845 0.023828756 0.0000000 0.08663166
## 4 0.07283321 0.000000000 0.05025492 0.010196650 1.0000000 0.11070648
## 5 0.08689356 0.000724113 0.05575670 0.013758146 0.2418537 0.08472122
## zwieback
## 1 0.003706449
## 2 0.014102564
## 3 0.007067851
## 4 0.004369993
## 5 0.007965243
##
## Clustering vector:
## [1] 3 3 4 3 5 4 3 5 3 4 5 2 3 1 3 3 3 3 3 3 5 3 4 3 5 3 3 1 5 1 3 5 5 5 3 1 3
## [38] 3 5 3 1 2 3 3 1 3 3 3 3 2 3 3 5 5 1 4 3 3 3 3 5 3 4 3 1 4 3 3 4 4 3 4 4 1
## [75] 3 5 4 3 1 3 3 4 3 3 3 3 3 5 3 1 3 3 3 3 3 3 3 5 4 3 1 1 3 4 1 3 3 1 3 3 5
## [112] 3 4 3 3 4 4 5 1 5 3 3 1 5 3 2 3 3 3 3 3 4 3 1 3 5 1 3 3 3 4 5 4 4 3 3 2 1
## [149] 3 3 5 3 3 5 2 3 3 1 5 3 4 1 3 3 5 1 4 4 3 5 2 5 3 3 1 4 4 3 3 5 4 5 5 1 3
## [186] 2 3 3 4 5 3 3 3 3 1 4 3 3 3 3 3 3 3 3 4 3 5 3 3 1 1 3 5 1 4 3 3 3 3 3 1 3
## [223] 2 3 3 1 3 3 3 3 5 5 4 3 3 5 3 5 4 2 3 5 4 3 4 3 1 3 5 4 1 2 3 3 5 5 1 1 2
## [260] 4 5 3 3 3 3 3 3 2 3 3 1 3 3 4 2 2 2 4 5 3 3 4 3 3 4 4 3 3 3 5 3 5 2 5 4 3
## [297] 3 3 3 5 3 2 3 3 1 3 3 3 2 3 4 3 3 3 5 3 1 3 1 3 3 3 4 3 5 5 3 1 5 3 1 1 3
## [334] 1 3 3 1 3 3 5 4 3 3 3 1 5 3 4 4 4 3 3 3 3 3 1 3 3 3 4 4 4 3 3 4 2 5 3 3 3
## [371] 5 3 3 5 3 4 4 3 3 3 3 3 3 3 3 5 3 3 3 4 3 3 1 1 3 4 3 3 4 5 3 5 2 5 5 3 3
## [408] 3 3 3 3 5 5 1 3 5 1 3 3 5 3 1 4 3 3 3 3 3 1 4 1 1 5 3 3 3 3 3 5 1 5 3 5 1
## [445] 3 3 5 1 5 5 4 3 4 2 3 5 3 3 3 3 3 3 3 4 3 3 5 1 4 3 5 3 4 3 5 4 5 3 1 3 3
## [482] 2 1 3 3 3 5 3 5 1 3 3 1 4 3 3 3 5 5 5 3 4 3 1 3 1 1 4 5 3 3 3 3 3 1 4 3 1
## [519] 5 3 3 3 5 5 3 5 1 4 3 1 3 3 1 4 1 1 3 4 4 3 3 3 2 5 3 1 4 4 4 5 3 3 3 3 1
## [556] 3 3 5 3 3 3 2 4 2 3 1 3 3 4 3 3 5 2 3 3 3 3 3 3 4 3 3 3 3 3 4 4 2 3 3 3 3
## [593] 3 1 5 2 1 2 3 3 3 3 3 4 2 3 3 4 2 3 1 2 5 3 5 4 1 3 3 4 3 2 3 3 2 4 3 5 4
## [630] 4 5 4 4 5 3 5 3 5 3 3 3 1 5 1 1 3 3 1 5 1 1 4 3 5 5 3 3 3 2 4 3 5 3 3 3 1
## [667] 3 4 5 3 3 3 4 3 3 4 3 4 2 4 5 4 3 3 5 4 3 3 3 3 1 3 3 3 4 1 5 1 4 3 4 3 3
## [704] 1 4 3 5 4 5 5 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 1 3 4 5 4 5 3 3 3 3 3 5
## [741] 2 1 3 3 3 3 3 3 1 3 3 3 1 5 3 3 3 3 5 3 2 4 5 3 5 3 1 4 4 3 5 3 1 5 4 5 5
## [778] 5 3 5 3 2 4 1 4 3 3 3 3 5 3 4 4 3 1 2 2 4 3 3 4 5 3 4 3 3 1 3 4 4 2 4 3 3
## [815] 3 3 4 5 3 3 2 4 4 2 3 4 3 5 3 4 4 5 2 3 3 4 3 3 3 4 4 1 1 2 3 4 5 5 2 5 2
## [852] 3 5 3 2 4 3 3 3 2 2 2 3 3 2 3 1 3 1 3 3 4 3 2 4 3 3 3 3 3 3 3 3 1 3 4 3 3
## [889] 1 5 3 3 5 4 5 4 4 3 1 4 1 5 1 1 2 3 1 4 3 4 3 1 3 1 3 3 2 1 1 1 2 2 4 2 1
## [926] 1 3 4 3 1 4 4 3 3 3 3 4 3 3 3 3 3 4 3 3 5 4 1 2 5 5 3 4 3 3 3 3 4 4 3 3 5
## [963] 5 3 3 3 2 3 5 3 2 1 3 3 2 3 3 3 5 2 2 1 3 2 4 4 3 1 5 2 2 3 3 3 3 5 2 3 3
## [1000] 5 1 2 3 5 3 3 3 3 4 4 3 5 4 2 3 3 2 3 4 4 3 3 4 3 1 3 5 3 3 3 4 3 3 1 3 4
## [1037] 3 3 3 4 3 5 5 3 5 5 2 3 3 4 3 4 4 1 3 3 1 1 4 3 3 1 4 2 3 2 5 2 3 3 3 3 1
## [1074] 2 5 3 5 1 3 1 1 1 3 2 2 3 3 3 3 2 5 2 4 3 3 1 3 3 1 3 3 2 5 3 1 5 3 3 5 3
## [1111] 3 1 3 3 2 3 3 3 3 1 3 2 5 5 3 3 2 1 3 3 3 3 3 5 5 3 3 5 3 5 3 1 3 1 5 1 3
## [1148] 2 2 5 3 3 5 3 3 3 1 3 3 3 3 3 1 3 1 5 4 5 5 5 2 3 3 3 5 3 3 3 1 1 3 3 2 3
## [1185] 2 3 3 4 4 4 3 3 1 3 3 3 4 2 4 3 5 2 3 3 5 4 1 1 4 5 1 2 4 3 3 