UL_Association Rules
Sevinj Guluyeva
2023-02-06
Introduction
In my project I will show association rules between Product types and Ratings. I have taken my data from Kaggle.(https://www.kaggle.com/datasets/aungpyaeap/supermarket-sales) The growth of supermarkets in most populated cities are increasing and marketcompetitions are also high. We will compare the different types of products. In this dataset, we can see different branches, cities, gender, payment and etc. But for association rules we needtwo main columns: product-line and rating.
I will use two different algorithm for association rules: 1) Apriori 2)ECLAT
Firstly we have to install “arules” and read our datasets.
library(arules)## Loading required package: Matrix##
## Attaching package: 'arules'## The following objects are masked from 'package:base':
##
## abbreviate, writelibrary(arulesViz)
data <-read.csv("C:/Users/user/Downloads/supermarket_sales - Sheet1.csv", sep = ",")
str(data)## 'data.frame': 1000 obs. of 17 variables:
## $ Invoice.ID : chr "750-67-8428" "226-31-3081" "631-41-3108" "123-19-1176" ...
## $ Branch : chr "A" "C" "A" "A" ...
## $ City : chr "Yangon" "Naypyitaw" "Yangon" "Yangon" ...
## $ Customer_type : chr "Member" "Normal" "Normal" "Member" ...
## $ Gender : chr "Female" "Female" "Male" "Male" ...
## $ Product_line : chr "Health and beauty" "Electronic accessories" "Home and lifestyle" "Health and beauty" ...
## $ Unit.price : num 74.7 15.3 46.3 58.2 86.3 ...
## $ Quantity : int 7 5 7 8 7 7 6 10 2 3 ...
## $ Tax.5. : num 26.14 3.82 16.22 23.29 30.21 ...
## $ Total : num 549 80.2 340.5 489 634.4 ...
## $ Date : chr "1/5/2019" "3/8/2019" "3/3/2019" "1/27/2019" ...
## $ Time : chr "13:08" "10:29" "13:23" "20:33" ...
## $ Payment : chr "Ewallet" "Cash" "Credit card" "Ewallet" ...
## $ cogs : num 522.8 76.4 324.3 465.8 604.2 ...
## $ gross.margin.percentage: num 4.76 4.76 4.76 4.76 4.76 ...
## $ gross.income : num 26.14 3.82 16.22 23.29 30.21 ...
## $ Rating : num 9.1 9.6 7.4 8.4 5.3 4.1 5.8 8 7.2 5.9 ...Next by using two main colums we set our data again.
data <- subset(data, select = c(Product_line, Rating))str(data)## 'data.frame': 1000 obs. of 2 variables:
## $ Product_line: chr "Health and beauty" "Electronic accessories" "Home and lifestyle" "Health and beauty" ...
## $ Rating : num 9.1 9.6 7.4 8.4 5.3 4.1 5.8 8 7.2 5.9 ...transaction <- as(split(data[,"Product_line"], data[, "Rating"]), "transactions")## Warning in asMethod(object): removing duplicated items in transactionssummary(transaction)## transactions as itemMatrix in sparse format with
## 61 rows (elements/itemsets/transactions) and
## 6 columns (items) and a density of 0.931694
##
## most frequent items:
## Fashion accessories Electronic accessories Sports and travel
## 59 58 57
## Food and beverages Home and lifestyle (Other)
## 56 56 55
##
## element (itemset/transaction) length distribution:
## sizes
## 3 4 5 6
## 1 2 18 40
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.00 5.00 6.00 5.59 6.00 6.00
##
## includes extended item information - examples:
## labels
## 1 Electronic accessories
## 2 Fashion accessories
## 3 Food and beverages
##
## includes extended transaction information - examples:
## transactionID
## 1 4
## 2 4.1
## 3 4.2In the summary we can see most frequent items. From the reuslts you can see fashion accessories are most frequent.
inspect(transaction[1:10])## items transactionID
## [1] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} 4
## [2] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 4.1
## [3] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 4.2
## [4] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 4.3
## [5] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 4.4
## [6] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} 4.5
## [7] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 4.6
## [8] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Home and lifestyle} 4.7
## [9] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 4.8
## [10] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 4.9By creating plots we can see exactly.
itemFrequencyPlot(transaction, topN = 15, type="absolute", main="Item Frequency", col ="#733C3C") 
itemFrequencyPlot(transaction, topN = 15, type="relative", main="Item Frequency", col = "#8FBDD3") 
Now we can visualize the sparse matrix for the first 5 items.
image(transaction[1:5])
Let’s look at random selection of 20 items.
image(sample(transaction,20))
Apriori Algorithm
rules <- apriori(transaction, parameter = list(support = 0.006, confidence = 0.25, minlen = 2))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.25 0.1 1 none FALSE TRUE 5 0.006 2
## 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: 0
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[6 item(s), 61 transaction(s)] done [0.00s].