4 2 2 5 2 3
## [1222] 5 3 3 3 3 5 5 2 4 3 3 1 3 5 4 4 3 3 2 3 1 5 2 5 3 1 4 3 3 3 3 2 1 4 2 3 3
## [1259] 3 3 4 3 2 1 3 3 5 2 3 2 3 5 3 1 5 3 3 3 2 3 3 5 3 2 2 1 1 3 3 4 4 3 3 2 3
## [1296] 1 3 1 3 3 5 5 4 3 5 3 4 2 5 2 5 1 2 3 5 3 3 3 5 3 3 3 2 2 1 3 3 3 3 3 4 2
## [1333] 4 1 1 1 3 2 5 5 3 3 3 4 3 2 4 4 3 1 3 2 3 2 3 3 3 5 4 3 5 3 1 1 3 5 3 3 3
## [1370] 3 3 5 3 4 2 3 3 1 3 3 1 4 3 3 4 5 3 5 1 3 3 2 2 3 3 3 1 3 1 1 3 3 3 3 3 5
## [1407] 4 3 1 1 4 3 3 5 3 3 3 5 3 1 1 3 3 1 3 4 4 3 3 3 4 4 3 4 1 1 3 3 1 3 3 3 4
## [1444] 4 5 4 3 3 3 3 3 3 3 1 3 1 3 3 3 4 1 3 3 3 3 3 3 3 2 3 3 4 3 5 3 1 4 1 5 3
## [1481] 4 3 4 3 1 3 5 3 5 5 3 3 2 3 2 3 5 3 3 1 4 3 3 3 3 3 5 5 1 3 1 5 3 5 4 3 2
## [1518] 3 4 3 3 3 4 3 1 5 3 3 1 3 3 3 3 5 4 4 3 4 5 3 5 5 5 5 3 3 3 3 4 3 5 4 3 3
## [1555] 5 3 3 2 5 3 3 4 3 3 3 4 2 1 3 3 3 3 3 3 3 5 3 2 3 3 3 3 3 3 3 3 3 3 1 2 3
## [1592] 2 3 5 3 3 3 1 3 5 3 3 5 3 1 3 2 4 1 3 3 3 2 3 3 3 4 1 3 3 5 5 5 3 1 3 3 1
## [1629] 4 3 1 3 3 3 3 3 3 1 5 3 4 3 3 3 3 3 3 3 3 4 5 4 3 2 3 3 3 5 4 3 5 5 4 4 4
## [1666] 5 4 2 1 1 4 4 3 3 3 5 3 5 1 2 3 5 2 3 3 3 2 4 1 1 3 1 4 3 5 5 1 5 3 3 3 1
## [1703] 3 5 4 5 5 1 3 4 2 3 1 3 3 3 2 3 5 3 4 2 3 3 2 4 4 3 3 1 3 3 3 3 3 5 1 3 4
## [1740] 4 3 3 5 1 1 3 3 3 3 3 4 3 3 2 1 5 3 5 3 1 3 3 1 3 4 4 5 3 3 5 3 1 2 2 5 3
## [1777] 1 3 3 5 4 3 3 1 3 4 4 3 3 4 4 1 1 4 4 3 4 2 3 3 3 3 5 3 3 2 3 1 3 5 3 3 1
## [1814] 3 2 3 3 1 4 3 3 3 3 4 1 4 2 3 3 4 4 3 3 1 3 4 5 3 3 3 5 3 5 3 3 2 2 3 3 4
## [1851] 1 3 4 2 3 3 4 1 3 3 3 3 3 5 3 3 3 4 4 1 4 3 4 4 5 3 3 3 2 1 1 2 5 3 5 3 4
## [1888] 3 5 1 3 4 5 1 3 5 1 4 4 1 3 3 5 4 4 2 3 3 3 3 3 3 2 2 3 1 3 2 1 4 2 2 5 5
## [1925] 3 3 4 3 1 3 3 3 2 4 1 1 1 5 4 3 5 2 1 2 3 5 3 4 5 4 3 4 4 3 3 3 3 3 3 3 3
## [1962] 3 3 3 3 2 3 3 4 3 3 1 1 3 1 3 3 1 3 3 1 3 1 3 3 3 3 5 4 3 2 1 3 3 2 3 4 1
## [1999] 3 1 3 5 5 1 2 3 5 5 4 3 5 4 3 5 5 2 3 2 3 1 5 4 1 3 4 1 5 3 1 3 3 3 3 3 5
## [2036] 4 3 3 3 4 4 3 4 3 3 3 4 4 3 3 3 2 3 5 2 5 3 3 3 5 4 1 1 5 3 3 3 4 3 3 1 4
## [2073] 3 1 3 1 4 3 3 3 1 3 4 1 1 1 3 4 2 2 3 3 3 4 5 1 3 1 5 4 4 3 3 1 3 5 1 5 3
## [2110] 3 1 3 3 3 3 1 3 4 3 3 5 2 3 2 3 3 3 1 1 3 4 3 5 4 5 5 3 5 5 3 1 3 3 4 3 3
## [2147] 1 4 4 1 1 3 3 3 3 3 1 4 3 3 5 5 3 3 3 2 3 3 5 2 5 4 4 3 3 3 5 5 3 1 1 3 1
## [2184] 5 3 5 3 5 4 3 1 5 3 3 4 3 1 3 2 3 3 3 3 3 3 1 4 3 1 3 3 5 5 2 3 4 4 5 3 1
## [2221] 1 3 5 1 1 4 1 4 5 3 4 3 5 1 1 3 1 3 3 1 4 3 5 1 1 4 3 3 1 3 3 3 4 5 3 5 4
## [2258] 3 4 3 1 5 3 4 3 3 3 1 3 3 5 3 3 5 3 3 5 3 3 1 3 3 3 3 1 3 1 1 5 4 3 5 3 3
## [2295] 3 3 3 3 3 4 5 3 4 3 3 4 4 4 1 5 3 3 4 5 4 5 1 3 3 5 5 3 5 2 3 3 3 1 4 4 4
## [2332] 3 4 3 5 4 5 3 3 3 3 1 3 2 4 2 3 3 2 1 3 3 3 5 3 3 5 1 3 3 3 3 3 3 5 4 3 3
## [2369] 3 3 4 4 5 3 3 3 5 3 3 3 1 3 3 1 3 4 3 5 3 4 2 3 3 4 3 1 3 3 3 3 1 4 1 1 3
## [2406] 1 3 3 5 4 3 4 3 3 5 3 4 5 3 3 3 3 3 3 3 1 3 5 3 1 4 5 4 3 5 2 3 3 3 3 3 3
## [2443] 4 1 2 3 3 3 1 4 3 3 4 3 2 4 3 1 3 3 3 2 1 1 3 3 4 2 3 2 1 3 5 1 3 1 3 4 5
## [2480] 1 3 3 3 3 3 3 5 3 3 4 3 3 5 3 3 3 5 3 5 3 1 2 3 3 4 3 3 2 3 3 3 3 3 2 3 3
## [2517] 2 3 1 5 1 1 3 3 3 4 2 1 5 3 4 3 2 3 3 2 3 5 3 4 1 3 2 5 4 5 3 3 3 5 2 3 1
## [2554] 2 4 