## sorting and recoding items ... [6 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.00s].
## writing ... [186 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].From The result we can see the indexes of support, confidence, coverage, lift,count, lhs, rhs.
inspect(rules[1:10])## lhs rhs support confidence
## [1] {Health and beauty} => {Home and lifestyle} 0.8196721 0.9090909
## [2] {Home and lifestyle} => {Health and beauty} 0.8196721 0.8928571
## [3] {Health and beauty} => {Food and beverages} 0.8196721 0.9090909
## [4] {Food and beverages} => {Health and beauty} 0.8196721 0.8928571
## [5] {Health and beauty} => {Sports and travel} 0.8360656 0.9272727
## [6] {Sports and travel} => {Health and beauty} 0.8360656 0.8947368
## [7] {Health and beauty} => {Electronic accessories} 0.8524590 0.9454545
## [8] {Electronic accessories} => {Health and beauty} 0.8524590 0.8965517
## [9] {Health and beauty} => {Fashion accessories} 0.8688525 0.9636364
## [10] {Fashion accessories} => {Health and beauty} 0.8688525 0.8983051
## coverage lift count
## [1] 0.9016393 0.9902597 50
## [2] 0.9180328 0.9902597 50
## [3] 0.9016393 0.9902597 50
## [4] 0.9180328 0.9902597 50
## [5] 0.9016393 0.9923445 51
## [6] 0.9344262 0.9923445 51
## [7] 0.9016393 0.9943574 52
## [8] 0.9508197 0.9943574 52
## [9] 0.9016393 0.9963020 53
## [10] 0.9672131 0.9963020 53I showed the results individually for each parameters.
inspect(sort(rules, by = "lift")[1:5])## lhs rhs support confidence coverage lift count
## [1] {Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.8196721 0.9615385 0.8524590 1.047390 50
## [2] {Fashion accessories,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.8032787 0.9607843 0.8360656 1.046569 49
## [3] {Electronic accessories,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.7704918 0.9591837 0.8032787 1.044825 47
## [4] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.7540984 0.9583333 0.7868852 1.043899 46
## [5] {Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.7213115 0.9565217 0.7540984 1.041925 44inspect(sort(rules, by = "confidence")[1:5])## lhs rhs support confidence coverage lift count
## [1] {Home and lifestyle} => {Fashion accessories} 0.9016393 0.9821429 0.9180328 1.015436 55
## [2] {Food and beverages} => {Fashion accessories} 0.9016393 0.9821429 0.9180328 1.015436 55
## [3] {Food and beverages,
## Home and lifestyle} => {Fashion accessories} 0.8524590 0.9811321 0.8688525 1.014391 52
## [4] {Electronic accessories,
## Home and lifestyle} => {Fashion accessories} 0.8524590 0.9811321 0.8688525 1.014391 52
## [5] {Food and beverages,
## Sports and travel} => {Fashion accessories} 0.8524590 0.9811321 0.8688525 1.014391 52inspect(sort(rules, by = "support")[1:5])## lhs rhs support confidence
## [1] {Electronic accessories} => {Fashion accessories} 0.9180328 0.9655172
## [2] {Fashion accessories} => {Electronic accessories} 0.9180328 0.9491525
## [3] {Home and lifestyle} => {Fashion accessories} 0.9016393 0.9821429
## [4] {Fashion accessories} => {Home and lifestyle} 0.9016393 0.9322034
## [5] {Food and beverages} => {Fashion accessories} 0.9016393 0.9821429
## coverage lift count
## [1] 0.9508197 0.9982466 56
## [2] 0.9672131 0.9982466 56
## [3] 0.9180328 1.0154358 55
## [4] 0.9672131 1.0154358 55
## [5] 0.9180328 1.0154358 55inspect(sort(rules, by = "count")[1:5])## lhs rhs support confidence
## [1] {Electronic accessories} => {Fashion accessories} 0.9180328 0.9655172
## [2] {Fashion accessories} => {Electronic accessories} 0.9180328 0.9491525
## [3] {Home and lifestyle} => {Fashion accessories} 0.9016393 0.9821429
## [4] {Fashion accessories} => {Home and lifestyle} 0.9016393 0.9322034
## [5] {Food and beverages} => {Fashion accessories} 0.9016393 0.9821429
## coverage lift count
## [1] 0.9508197 0.9982466 56
## [2] 0.9672131 0.9982466 56
## [3] 0.9180328 1.0154358 55
## [4] 0.9672131 1.0154358 55
## [5] 0.9180328 1.0154358 55In this plot we see the lists of products and their lift and support levels.
plot(rules, method="grouped") 
In this plot we can see the results clearly.
plot(sort(rules, by = "confidence")[1:100], method="graph")
From the graph you see the the colors from light to dark. This shows the frequency of items.
plot(rules, shading="order", control=list(main="Two-key plot"))## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
ECLAT algorithm
The ECLAT algorithm stands for Equivalence Class Clustering and bottom-up Lattice Traversal. It is one of the popular methods of Association Rule mining. It is a more efficient and scalable version of the Apriori algorithm.
freq.items<-eclat(transaction, parameter=list(supp=0.006, maxlen=15)) ## Eclat
##
## parameter specification:
## tidLists support minlen maxlen target ext
## FALSE 0.006 1 15 frequent itemsets TRUE
##
## algorithmic control:
## sparse sort verbose
## 7 -2 TRUE
##
## Absolute minimum support count: 0
##
## create itemset ...
## set transactions ...[6 item(s), 61 transaction(s)] done [0.00s].
## sorting and recoding items ... [6 item(s)] done [0.00s].
## creating bit matrix ... [6 row(s), 61 column(s)] done [0.00s].
## writing ... [63 set(s)] done [0.00s].
## Creating S4 object ... done [0.00s].inspect(freq.items)## items support count
## [1] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.6557377 40
## [2] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.7049180 43
## [3] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.6721311 41
## [4] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} 0.7049180 43
## [5] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} 0.7540984 46
## [6] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} 0.7213115 44
## [7] {Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.7213115 44
## [8] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.6885246 42
## [9] {Fashion accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.7377049 45
## [10] {Electronic accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.7049180 43
## [11] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Home and lifestyle} 0.7540984 46
## [12] {Fashion accessories,
## Health and beauty,
## Home and lifestyle} 0.8032787 49
## [13] {Electronic accessories,
## Health and beauty,
## Home and lifestyle} 0.7704918 47
## [14] {Health and beauty,
## Home and lifestyle,
## Sports and travel} 0.7540984 46
## [15] {Food and beverages,
## Health and beauty,
## Home and lifestyle} 0.7704918 47
## [16] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} 0.7049180 43
## [17] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} 0.7540984 46
## [18] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} 0.7213115 44
## [19] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty} 0.7540984 46
## [20] {Fashion accessories,
## Food and beverages,
## Health and beauty} 0.8032787 49
## [21] {Electronic accessories,
## Food and beverages,
## Health and beauty} 0.7704918 47
## [22] {Food and beverages,
## Health and beauty,
## Sports and travel} 0.7704918 47
## [23] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Sports and travel} 0.7540984 46
## [24] {Fashion accessories,
## Health and beauty,
## Sports and travel} 0.8032787 49
## [25] {Electronic accessories,
## Health and beauty,
## Sports and travel} 0.7868852 48
## [26] {Electronic accessories,
## Fashion accessories,
## Health and beauty} 0.8196721 50
## [27] {Fashion accessories,
## Health and beauty} 0.8688525 53
## [28] {Electronic accessories,
## Health and beauty} 0.8524590 52
## [29] {Health and beauty,
## Sports and travel} 0.8360656 51
## [30] {Food and beverages,
## Health and beauty} 0.8196721 50
## [31] {Health and beauty,
## Home and lifestyle} 0.8196721 50
## [32] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} 0.7540984 46
## [33] {Fashion accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} 0.8032787 49
## [34] {Electronic accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} 0.7704918 47
## [35] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Home and lifestyle} 0.8032787 49
## [36] {Fashion accessories,
## Food and beverages,
## Home and lifestyle} 0.8524590 52
## [37] {Electronic accessories,
## Food and beverages,
## Home and lifestyle} 0.8196721 50
## [38] {Food and beverages,
## Home and lifestyle,
## Sports and travel} 0.8196721 50
## [39] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle,
## Sports and travel} 0.7868852 48
## [40] {Fashion accessories,
## Home and lifestyle,
## Sports and travel} 0.8360656 51
## [41] {Electronic accessories,
## Home and lifestyle,
## Sports and travel} 0.8032787 49
## [42] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle} 0.8524590 52
## [43] {Fashion accessories,
## Home and lifestyle} 0.9016393 55
## [44] {Electronic accessories,
## Home and lifestyle} 0.8688525 53
## [45] {Home and lifestyle,
## Sports and travel} 0.8524590 52
## [46] {Food and beverages,