4 3 3 1 1 2 3 4 3 3 2 1 4 3 3 3 1 3 2 1 3 1 4 3 3 5 3 4 3 5 3 1 2 5 5
## [2591] 3 3 3 3 4 3 2 3 5 2 3 3 3 4 3 3 3 3 4 3 4 5 3 1 4 1 1 3 3 4 3 4 3 5 4 3 3
## [2628] 3 5 5 3 2 4 3 4 4 5 4 3 3 1 5 3 3 1 1 4 3 3 3 3 5 3 3 3 1 3 5 3 3 3 2 5 1
## [2665] 4 4 3 5 3 3 1 1 3 5 4 3 3 3 3 2 3 5 1 2 3 1 3 3 1 3 5 1 3 3 5 1 3 3 3 5 3
## [2702] 3 2 3 2 3 3 5 3 2 3 3 3 1 1 4 4 1 1 3 3 1 4 4 3 4 3 5 1 3 5 1 5 5 3 3 5 3
## [2739] 4 3 4 4 3 5 2 3 3 3 3 2 3 3 5 3 3 5 3 3 1 3 1 4 5 5 3 2 3 3 1 3 3 3 4 3 3
## [2776] 5 3 5 4 3 2 2 3 3 3 1 3 3 1 4 3 3 3 3 3 3 1 3 3 1 3 3 5 1 1 3 3 3 1 1 3 3
## [2813] 3 3 4 5 3 3 3 4 3 3 3 3 1 5 3 3 3 1 4 3 3 3 3 4 4 3 4 3 1 3 2 3 3 3 3 1 4
## [2850] 3 4 3 3 3 3 3 5 3 3 3 3 3 5 2 3 4 3 3 1 3 3 3 3 3 4 3 3 3 3 3 2 1 4 1 4 4
## [2887] 4 4 1 3 3 3 5 3 3 3 3 3 5 5 3 1 3 4 1 3 1 1 1 2 5 1 3 3 3 3 3 4 3 3 3 3 3
## [2924] 3 3 3 3 2 1 3 4 3 3 3 3 3 3 4 2 1 3 3 5 1 3 3 3 2 3 3 5 1 4 2 5 3 2 3 3 1
## [2961] 5 4 5 3 4 3 1 4 2 3 2 5 4 2 4 3 3 3 3 1 3 5 2 3 2 3 3 2 3 5 1 5 3 3 3 2 4
## [2998] 3 4 4 3 1 2 3 5 2 3 3 5 2 4 1 5 3 3 2 5 2 5 3 4 4 5 3 3 1 5 5 3 3 4 2 5 3
## [3035] 3 5 3 3 4 3 5 2 1 4 1 2 3 3 2 1 3 5 4 5 4 5 5 3 5 3 3 1 3 1 3 1 5 3 3 4 1
## [3072] 4 3 4 3 3 1 1 4 2 3 5 3 5 1 1 2 3 3 3 2 3 3 3 3 3 1 3 3 1 3 3 1 5 3 3 3 1
## [3109] 3 3 3 1 2 1 3 3 3 3 5 1 1 3 3 5 3 3 3 3 3 3 1 3 5 5 1 5 3 3 3 3 3 1 3 3 3
## [3146] 4 5 4 2 2 5 3 5 5 3 3 2 3 4 3 3 5 3 3 3 3 3 2 4 5 3 3 5 4 3 2 3 2 4 1 3 3
## [3183] 2 3 1 4 3 3 3 5 3 3 2 3 5 4 2 4 5 3 3 3 3 5 5 1 5 3 2 5 3 3 3 5 5 5 1 5 3
## [3220] 5 2 2 2 3 1 3 3 1 3 3 3 3 3 5 3 3 3 1 3 3 4 2 4 2 1 4 3 3 5 3 3 3 3 3 3 2
## [3257] 1 1 1 5 2 3 5 1 3 5 3 3 5 3 2 1 3 3 5 1 1 3 1 3 1 4 4 3 5 5 3 3 4 3 3 5 1
## [3294] 3 1 5 3 5 3 4 1 3 4 3 3 2 3 2 3 3 3 3 3 3 3 4 3 5 5 3 1 3 3 2 3 1 3 3 3 2
## [3331] 5 4 3 3 2 5 1 5 5 4 3 3 1 3 5 3 3 3 3 5 3 3 3 3 4 3 3 5 1 3 3 3 1 4 3 3 1
## [3368] 3 3 3 1 4 3 3 4 3 3 3 1 3 2 1 5 5 3 3 3 1 1 2 4 4 1 1 1 5 3 3 3 3 3 1 1 4
## [3405] 4 4 3 3 3 4 4 1 3 3 4 3 3 5 3 5 3 4 3 5 3 3 3 5 4 3 1 1 3 3 4 1 4 3 3 4 3
## [3442] 2 1 3 3 1 3 1 4 3 5 1 3 4 1 3 3 3 3 5 3 3 1 3 3 2 3 4 4 1 3 3 1 3 2 1 1 1
## [3479] 3 3 3 1 3 3 3 3 4 3 3 2 4 3 5 1 2 4 3 3 3 2 2 1 5 1 3 4 3 2 4 3 3 3 3 3 5
## [3516] 1 1 3 4 1 3 3 3 1 3 3 5 3 3 3 3 4 3 3 3 3 3 5 3 3 4 3 3 4 3 4 4 1 1 3 5 3
## [3553] 3 3 3 2 4 2 3 5 3 5 3 3 3 4 3 4 1 3 3 3 3 3 3 4 5 3 3 3 1 1 3 3 3 4 3 3 3
## [3590] 1 2 3 4 5 3 4 3 3 3 1 4 3 3 3 3 3 3 5 5 1 2 3 3 4 4 3 1 3 1 3 3 2 1 3 5 3
## [3627] 1 5 3 5 5 2 1 4 3 3 3 1 3 4 2 4 1 4 3 3 3 3 3 3 3 3 1 3 3 2 3 1 1 3 3 5 3
## [3664] 3 3 2 1 3 2 3 3 4 5 2 3 5 3 5 5 3 3 3 3 3 4 3 2 5 3 3 2 4 4 4 1 5 3 3 3 3
## [3701] 3 5 1 1 3 4 3 5 3 4 1 1 3 3 3 2 3 5 3 5 3 3 3 3 5 3 4 1 3 2 3 3 3 1 1 3 3
## [3738] 4 4 3 4 1 3 4 3 3 3 3 3 1 2 5 3 1 5 3 3 3 5 3 4 5 3 3 3 3 3 4 3 3 3 3 3 3
## [3775] 3 3 3 5 3 3 5 3 3 3 3 3 3 3 3 4 5 3 3 3 3 3 4 3 3 4 5 3 3 3 3 3 3 1 3 3 4
## [3812] 3 3 5 5 3 3 5 2 3 5 4 1 3 3 3 3 5 3 3 1 3 5 1 3 3 3 4 1 4 5 5 3 3 2 2 3 3
## [3849] 5 5 3 5 3 5 5 4 3 1 3 3 3 3 3 1 2 3 1 1 3 3 1 3 3 3 1 4 3 4 3 3 1 5 3 2 2
## [3886] 3 4 4 1 3 2 5 3 3 2 2 3 1 4 3 3 3 2 4 5 3 5 5 3 3 5 4 3 4 4 4 3 4 3 3 3 3
## [3923] 3 5 1 3 3 1 3 5 1 3 1 5 4 4 3 2 3 2 3 2 3 3 3 3 3 5 4 5 4 5 5 5 2 5 3 3 3
## [3960] 1 3 1 4 4 3 1 3 2 3 2 2 2 4 5 3 3 5 5 4 1 3 3 1 4 2 1 3 3 4 3 3 2 3 5 3 3
## [3997] 5 3 3 3 2 3 3 3 4 3 3 3 3 1 4 4 3 1 5 4 2 3 1 5 3 3 3 3 1 1 3 1 4 3 3 5 2
## [4034] 2 1 2 4 5 3 1 3 5 3 1 5 3 4 4 5 4 3 2 5 2 3 2 1 4 2 2 4 3 3 2 3 5 3 5 3 3
## [4071] 3 2 4 2 3 3 4 3 1 5 5 1 1 2 3 3 1 5 4 5 4 1 1 3 3 4 2 3 4 1 4 4 4 4 2 3 2
## [4108] 5 3 1 1 1 4 3 3 1 3 3 2 2 1 4 3 4 3 5 2 4 1 5 3 4 4 3 5 3 5 1 3 4 3 3 3 3
## [4145] 2 3 3 3 3 3 5 3 1 3 3 3 5 3 2 5 4 1 5 5 4 5 2 2 3 3 1 1 3 4 4 3 3 3 1 2 1
## [4182] 1 2 5 3 5 3 1 1 3 2 3 5 3 3 3 3 3 3 3 3 3 1 3 2 5 3 3 5 3 4 3 3 2 3 3 2 3
## [4219] 5 3 3 5 5 3 3 4 4 3 5 5 2 5 5 1 2 4 3 4 1 3 3 1 3 3 4 3 2 2 1 5 3 1 3 3 3
## [4256] 5 4 5 3 1 4 3 1 3 3 3 3 3 3 4 3 5 3 4 4 3 4 3 3 5 3 1 1 3 3 3 4 2 5 4 4 3
## [4293] 3 4 5 3 4 3 3 3 4 5 2 1 5 3 2 3 3 3 1 4 2 2 4 3 5 4 5 3 4 3 3 5 4 1 4 5 5
## [4330] 2 3 5 2 1 3 2 4 4 5 4 3 3 2 1 5 2 4 3 4 1 1 3 3 5 2 3 5 5 3 5 4 3 5 3 3 3
## [4367] 2 4 5 5 1 5 3 4 2 5 3 5 4 3 2 4 4 1 3 5 3 3 2 1 2 3 4 3 2 5 5 3 5 2 3 3 3
## [4404] 3 2 4 3 3 3 2 1 5 3 3 2 2 2 3 4 2 5 3 4 3 3 3 4 3 2 3 2 1 4 3 3 3 3 3 3 4
## [4441] 3 4 1 5 3 2 3 2 2 2 5 3 3 3 2 3 2 3 5 5 5 3 5 3 3 3 3 4 3 3 1 2 3 3 3 5 3
## [4478] 3 4 5 3 3 4 3 4 3 4 5 3 3 3 2 3 5 3 3 3 3 2 4 3 1 3 5 2 3 1 3 1 3 4 3 4 5
## [4515] 3 5 2 1 2 3 1 2 2 3 3 4 3 3 5 1 2 1 3 3 3 1 4 3 2 2 1 3 5 5 3 5 3 1 2 5 1
## [4552] 3 3 5 1 5 3 5 1 3 3 3 3 3 1 2 3 3 2 3 2 3 3 5 5 3 4 3 4 3 1 3 3 3 1 1 3 1
## [4589] 3 3 3 5 2 3 3 3 3 3 1 3 3 3 3 3 3 1 1 3 3 2 1 1 5 4 1 4 3 3 1 1 3 4 4 1 3
## [4626] 5 2 3 2 3 3 3 3 3 2 4 3 3 4 1 3 3 2 1 3 3 4 3 3 3 3 2 1 1 3 4 3 3 3 1 3 3
## [4663] 3 1 5 5 3 3 3 3 3 3 5 4 3 3 5 4 1 5 2 2 3 3 3 3 2 3 3 3 1 3 4 1 5 4 1 3 3
## [4700] 4 3 3 3 4 3 4 5 3 3 3 3 5 3 5 3 4 3 4 4 3 5 2 3 1 5 4 3 3 4 1 5 5 3 3 3 1
## [4737] 3 3 4 4 5 5 3 3 4 2 3 3 1 3 3 3 3 3 3 3 3 3 1 5 4 3 3 3 1 1 4 3 3 1 3 1 5
## [4774] 2 1 3 1 3 3 4 5 4 3 5 3 3 4 3 3 3 3 3 3 3 4 1 3 3 1 3 4 3 1 3 3 3 3 3 3 3
## [4811] 3 3 3 1 3 4 3 3 3 1 5 3 1 3 3 3 3 1 4 1 3 3 3 4 3 3 4 3 5 3 5 2 4 3 3 3 5
## [4848] 2 1 3 3 3 3 3 4 4 3 3 3 3 3 3 4 3 3 5 1 5 3 3 3 4 3 1 1 3 3 1 3 3 3 3 3 3
## [4885] 4 3 3 4 3 3 4 1 5 3 3 3 5 1 4 3 4 1 1 4 3 3 3 3 1 3 1 3 1 3 4 4 5 3 3 3 3
## [4922] 3 4 5 1 3 3 3 3 3 3 1 3 5 3 1 1 3 3 5 4 3 3 5 5 3 3 4 5 4 4 1 1 3 3 3 4 3
## [4959] 1 2 1 5 1 1 3 3 3 5 3 5 3 3 3 3 3 2 3 3 4 3 1 1 3 5 1 1 1 3 3 5 2 4 3 2 3
## [4996] 5 5 3 3 3 3 2 4 3 5 3 4 3 4 3 1 4 1 3 3 3 3 3 5 3 3 1 3 3 4 5 3 5 1 1 4 3
## [5033] 3 5 3 3 1 3 3 3 3 3 3 3 4 1 3 4 2 5 4 3 3 3 1 3 1 3 3 3 4 3 2 1 1 4 2 3 1
## [5070] 5 4 4 1 4 3 3 3 2 3 3 4 3 4 3 3 3 1 4 3 5 3 3 3 3 3 1 3 4 1 1 4 3 4 3 3 3
## [5107] 2 1 4 3 5 1 3 3 5 3 3 3 5 3 3 3 5 3 3 3 1 2 3 4 4 3 5 2 3 3 3 3 3 3 3 3 3
## [5144] 1 3 3 1 3 3 3 3 3 3 3 3 3 3 3 4 3 3 4 5 2 5 3 5 3 5 3 3 5 5 3 5 3 3 4 1 3
## [5181] 3 3 1 3 3 3 1 3 5 3 3 1 3 4 5 5 3 1 1 5 1 3 3 3 5 5 3 3 4 3 4 3 3 3 1 2 3
## [5218] 1 3 5 1 1 3 3 3 4 1 3 5 3 3 3 3 3 3 3 5 3 5 1 2 2 2 5 