## Home and lifestyle} 0.8688525 53
## [47] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Sports and travel} 0.8032787 49
## [48] {Fashion accessories,
## Food and beverages,
## Sports and travel} 0.8524590 52
## [49] {Electronic accessories,
## Food and beverages,
## Sports and travel} 0.8196721 50
## [50] {Electronic accessories,
## Fashion accessories,
## Food and beverages} 0.8524590 52
## [51] {Fashion accessories,
## Food and beverages} 0.9016393 55
## [52] {Electronic accessories,
## Food and beverages} 0.8688525 53
## [53] {Food and beverages,
## Sports and travel} 0.8688525 53
## [54] {Electronic accessories,
## Fashion accessories,
## Sports and travel} 0.8524590 52
## [55] {Fashion accessories,
## Sports and travel} 0.9016393 55
## [56] {Electronic accessories,
## Sports and travel} 0.8852459 54
## [57] {Electronic accessories,
## Fashion accessories} 0.9180328 56
## [58] {Fashion accessories} 0.9672131 59
## [59] {Electronic accessories} 0.9508197 58
## [60] {Sports and travel} 0.9344262 57
## [61] {Food and beverages} 0.9180328 56
## [62] {Home and lifestyle} 0.9180328 56
## [63] {Health and beauty} 0.9016393 55When we set “confidence” we got 186 rules.
freq.rules<-ruleInduction(freq.items, transaction, confidence=0.5)freq.rules## set of 186 rulesfreq.items<-eclat(transaction, parameter=list(supp=0.05, maxlen=15)) ## Eclat
##
## parameter specification:
## tidLists support minlen maxlen target ext
## FALSE 0.05 1 15 frequent itemsets TRUE
##
## algorithmic control:
## sparse sort verbose
## 7 -2 TRUE
##
## Absolute minimum support count: 3
##
## create itemset ...
## set transactions ...[6 item(s), 61 transaction(s)] done [0.00s].
## sorting and recoding items ... [6 item(s)] done [0.00s].
## creating bit matrix ... [6 row(s), 61 column(s)] done [0.00s].
## writing ... [63 set(s)] done [0.00s].
## Creating S4 object ... done [0.00s].inspect(freq.rules)## lhs rhs support confidence lift itemset
## [1] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.6557377 0.9302326 0.9783480 1
## [2] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.6557377 0.9756098 1.0086813 1
## [3] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.6557377 0.9523810 1.0374150 1
## [4] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.6557377 0.8695652 0.9644269 1
## [5] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.6557377 0.9302326 1.0132890 1
## [6] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.6557377 0.9302326 0.9955120 1
## [7] {Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.7049180 0.9772727 1.0104006 2
## [8] {Fashion accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.7049180 0.9555556 1.0408730 2
## [9] {Fashion accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.7049180 0.8775510 0.9732839 2
## [10] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.7049180 0.9347826 1.0182453 2
## [11] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.7049180 0.9347826 1.0003814 2
## [12] {Food and beverages,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.6721311 0.9318182 0.9800157 3
## [13] {Electronic accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.6721311 0.9534884 1.0386213 3
## [14] {Electronic accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.6721311 0.8723404 0.9675048 3
## [15] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.6721311 0.9318182 1.0150162 3
## [16] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.6721311 0.9318182 0.9972089 3
## [17] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Electronic accessories} 0.7049180 0.9347826 0.9831334 4
## [18] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Fashion accessories} 0.7049180 0.9772727 1.0104006 4
## [19] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Home and lifestyle} => {Food and beverages} 0.7049180 0.9347826 1.0182453 4
## [20] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Home and lifestyle} => {Health and beauty} 0.7049180 0.8775510 0.9732839 4
## [21] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty} => {Home and lifestyle} 0.7049180 0.9347826 1.0182453 4
## [22] {Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Fashion accessories} 0.7540984 0.9787234 1.0119005 5
## [23] {Fashion accessories,
## Health and beauty,
## Home and lifestyle} => {Food and beverages} 0.7540984 0.9387755 1.0225948 5
## [24] {Fashion accessories,
## Food and beverages,
## Home and lifestyle} => {Health and beauty} 0.7540984 0.8846154 0.9811189 5
## [25] {Fashion accessories,
## Food and beverages,
## Health and beauty} => {Home and lifestyle} 0.7540984 0.9387755 1.0225948 5
## [26] {Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Electronic accessories} 0.7213115 0.9361702 0.9845928 6
## [27] {Electronic accessories,
## Health and beauty,
## Home and lifestyle} => {Food and beverages} 0.7213115 0.9361702 1.0197568 6
## [28] {Electronic accessories,
## Food and beverages,
## Home and lifestyle} => {Health and beauty} 0.7213115 0.8800000 0.9760000 6
## [29] {Electronic accessories,
## Food and beverages,
## Health and beauty} => {Home and lifestyle} 0.7213115 0.9361702 1.0197568 6
## [30] {Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.7213115 0.9565217 1.0419255 7
## [31] {Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.7213115 0.8800000 0.9760000 7
## [32] {Food and beverages,
## Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.7213115 0.9361702 1.0197568 7
## [33] {Food and beverages,
## Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.7213115 0.9361702 1.0018664 7
## [34] {Fashion accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.6885246 0.9333333 0.9816092 8
## [35] {Electronic accessories,
## Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.6885246 0.9767442 1.0098542 8
## [36] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.6885246 0.8750000 0.9704545 8
## [37] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.6885246 0.9130435 0.9945652 8
## [38] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.6885246 0.9130435 0.9771167 8
## [39] {Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.7377049 0.9782609 1.0114223 9
## [40] {Fashion accessories,
## Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.7377049 0.8823529 0.9786096 9
## [41] {Fashion accessories,
## Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.7377049 0.9183673 1.0003644 9
## [42] {Fashion accessories,
## Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.7377049 0.9183673 0.9828142 9
## [43] {Health and beauty,
## Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.7049180 0.9347826 0.9831334 10
## [44] {Electronic accessories,
## Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.7049180 0.8775510 0.9732839 10
## [45] {Electronic accessories,
## Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.7049180 0.8958333 0.9758185 10
## [46] {Electronic accessories,
## Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.7049180 0.9148936 0.9790967 10
## [47] {Fashion accessories,
## Health and beauty,
## Home and lifestyle} => {Electronic accessories} 0.7540984 0.9387755 0.9873329 11
## [48] {Electronic accessories,
## Health and beauty,
## Home and lifestyle} => {Fashion accessories} 0.7540984 0.9787234 1.0119005 11
## [49] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle} => {Health and beauty} 0.7540984 0.8846154 0.9811189 11
## [50] {Electronic accessories,
## Fashion accessories,
## Health and beauty} => {Home and lifestyle} 0.7540984 0.9200000 1.0021429 11
## [51] {Health and beauty,
## Home and lifestyle} => {Fashion accessories} 0.8032787 0.9800000 1.0132203 12
## [52] {Fashion accessories,
## Home and lifestyle} => {Health and beauty} 0.8032787 0.8909091 0.9880992 12
## [53] {Fashion accessories,
## Health and beauty} => {Home and lifestyle} 0.8032787 0.9245283 1.0070755 12
## [54] {Health and beauty,
## Home and lifestyle} => {Electronic accessories} 0.7704918 0.9400000 0.9886207 13
## [55] {Electronic accessories,
## Home and lifestyle} => {Health and beauty} 0.7704918 0.8867925 0.9835334 13
## [56] {Electronic accessories,
## Health and beauty} => {Home and lifestyle} 0.7704918 0.9038462 0.9845467 13
## [57] {Home and lifestyle,
## Sports and travel} => {Health and beauty} 0.7540984 0.8846154 0.9811189 14
## [58] {Health and beauty,
## Sports and travel} => {Home and lifestyle} 0.7540984 0.9019608 0.9824930 14
## [59] {Health and beauty,
## Home and lifestyle} => {Sports and travel} 0.7540984 0.9200000 0.9845614 14
## [60] {Health and beauty,
## Home and lifestyle} => {Food and beverages} 0.7704918 0.9400000 1.0239286 15
## [61] {Food and beverages,
## Home and lifestyle} => {Health and beauty} 0.7704918 0.8867925 0.9835334 15
## [62] {Food and beverages,
## Health and beauty} => {Home and lifestyle} 0.7704918 0.9400000 1.0239286 15
## [63] {Fashion accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} => {Electronic accessories} 0.7049180 0.9347826 0.9831334 16
## [64] {Electronic accessories,
## Food and beverages,
## Health and beauty,
## Sports and travel} => {Fashion accessories} 0.7049180 0.9772727 1.0104006 16
## [65] {Electronic accessories,
## Fashion accessories,
## Health and beauty,
## Sports and travel} => {Food and beverages} 0.7049180 0.9347826 1.0182453 16
## [66] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Sports