5 5 3 1 3 3 3 3 3 5
## [5255] 3 3 1 4 3 3 3 4 3 5 3 3 1 1 2 5 4 3 3 4 3 1 3 3 3 3 4 1 1 4 5 3 2 3 3 3 3
## [5292] 1 3 1 5 5 4 5 3 4 3 3 3 3 1 2 3 3 4 3 4 1 2 3 1 2 3 3 3 1 3 4 2 3 4 3 5 3
## [5329] 3 4 1 3 3 3 3 5 3 5 4 4 3 3 4 1 3 3 3 5 3 3 3 3 1 3 3 3 3 1 5 2 3 1 3 4 2
## [5366] 4 3 3 1 3 3 3 1 5 4 3 3 3 4 3 3 3 3 5 4 4 3 3 1 3 3 5 3 1 3 3 5 4 3 3 3 2
## [5403] 3 1 3 1 1 5 1 3 1 3 3 5 3 3 3 2 1 3 3 1 2 2 2 3 5 3 3 4 1 1 3 4 4 4 3 3 3
## [5440] 5 4 3 1 4 2 3 4 3 4 3 4 4 3 3 3 5 3 3 3 4 3 5 3 5 1 3 4 4 3 5 3 2 3 2 3 3
## [5477] 2 4 5 3 3 2 2 5 3 5 3 3 4 3 2 4 3 5 1 3 3 3 4 2 5 3 1 3 2 3 1 3 4 4 4 4 4
## [5514] 3 5 3 5 5 3 4 3 1 3 1 5 3 2 5 5 2 3 3 5 1 5 1 4 5 3 4 1 2 3 3 3 3 3 5 2 5
## [5551] 2 5 2 3 2 3 3 4 2 1 3 3 3 3 1 3 3 3 4 4 3 1 4 3 3 3 2 3 4 1 3 1 2 1 5 1 3
## [5588] 1 3 3 3 1 3 4 5 5 3 1 3 3 3 2 3 3 4 3 3 3 3 3 2 1 4 5 5 3 3 3 4 1 5 5 5 5
## [5625] 5 3 4 3 1 3 4 3 3 2 2 4 4 3 4 4 5 2 4 5 5 5 5 5 3 2 5 1 3 3 3 1 5 3 3 5 5
## [5662] 1 5 3 4 3 3 5 5 5 1 2 5 3 4 1 5 2 4 1 3 1 5 5 2 4 1 2 5 3 4 2 3 5 1 3 4 4
## [5699] 2 3 1 5 1 5 5 3 2 3 5 4 1 3 3 5 1 3 3 5 4 4 2 3 5 4 5 1 1 4 1 4 3 2 2 2 4
## [5736] 5 2 3 5 4 3 3 5 3 4 1 3 1 3 2 3 2 3 2 1 3 4 3 1 3 3 1 4 2 3 2 3 5 3 3 5 1
## [5773] 3 5 5 3 3 3 3 5 2 5 3 4 2 5 5 5 5 3 3 3 3 1 4 5 3 1 5 1 3 5 5 2 2 5 5 5 1
## [5810] 2 5 3 1 3 3 4 5 5 3 1 1 2 3 1 5 3 3 3 1 3 4 4 3 5 1 3 3 1 3 3 3 3 3 3 3 3
## [5847] 3 3 4 3 3 1 3 5 1 3 5 3 3 2 3 3 4 1 3 4 1 5 1 5 3 3 3 4 3 3 3 5 3 1 3 1 3
## [5884] 3 1 5 4 5 3 3 5 5 3 3 3 5 5 5 3 2 3 5 4 5 2 3 3 4 4 3 5 5 5 3 3 5 3 1 1 3
## [5921] 5 5 5 4 3 1 4 3 1 1 1 5 3 1 1 1 3 3 2 2 1 3 3 3 3 4 1 3 3 3 5 2 4 5 3 3 5
## [5958] 4 3 3 3 5 3 1 3 4 2 4 4 5 4 5 3 3 5 4 3 4 4 5 3 4 4 3 3 1 5 3 1 1 1 1 3 3
## [5995] 4 3 5 3 3 3 4 3 3 3 4 3 4 4 3 3 3 4 3 3 1 3 5 3 1 3 1 3 3 1 3 3 5 3 1 1 3
## [6032] 3 3 3 1 5 5 1 3 3 3 3 3 4 3 3 3 3 3 2 4 4 3 3 4 3 3 3 3 3 3 1 4 1 3 1 3 5
## [6069] 1 4 5 5 3 3 3 1 3 4 3 3 3 3 4 3 3 1 3 3 4 3 4 1 5 1 4 1 5 1 3 2 1 3 3 4 3
## [6106] 3 5 1 3 4 4 3 3 1 3 3 3 1 1 4 5 3 1 1 3 1 3 3 1 3 3 4 3 3 5 3 1 3 1 3 1 3
## [6143] 3 3 5 3 3 3 3 4 5 3 2 3 1 3 3 4 3 3 5 5 1 3 3 1 3 4 3 2 1 1 3 3 3 5 3 2 3
## [6180] 3 1 3 3 3 1 3 3 3 3 2 4 3 3 1 3 1 1 3 4 2 2 5 1 3 1 3 3 3 5 3 2 3 5 1 4 4
## [6217] 3 3 3 3 4 3 3 2 5 3 3 2 3 3 3 3 3 1 1 5 3 3 1 3 5 3 1 4 3 1 1 3 3 3 4 3 4
## [6254] 3 4 5 3 4 4 3 5 1 5 3 2 5 3 3 3 3 4 3 1 5 3 4 3 3 3 5 3 2 1 3 4 3 3 5 4 2
## [6291] 3 3 1 1 3 3 3 3 5 3 3 4 1 1 3 3 4 3 1 1 5 2 4 1 4 3 1 3 1 5 1 3 1 2 5 3 4
## [6328] 5 5 3 3 3 1 3 5 2 5 1 5 5 3 3 3 5 1 3 3 5 3 1 3 1 5 3 3 4 3 1 3 3 5 3 3 3
## [6365] 3 3 3 3 5 5 1 5 3 3 5 1 1 3 3 3 1 3 3 1 3 5 4 4 3 3 3 5 3 1 5 4 5 3 5 3 3
## [6402] 1 4 3 3 3 3 3 4 3 3 3 1 3 1 3 3 1 3 4 3 3 1 3 3 3 3 1 3 1 1 5 5 3 3 5 4 3
## [6439] 5 3 3 3 3 3 3 5 1 3 1 1 3 3 3 3 3 3 3 4 3 1 1 1 3 3 3 3 3 3 4 3 2 3 3 5 5
## [6476] 1 3 3 2 3 3 4 2 3 3 3 3 3 4 5 3 4 3 3 3 5 3 3 1 5 1 3 3 1 3 5 3 3 4 4 5 2
## [6513] 3 5 3 2 3 3 3 3 3 3 3 5 3 3 3 4 3 4 4 5 3 3 3 3 3 1 3 3 4 4 3 3 3 3 5 5 3
## [6550] 3 3 4 4 3 3 3 5 2 4 3 1 3 1 5 3 3 5 1 3 1 1 2 4 4 3 3 1 3 5 1 3 3 3 3 3 3
## [6587] 