and travel} => {Health and beauty} 0.7049180 0.8775510 0.9732839 16
## [67] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Health and beauty} => {Sports and travel} 0.7049180 0.9347826 1.0003814 16
## [68] {Food and beverages,
## Health and beauty,
## Sports and travel} => {Fashion accessories} 0.7540984 0.9787234 1.0119005 17
## [69] {Fashion accessories,
## Health and beauty,
## Sports and travel} => {Food and beverages} 0.7540984 0.9387755 1.0225948 17
## [70] {Fashion accessories,
## Food and beverages,
## Sports and travel} => {Health and beauty} 0.7540984 0.8846154 0.9811189 17
## [71] {Fashion accessories,
## Food and beverages,
## Health and beauty} => {Sports and travel} 0.7540984 0.9387755 1.0046545 17
## [72] {Food and beverages,
## Health and beauty,
## Sports and travel} => {Electronic accessories} 0.7213115 0.9361702 0.9845928 18
## [73] {Electronic accessories,
## Health and beauty,
## Sports and travel} => {Food and beverages} 0.7213115 0.9166667 0.9985119 18
## [74] {Electronic accessories,
## Food and beverages,
## Sports and travel} => {Health and beauty} 0.7213115 0.8800000 0.9760000 18
## [75] {Electronic accessories,
## Food and beverages,
## Health and beauty} => {Sports and travel} 0.7213115 0.9361702 1.0018664 18
## [76] {Fashion accessories,
## Food and beverages,
## Health and beauty} => {Electronic accessories} 0.7540984 0.9387755 0.9873329 19
## [77] {Electronic accessories,
## Food and beverages,
## Health and beauty} => {Fashion accessories} 0.7540984 0.9787234 1.0119005 19
## [78] {Electronic accessories,
## Fashion accessories,
## Health and beauty} => {Food and beverages} 0.7540984 0.9200000 1.0021429 19
## [79] {Electronic accessories,
## Fashion accessories,
## Food and beverages} => {Health and beauty} 0.7540984 0.8846154 0.9811189 19
## [80] {Food and beverages,
## Health and beauty} => {Fashion accessories} 0.8032787 0.9800000 1.0132203 20
## [81] {Fashion accessories,
## Health and beauty} => {Food and beverages} 0.8032787 0.9245283 1.0070755 20
## [82] {Fashion accessories,
## Food and beverages} => {Health and beauty} 0.8032787 0.8909091 0.9880992 20
## [83] {Food and beverages,
## Health and beauty} => {Electronic accessories} 0.7704918 0.9400000 0.9886207 21
## [84] {Electronic accessories,
## Health and beauty} => {Food and beverages} 0.7704918 0.9038462 0.9845467 21
## [85] {Electronic accessories,
## Food and beverages} => {Health and beauty} 0.7704918 0.8867925 0.9835334 21
## [86] {Health and beauty,
## Sports and travel} => {Food and beverages} 0.7704918 0.9215686 1.0038515 22
## [87] {Food and beverages,
## Sports and travel} => {Health and beauty} 0.7704918 0.8867925 0.9835334 22
## [88] {Food and beverages,
## Health and beauty} => {Sports and travel} 0.7704918 0.9400000 1.0059649 22
## [89] {Fashion accessories,
## Health and beauty,
## Sports and travel} => {Electronic accessories} 0.7540984 0.9387755 0.9873329 23
## [90] {Electronic accessories,
## Health and beauty,
## Sports and travel} => {Fashion accessories} 0.7540984 0.9583333 0.9908192 23
## [91] {Electronic accessories,
## Fashion accessories,
## Sports and travel} => {Health and beauty} 0.7540984 0.8846154 0.9811189 23
## [92] {Electronic accessories,
## Fashion accessories,
## Health and beauty} => {Sports and travel} 0.7540984 0.9200000 0.9845614 23
## [93] {Health and beauty,
## Sports and travel} => {Fashion accessories} 0.8032787 0.9607843 0.9933533 24
## [94] {Fashion accessories,
## Sports and travel} => {Health and beauty} 0.8032787 0.8909091 0.9880992 24
## [95] {Fashion accessories,
## Health and beauty} => {Sports and travel} 0.8032787 0.9245283 0.9894075 24
## [96] {Health and beauty,
## Sports and travel} => {Electronic accessories} 0.7868852 0.9411765 0.9898580 25
## [97] {Electronic accessories,
## Sports and travel} => {Health and beauty} 0.7868852 0.8888889 0.9858586 25
## [98] {Electronic accessories,
## Health and beauty} => {Sports and travel} 0.7868852 0.9230769 0.9878543 25
## [99] {Fashion accessories,
## Health and beauty} => {Electronic accessories} 0.8196721 0.9433962 0.9921926 26
## [100] {Electronic accessories,
## Health and beauty} => {Fashion accessories} 0.8196721 0.9615385 0.9941330 26
## [101] {Electronic accessories,
## Fashion accessories} => {Health and beauty} 0.8196721 0.8928571 0.9902597 26
## [102] {Health and beauty} => {Fashion accessories} 0.8688525 0.9636364 0.9963020 27
## [103] {Fashion accessories} => {Health and beauty} 0.8688525 0.8983051 0.9963020 27
## [104] {Health and beauty} => {Electronic accessories} 0.8524590 0.9454545 0.9943574 28
## [105] {Electronic accessories} => {Health and beauty} 0.8524590 0.8965517 0.9943574 28
## [106] {Sports and travel} => {Health and beauty} 0.8360656 0.8947368 0.9923445 29
## [107] {Health and beauty} => {Sports and travel} 0.8360656 0.9272727 0.9923445 29
## [108] {Health and beauty} => {Food and beverages} 0.8196721 0.9090909 0.9902597 30
## [109] {Food and beverages} => {Health and beauty} 0.8196721 0.8928571 0.9902597 30
## [110] {Home and lifestyle} => {Health and beauty} 0.8196721 0.8928571 0.9902597 31
## [111] {Health and beauty} => {Home and lifestyle} 0.8196721 0.9090909 0.9902597 31
## [112] {Fashion accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.7540984 0.9387755 0.9873329 32
## [113] {Electronic accessories,
## Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.7540984 0.9787234 1.0119005 32
## [114] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.7540984 0.9583333 1.0438988 32
## [115] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Sports and travel} => {Home and lifestyle} 0.7540984 0.9387755 1.0225948 32
## [116] {Electronic accessories,
## Fashion accessories,
## Food and beverages,
## Home and lifestyle} => {Sports and travel} 0.7540984 0.9387755 1.0046545 32
## [117] {Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.8032787 0.9800000 1.0132203 33
## [118] {Fashion accessories,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.8032787 0.9607843 1.0465686 33
## [119] {Fashion accessories,
## Food and beverages,
## Sports and travel} => {Home and lifestyle} 0.8032787 0.9423077 1.0264423 33
## [120] {Fashion accessories,
## Food and beverages,
## Home and lifestyle} => {Sports and travel} 0.8032787 0.9423077 1.0084345 33
## [121] {Food and beverages,
## Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.7704918 0.9400000 0.9886207 34
## [122] {Electronic accessories,
## Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.7704918 0.9591837 1.0448251 34
## [123] {Electronic accessories,
## Food and beverages,
## Sports and travel} => {Home and lifestyle} 0.7704918 0.9400000 1.0239286 34
## [124] {Electronic accessories,
## Food and beverages,
## Home and lifestyle} => {Sports and travel} 0.7704918 0.9400000 1.0059649 34
## [125] {Fashion accessories,
## Food and beverages,
## Home and lifestyle} => {Electronic accessories} 0.8032787 0.9423077 0.9910477 35
## [126] {Electronic accessories,
## Food and beverages,
## Home and lifestyle} => {Fashion accessories} 0.8032787 0.9800000 1.0132203 35
## [127] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle} => {Food and beverages} 0.8032787 0.9423077 1.0264423 35
## [128] {Electronic accessories,
## Fashion accessories,
## Food and beverages} => {Home and lifestyle} 0.8032787 0.9423077 1.0264423 35
## [129] {Food and beverages,
## Home and lifestyle} => {Fashion accessories} 0.8524590 0.9811321 1.0143908 36
## [130] {Fashion accessories,
## Home and lifestyle} => {Food and beverages} 0.8524590 0.9454545 1.0298701 36
## [131] {Fashion accessories,
## Food and beverages} => {Home and lifestyle} 0.8524590 0.9454545 1.0298701 36
## [132] {Food and beverages,
## Home and lifestyle} => {Electronic accessories} 0.8196721 0.9433962 0.9921926 37
## [133] {Electronic accessories,
## Home and lifestyle} => {Food and beverages} 0.8196721 0.9433962 1.0276280 37
## [134] {Electronic accessories,
## Food and beverages} => {Home and lifestyle} 0.8196721 0.9433962 1.0276280 37
## [135] {Home and lifestyle,
## Sports and travel} => {Food and beverages} 0.8196721 0.9615385 1.0473901 38
## [136] {Food and beverages,
## Sports and travel} => {Home and lifestyle} 0.8196721 0.9433962 1.0276280 38
## [137] {Food and beverages,
## Home and lifestyle} => {Sports and travel} 0.8196721 0.9433962 1.0095995 38
## [138] {Fashion accessories,
## Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.7868852 0.9411765 0.9898580 39
## [139] {Electronic accessories,
## Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.7868852 0.9795918 1.0127983 39