4 1 3 3 2 3 3 1 1 1 3 3 4 3 4 3 5 1 1 1 3 5 1 3 3 3 5 3 1 3 3 2 3 5 3 3 5
## [6624] 3 5 3 3 3 2 2 1 1 1 2 3 5 3 3 3 3 2 3 3 4 3 3 2 3 3 3 3 1 3 3 4 3 3 3 3 5
## [6661] 3 3 3 3 3 5 3 3 3 3 5 3 4 3 3 3 3 4 4 2 2 4 1 3 1 3 4 2 2 1 3 3 4 4 5 3 3
## [6698] 4 4 2 3 1 4 5 4 1 4 4 2 3 2 4 4 3 3 5 5 4 3 3 1 2 4 3 1 3 1 1 3 3 5 4 3 4
## [6735] 3 1 1 3 5 5 5 3 3 4 1 4 5 5 1 1 3 5 5 2 3 2 4 4 3 4 4 3 5 5 3 3 1 4 4 5 3
## [6772] 4 3 5 3 5 1 3 2 4 2 4 3 5 2 3 4 2 5 3 5 4 3 4 4 1 1 3 2 3 3 5 2 1 2 1 1 1
## [6809] 2 5 2 2 3 3 3 3 5 3 5 3 5 4 5 3 2 5 4 5 2 5 3 1 2 3 4 3 4 3 3 3 2 3 3 1 5
## [6846] 1 1 3 3 5 3 2 3 3 5 4 1 3 5 1 4 3 2 2 5 3 3 3 3 3 2 3 3 3 3 1 3 5 3 3 1 5
## [6883] 3 5 3 3 5 3 3 3 1 5 3 3 3 1 5 1 3 3 1 3 5 3 4 1 3 1 3 3 3 1 1 3 3 3 5 3 3
## [6920] 3 5 3 1 3 1 4 3 4 3 3 3 3 3 5 3 3 2 4 3 3 3 2 3 3 3 1 5 1 3 5 3 2 1 4 3 3
## [6957] 3 3 3 1 3 5 3 5 3 1 3 1 3 3 4 1 4 3 2 3 4 4 3 3 1 3 3 1 4 3 3 3 1 5 3 3 3
## [6994] 3 4 5 5 3 1 1 3 1 3 3 3 1 5 3 3 3 4 1 5 5 3 1 4 3 3 5 3 1 3 4 3 1 3 4 3 4
## [7031] 3 5 3 3 3 5 3 3 5 1 3 3 3 3 1 4 1 3 3 1 3 4 3 3 4 3 3 3 1 4 5 3 3 3 3 4 3
## [7068] 5 2 3 3 3 3 3 3 3 2 3 3 1 3 4 4 4 2 2 3 3 3 3 1 3 1 2 5 3 3 2 1 3 3 1 1 3
## [7105] 3 1 5 3 4 3 3 3 1 5 3 5 4 4 4 3 4 3 5 3 3 3 3 3 3 4 3 2 2 5 5 3 4 4 3 4 3
## [7142] 3 4 5 2 5 3 4 3 1 3 3 3 3 4 3 3 3 5 5 3 4 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 5
## [7179] 1 3 4 4 5 4 4 3 3 4 3 5 3 3 3 4 3 4 3 3 3 3 2 1 4 3 3 4 3 3 1 5 5 3 5 3 3
## [7216] 3 4 1 5 3 4 3 3 3 3 2 1 4 1 3 3 5 3 1 3 5 3 3 3 3 3 4 3 3 3 3 3 1 2 5 3 4
## [7253] 5 1 3 4 4 2 4 4 5 5 3 3 3 3 1 3 3 2 1 3 4 3 3 3 3 3 4 3 3 3 5 4 2 3 4 4 3
## [7290] 1 4 3 3 1 3 3 5 3 5 3 5 3 5 2 3 2 3 3 3 3 1 3 4 3 3 1 3 5 5 3 1 3 3 1 2 3
## [7327] 1 3 3 3 3 3 4 3 5 3 3 4 4 3 3 4 1 1 3 3 1 3 3 3 5 3 3 4 4 3 4 3 3 3 3 4 3
## [7364] 4 3 5 5 4 3 3 3 3 3 3 3 4 3 3 3 3 1 3 4 3 4 1 3 3 3 5 3 3 4 3 3 5 4 3 3 3
## [7401] 1 3 3 3 3 3 3 5 3 3 3 3 3 1 3 3 3 2 4 3 3 3 3 3 3 2 3 4 3 3 3 3 3 1 5 3 4
## [7438] 3 4 3 3 3 4 3 2 3 3 4 1 3 3 1 5 1 5 4 4 4 3 3 3 5 4 4 1 3 3 3 5 5 4 1 2 2
## [7475] 3 3 3 1 3 1 1 1 4 2 3 3 4 3 3 1 3 2 2 3 5 3 3 3 1 5 5 3 1 3 3 3 3 4 2 2 3
## [7512] 3 3 5 3 5 5 1 4 4 1 3 3 5 3 3 4 3 1 1 1 4 3 5 3 3 4 3 4 3 5 5 2 3 5 3 3 5
## [7549] 3 2 3 4 4 2 5 3 3 5 5 1 3 3 3 3 3 5 3 5 3 1 5 4 3 5 5 4 3 1 3 3 3 2 3 3 1
## [7586] 3 3 3 1 3 1 4 5 3 2 3 4 5 5 3 3 3 3 4 3 5 5 4 3 3 4 3 5 3 3 3 3 3 3 3 3 3
## [7623] 3 3 1 2 3 3 3 3 3 1 1 4 1 1 3 3 3 2 2 3 4 3 3 5 3 4 3 3 1 4 4 3 3 4 3 3 3
## [7660] 5 3 5 3 3 3 4 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 5 5 3 3 3 1 5 1 4 3 1 3 3 3 3
## [7697] 4 5 4 3 4 5 1 3 2 1 3 3 3 2 3 4 3 3 3 1 4 5 5 3 3 4 3 4 3 5 5 3 1 4 3 3 4
## [7734] 3 3 1 3 3 1 3 3 2 5 3 1 3 5 4 3 3 3 5 3 4 5 3 5 3 4 5 3 3 4 5 5 2 3 5 1 4
## [7771] 4 4 3 3 3 4 5 1 3 1 4 4 5 3 1 5 3 1 3 3 1 4 3 3 3 3 4 4 1 3 4 3 3 2 3 5 5
## [7808] 5 3 5 4 2 4 1 3 1 2 1 1 3 3 3 3 4 4 2 4 2 1 4 3 1 4 3 5 3 4 5 3 3 3 4 5 1
## [7845] 3 4 2 1 3 5 3 3 3 4 4 4 2 3 2 3 3 3 3 5 4 5 3 3 4 4 3 3 3 5 3 4 3 1 4 5 3
## [7882] 3 4 3 5 3 3 3 4 3 4 3 4 3 3 3 1 4 4 3 3 3 4 3 4 3 1 3 3 3 