## [140] {Electronic accessories,
## Fashion accessories,
## Sports and travel} => {Home and lifestyle} 0.7868852 0.9230769 1.0054945 39
## [141] {Electronic accessories,
## Fashion accessories,
## Home and lifestyle} => {Sports and travel} 0.7868852 0.9230769 0.9878543 39
## [142] {Home and lifestyle,
## Sports and travel} => {Fashion accessories} 0.8360656 0.9807692 1.0140156 40
## [143] {Fashion accessories,
## Sports and travel} => {Home and lifestyle} 0.8360656 0.9272727 1.0100649 40
## [144] {Fashion accessories,
## Home and lifestyle} => {Sports and travel} 0.8360656 0.9272727 0.9923445 40
## [145] {Home and lifestyle,
## Sports and travel} => {Electronic accessories} 0.8032787 0.9423077 0.9910477 41
## [146] {Electronic accessories,
## Sports and travel} => {Home and lifestyle} 0.8032787 0.9074074 0.9884259 41
## [147] {Electronic accessories,
## Home and lifestyle} => {Sports and travel} 0.8032787 0.9245283 0.9894075 41
## [148] {Fashion accessories,
## Home and lifestyle} => {Electronic accessories} 0.8524590 0.9454545 0.9943574 42
## [149] {Electronic accessories,
## Home and lifestyle} => {Fashion accessories} 0.8524590 0.9811321 1.0143908 42
## [150] {Electronic accessories,
## Fashion accessories} => {Home and lifestyle} 0.8524590 0.9285714 1.0114796 42
## [151] {Home and lifestyle} => {Fashion accessories} 0.9016393 0.9821429 1.0154358 43
## [152] {Fashion accessories} => {Home and lifestyle} 0.9016393 0.9322034 1.0154358 43
## [153] {Home and lifestyle} => {Electronic accessories} 0.8688525 0.9464286 0.9953818 44
## [154] {Electronic accessories} => {Home and lifestyle} 0.8688525 0.9137931 0.9953818 44
## [155] {Sports and travel} => {Home and lifestyle} 0.8524590 0.9122807 0.9937343 45
## [156] {Home and lifestyle} => {Sports and travel} 0.8524590 0.9285714 0.9937343 45
## [157] {Home and lifestyle} => {Food and beverages} 0.8688525 0.9464286 1.0309311 46
## [158] {Food and beverages} => {Home and lifestyle} 0.8688525 0.9464286 1.0309311 46
## [159] {Fashion accessories,
## Food and beverages,
## Sports and travel} => {Electronic accessories} 0.8032787 0.9423077 0.9910477 47
## [160] {Electronic accessories,
## Food and beverages,
## Sports and travel} => {Fashion accessories} 0.8032787 0.9800000 1.0132203 47
## [161] {Electronic accessories,
## Fashion accessories,
## Sports and travel} => {Food and beverages} 0.8032787 0.9423077 1.0264423 47
## [162] {Electronic accessories,
## Fashion accessories,
## Food and beverages} => {Sports and travel} 0.8032787 0.9423077 1.0084345 47
## [163] {Food and beverages,
## Sports and travel} => {Fashion accessories} 0.8524590 0.9811321 1.0143908 48
## [164] {Fashion accessories,
## Sports and travel} => {Food and beverages} 0.8524590 0.9454545 1.0298701 48
## [165] {Fashion accessories,
## Food and beverages} => {Sports and travel} 0.8524590 0.9454545 1.0118022 48
## [166] {Food and beverages,
## Sports and travel} => {Electronic accessories} 0.8196721 0.9433962 0.9921926 49
## [167] {Electronic accessories,
## Sports and travel} => {Food and beverages} 0.8196721 0.9259259 1.0085979 49
## [168] {Electronic accessories,
## Food and beverages} => {Sports and travel} 0.8196721 0.9433962 1.0095995 49
## [169] {Fashion accessories,
## Food and beverages} => {Electronic accessories} 0.8524590 0.9454545 0.9943574 50
## [170] {Electronic accessories,
## Food and beverages} => {Fashion accessories} 0.8524590 0.9811321 1.0143908 50
## [171] {Electronic accessories,
## Fashion accessories} => {Food and beverages} 0.8524590 0.9285714 1.0114796 50
## [172] {Food and beverages} => {Fashion accessories} 0.9016393 0.9821429 1.0154358 51
## [173] {Fashion accessories} => {Food and beverages} 0.9016393 0.9322034 1.0154358 51
## [174] {Food and beverages} => {Electronic accessories} 0.8688525 0.9464286 0.9953818 52
## [175] {Electronic accessories} => {Food and beverages} 0.8688525 0.9137931 0.9953818 52
## [176] {Sports and travel} => {Food and beverages} 0.8688525 0.9298246 1.0128446 53
## [177] {Food and beverages} => {Sports and travel} 0.8688525 0.9464286 1.0128446 53
## [178] {Fashion accessories,
## Sports and travel} => {Electronic accessories} 0.8524590 0.9454545 0.9943574 54
## [179] {Electronic accessories,
## Sports and travel} => {Fashion accessories} 0.8524590 0.9629630 0.9956058 54
## [180] {Electronic accessories,
## Fashion accessories} => {Sports and travel} 0.8524590 0.9285714 0.9937343 54
## [181] {Sports and travel} => {Fashion accessories} 0.9016393 0.9649123 0.9976212 55
## [182] {Fashion accessories} => {Sports and travel} 0.9016393 0.9322034 0.9976212 55
## [183] {Sports and travel} => {Electronic accessories} 0.8852459 0.9473684 0.9963702 56
## [184] {Electronic accessories} => {Sports and travel} 0.8852459 0.9310345 0.9963702 56
## [185] {Fashion accessories} => {Electronic accessories} 0.9180328 0.9491525 0.9982466 57
## [186] {Electronic accessories} => {Fashion accessories} 0.9180328 0.9655172 0.9982466 57Conclusion
From the plots we can see clearly that in the ranking the sales of fashion accessories are more in comparision to others. In the second place we see Electronic accesories, then sports and travel, food and beverages, home and lifestyles, health and beauty accordingly. This means that in the tree branches people have prefered to buy fashion accessories.