3 3 3 3 3 4 3 4
## [7919] 3 4 3 3 4 5 4 3 3 1 3 4 3 1 3 3 1 5 1 5 3 3 3 3 1 2 3 5 3 3 4 3 4 3 3 3 3
## [7956] 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 1 3 1 3 3 4 1 5 1 2 3 3 3 3 3 3 5 4 2 3 3
## [7993] 2 3 1 3 2 1 3 4 1 3 3 1 3 3 3 3 5 3 3 3 1 3 4 5 3 2 5 3 4 3 3 3 3 4 4 4 3
## [8030] 3 1 3 3 3 3 3 5 3 3 3 5 3 3 2 1 3 4 4 1 1 4 1 3 3 5 5 4 3 3 3 3 3 4 3 3 5
## [8067] 4 5 1 3 4 3 3 3 3 3 3 3 4 3 3 3 3 2 4 3 3 3 4 3 4 1 2 3 3 3 4 4 3 3 3 4 3
## [8104] 5 3 3 2 4 3 1 3 3 3 1 5 3 5 3 2 3 3 3 3 3 1 5 3 3 5 3 3 1 3 3 1 3 3 3 5 3
## [8141] 4 3 3 5 4 3 5 3 5 3 1 3 3 3 3 3 3 5 2 3 3 5 4 3 3 3 3 3 1 4 3 3 3 5 3 5 3
## [8178] 3 3 3 3 1 3 5 4 5 1 5 1 1 3 3 3 3 1 4 4 1 1 3 3 3 4 3 3 1 3 1 3 5 3 3 3 1
## [8215] 1 3 4 3 3 3 3 3 5 3 1 1 3 3 3 4 2 4 5 5 5 4 3 3 5 2 3 3 2 3 3 3 1 4 1 3 4
## [8252] 3 1 3 2 3 4 3 3 3 1 3 1 4 4 3 3 5 3 3 3 3 5 3 1 1 3 2 3 3 5 1 3 3 2 4 5 5
## [8289] 4 4 3 3 3 2 5 3 5 3 3 3 3 2 1 3 4 5 3 3 4 4 3 3 3 5 3 3 1 2 3 4 1 3 3 4 3
## [8326] 3 5 3 3 4 3 5 3 3 3 3 3 3 1 4 3 3 1 3 5 3 3 4 4 3 3 1 5 4 3 2 1 5 3 4 3 4
## [8363] 3 3 3 4 3 2 3 3 2 3 3 3 3 1 3 3 1 5 3 2 1 3 4 3 4 5 3 3 5 3 3 3 2 1 3 2 4
## [8400] 3 3 5 3 1 4 3 4 3 1 1 3 3 2 3 5 3 3 3 1 1 3 4 3 3 4 1 3 1 1 3 3 5 3 1 3 1
## [8437] 5 3 3 3 3 1 1 5 4 3 4 1 3 3 4 3 1 4 3 3 3 3 1 5 3 3 1 1 3 5 3 1 3 1 5 3 5
## [8474] 5 3 1 3 4 4 3 3 4 1 3 3 1 3 3 3 2 3 3 3 3 3 1 1 5 1 1 3 3 1 3 3 1 3 4 2 3
## [8511] 3 3 3 4 5 3 1 3 4 3 3 1 3 3 3 3 4 1 2 4 3 5 2 3 2 1 4 5 1 4 1 3 5 3 4 3 3
## [8548] 3 5 3 1 3 3 2 3 3 3 3 3 2 4 3 1 5 5 3 4 3 3 3 3 3 3 5 3 3 3 3 3 1 1 3 3 1
## [8585] 2 4 3 3 3 4 2 4 4 3 3 3 4 4 3 2 3 3 5 5 3 3 3 3 3 5 5 3 3 3 3 2 3 3 3 2 3
## [8622] 3 3 1 3 3 4 4 5 3 1 3 1 1 3 3 3 5 3 4 3 4 2 3 5 3 3 3 4 3 3 3 3 3 3 5 3 3
## [8659] 3 5 1 1 4 3 4 5 3 4 5 3 3 3 3 1 3 5 5 4 2 3 4 4 1 3 2 3 5 4 3 3 3 5 5 2 3
## [8696] 2 3 3 3 1 3 2 3 2 3 1 3 1 4 4 2 3 2 1 2 1 3 4 4 1 5 3 3 3 3 5 3 3 3 5 3 3
## [8733] 1 2 3 3 1 3 3 3 3 4 2 3 4 3 3 5 4 3 3 4 5 1 5 3 2 1 2 1 1 3 4 3 2 4 3 3 4
## [8770] 1 3 4 1 4 3 3 5 3 3 3 3 3 3 3 5 3 4 3 5 1 3 3 5 1 3 1 1 3 3 4 3 3 3 3 3 4
## [8807] 3 3 5 1 1 3 3 2 3 5 3 1 1 1 1 3 2 3 4 3 3 1 5 2 3 4 3 2 1 2 1 3 4 3 3 3 3
## [8844] 2 1 3 5 2 3 2 1 5 4 3 4 5 3 2 3 4 5 5 2 5 4 5 3 3 3 2 1 4 3 3 2 3 3 3 3 3
## [8881] 1 3 2 2 3 4 3 5 3 1 1 2 2 3 2 5 1 5 3 5 3 4 2 1 3 3 4 3 1 3 3 3 5 4 3 3 2
## [8918] 3 2 5 3 3 1 3 5 4 3 5 3 3 2 3 2 5 3 3 3 4 5 3 4 2 4 4 5 3 1 4 3 5 2 3 3 3
## [8955] 1 5 3 2 3 5 1 3 1 3 2 4 5 3 5 1 3 2 3 5 3 5 4 2 4 3 1 4 1 3 4 3 2 3 3 3 1
## [8992] 1 1 2 3 3 5 4 5 1 4 2 1 4 3 3 3 5 3 5 3 1 5 1 2 3 3 5 3 2 5 3 3 3 4 4 4 3
## [9029] 5 5 3 5 4 4 1 1 2 1 5 5 3 3 2 5 5 3 5 1 5 3 3 1 3 3 2 5 3 3 3 3 3 3 2 3 5
## [9066] 2 5 3 1 4 4 4 5 1 5 5 2 3 3 4 1 2 3 3 2 5 5 3 5 3 5 2 5 1 2 2 3 3 5 5 1 3
## [9103] 3 3 2 2 3 3 3 2 2 3 4 2 3 2 3 2 4 3 5 3 5 5 1 5 5 3 4 1 2 3 5 3 5 3 5 1 2
## [9140] 3 5 1 3 3 1 5 5 4 3 3 3 3 3 4 3 3 5 3 3 3 3 1 3 5 3 3 3 5 5 2 5 1 2 2 4 2
## [9177] 4 3 3 2 2 5 5 2 3 4 2 5 3 5 3 5 3 3 2 3 1 3 3 2 1 4 1 3 3 2 2 5 1 3 3 2 3
## [9214] 2 3 5 5 3 3 3 5 3 1 1 1 5 3 3 3 5 3 2 1 3 5 2 3 3 3 1 3 3 3 3 2 2 3 3 3 2
## [9251] 3 5 5 3 3 3 3 3 4 5 1 4 1 5 3 3 3 3 3 3 3 4 2 3 5 3 5 5 1 3 3 3 5 3 3 4 4
## [9288] 3 5 3 3 5 3 3 3 4 3 3 3 4 3 3 5 3 2 5 3 1 5 5 3 3 3 3 4 4 3 5 5 3 3 3 1 3
## [9325] 1 4 3 4 2 3 4 5 1 5 5 3 3 4 3 3 1 2 3 3 3 1 2 5 1 3 1 1 3 1 2 3 3 3 1 3 3
## [9362] 3 4 3 3 5 5 3 3 3 5 3 4 3 2 3 4 3 4 3 3 3 3 4 3 3 1 3 5 3 4 3 3 1 1 1 3 3
## [9399] 4 3 3 5 2 3 3 3 1 4 4 1 3 2 5 3 5 3 1 4 3 3 3 3 5 5 3 1 4 5 2 4 3 4 3 1 2
## [9436] 4 3 2 3 1 1 1 3 4 3 1 4 4 1 3 5 2 5 3 5 5 1 4 5 5 5 3 3 5 3 3 3 5 3 3 3 3
## [9473] 4 5 1 5 1 3 1 3 2 4 3 3 4 1 4 3 3 3 3 4 1 3 3 3 3 1 3 5 3 4 3 3 3 3 3 3 4
## [9510] 2 4 3 5 2 3 3 3 3 3 5 3 5 1 5 3 3 5 3 4 3 3 3 3 4 3 1 3 5 1 3 3 5 3 4 3 2
## [9547] 4 3 3 3 3 3 3 3 4 3 3 3 1 3 3 3 4 3 4 3 3 3 4 3 3 5 2 4 1 5 3 4 4 4 3 4 3
## [9584] 1 1 3 3 2 3 3 3 3 3 2 2 1 3 3 3 3 4 3 3 3 5 1 3 4 5 3 3 4 3 4 4 3 2 3 4 3
## [9621] 3 1 2 3 5 1 3 5 3 1 3 1 3 3 1 5 5 4 4 4 3 3 3 3 4 4 3 3 3 3 3 3 5 2 4 3 2
## [9658] 3 4 3 2 5 5 3 4 5 3 3 4 3 3 3 3 5 4 4 3 2 5 3 1 5 1 1 3 3 3 3 5 3 3 3 3 3
## [9695] 3 3 3 4 4 3 4 4 3 4 5 3 3 4 3 3 3 4 3 3 2 1 3 5 4 3 3 3 3 5 3 2 4 3 3 5 3
## [9732] 3 4 3 2 3 3 3 1 3 2 3 5 5 2 3 4 1 1 3 3 2 4 2 3 3 3 4 3 4 4 3 3 3 3 4 5 5
## [9769] 2 1 3 1 3 5 3 3 5 4 4 1 4 4 3 4 1 3 3 3 4 1 3 2 2 3 4 3 2 3 3 5 5 1 2 5 3
## [9806] 3 4 3 3 5 1 5 3 4 4 3 3 2 3 2 3 2 3 3 3 5 5 2 1 5 2 3 2 1 5
##
## Within cluster sum of squares by cluster:
## [1] 4727.437 6816.337 12745.130 4746.715 6037.005
## (between_SS / total_SS = 11.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"#Cluster sizes
k_means$size## [1] 1349 780 4952 1373 1381#Top 5 items for each cluster
cluster_centers <- as.data.frame(k_means$centers)
row1 <- as.numeric(cluster_centers[1, ])
names(row1) <- colnames(cluster_centers)
head(sort(row1, decreasing = TRUE), 5)## soda rolls/buns bottled water whole milk shopping bags
## 1.0000000 0.1994070 0.1638251 0.1564122 0.1341735row2 <- as.numeric(cluster_centers[2, ])
names(row2) <- colnames(cluster_centers)
head(sort(row2, decreasing = TRUE), 5)## whole milk yogurt other vegetables root vegetables
## 0.7628205 0.6666667 0.6615385 0.4307692
## tropical fruit
## 0.3948718row3 <- as.numeric(cluster_centers[3, ])
names(row3) <- colnames(cluster_centers)
head(sort(row3, decreasing = TRUE), 5)## rolls/buns canned beer yogurt bottled water shopping bags
## 0.15125202 0.10601777 0.08663166 0.08400646 0.08400646row4 <- as.numeric(cluster_centers[4, ])
names(row4) <- colnames(cluster_centers)
head(sort(row4, decreasing = TRUE), 5)## whole milk rolls/buns root vegetables yogurt bottled water
## 1.0000000 0.2032047 0.1107065 0.1107065 0.1099782row5 <- as.numeric(cluster_centers[5, ])
names(row5) <- colnames(cluster_centers)
head(sort(row5, decreasing = TRUE), 5)## other vegetables whole milk rolls/buns root vegetables
## 1.0000000 0.2418537 0.1766836 0.1766836
## soda
## 0.1462708#Visualize the clusters
fviz_cluster(k_means, data = cluster_matrix,
geom = "point", stand = FALSE,
ellipse.type = "convex", ggtheme = theme_minimal(),
main = "Cluster Analysis of Transactions")