Grocery Data Set
This data set contains 1 month (30 days) of real-world point-of-sale transaction data from a typical local grocery outlet. The data set contains 9835 transactions and the items are aggregated to 169 categories. The following exercise uses market basket analysis to attempt to meet the objective of mining the top 5 association rules for the data set.
library(arules)
## Loading required package: Matrix
##
## Attaching package: 'arules'
## The following objects are masked from 'package:base':
##
## abbreviate, write
data("Groceries")
dim(Groceries)
## [1] 9835 169
set.seed(1)
Groceries <- as(Groceries, "transactions")
Groceries
## transactions in sparse format with
## 9835 transactions (rows) and
## 169 items (columns)
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 meat and sausage
## 2 sausage sausage meat and sausage
## 3 liver loaf sausage meat and sausage
The data set summary shows the top five most frequently purchased items. It also shows that most transactions were for the purchase of four items or less.
To observe some of the more frequently purchased items a bar chart is included in the next section of code.
aa=as(Groceries,"matrix") # transforms transaction matrix into incidence matrix
aa[1:2,] # print the first two rows of the incidence matrix
## frankfurter sausage liver loaf ham meat finished products
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE
## organic sausage chicken turkey pork beef hamburger meat fish
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## citrus fruit tropical fruit pip fruit grapes berries nuts/prunes
## [1,] TRUE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE TRUE FALSE FALSE FALSE FALSE
## root vegetables onions herbs other vegetables
## [1,] FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE
## packaged fruit/vegetables whole milk butter curd dessert butter milk
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE
## yogurt whipped/sour cream beverages UHT-milk condensed milk cream
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] TRUE FALSE FALSE FALSE FALSE FALSE
## soft cheese sliced cheese hard cheese cream cheese processed cheese
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## spread cheese curd cheese specialty cheese mayonnaise salad dressing
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## tidbits frozen vegetables frozen fruits frozen meals frozen fish
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## frozen chicken ice cream frozen dessert frozen potato products
## [1,] FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE
## domestic eggs rolls/buns white bread brown bread pastry
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## roll products semi-finished bread zwieback potato products flour
## [1,] FALSE TRUE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## salt rice pasta vinegar oil margarine specialty fat sugar
## [1,] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## artif. sweetener honey mustard ketchup spices soups ready soups
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## Instant food products sauces cereals organic products baking powder
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## preservation products pudding powder canned vegetables canned fruit
## [1,] FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE
## pickled vegetables specialty vegetables jam sweet spreads
## [1,] FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE
## meat spreads canned fish dog food cat food pet care baby food coffee
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## instant coffee tea cocoa drinks bottled water soda misc. beverages
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE
## fruit/vegetable juice syrup bottled beer canned beer brandy whisky
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE
## liquor rum liqueur liquor (appetizer) white wine red/blush wine
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE
## prosecco sparkling wine salty snack popcorn nut snack snack products
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE
## long life bakery product waffles cake bar chewing gum chocolate
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## cooking chocolate specialty chocolate specialty bar
## [1,] FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE
## chocolate marshmallow candy seasonal products detergent softener
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## decalcifier dish cleaner abrasive cleaner cleaner toilet cleaner
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## bathroom cleaner hair spray dental care male cosmetics
## [1,] FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE
## make up remover skin care female sanitary products baby cosmetics
## [1,] FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE
## soap rubbing alcohol hygiene articles napkins dishes cookware
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE FALSE
## kitchen utensil cling film/bags kitchen towels house keeping products
## [1,] FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE
## candles light bulbs sound storage medium newspapers photo/film
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
## pot plants flower soil/fertilizer flower (seeds) shopping bags bags
## [1,] FALSE FALSE FALSE FALSE FALSE
## [2,] FALSE FALSE FALSE FALSE FALSE
itemFrequencyPlot(Groceries[, itemFrequency(Groceries) > 0.06], cex.names = 1)
From the graph it can be observed that the top four items appear in over 15% of the transaction.
Overall association rules are mined from the data and a summary is run to provide basic descriptive statistics.
rules <- apriori(Groceries, parameter = list(support = 0.001, confidence = 0.8))
## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 0.001 1
## maxlen target ext
## 10 rules FALSE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 9
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [157 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.01s].
## writing ... [410 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].
rules
## set of 410 rules
summary(rules)
## set of 410 rules
##
## rule length distribution (lhs + rhs):sizes
## 3 4 5 6
## 29 229 140 12
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 4.000 4.000 4.329 5.000 6.000
##
## summary of quality measures:
## support confidence lift count
## Min. :0.001017 Min. :0.8000 Min. : 3.131 Min. :10.00
## 1st Qu.:0.001017 1st Qu.:0.8333 1st Qu.: 3.312 1st Qu.:10.00
## Median :0.001220 Median :0.8462 Median : 3.588 Median :12.00
## Mean :0.001247 Mean :0.8663 Mean : 3.951 Mean :12.27
## 3rd Qu.:0.001322 3rd Qu.:0.9091 3rd Qu.: 4.341 3rd Qu.:13.00
## Max. :0.003152 Max. :1.0000 Max. :11.235 Max. :31.00
##
## mining info:
## data ntransactions support confidence
## Groceries 9835 0.001 0.8
The rules are sorted by confidence in descending order to observe which five rules are most likely to occur.
inspect(sort(rules, by = "confidence")[1:10])
## lhs rhs support confidence lift count
## [1] {rice,
## sugar} => {whole milk} 0.001220132 1 3.913649 12
## [2] {canned fish,
## hygiene articles} => {whole milk} 0.001118454 1 3.913649 11
## [3] {root vegetables,
## butter,
## rice} => {whole milk} 0.001016777 1 3.913649 10
## [4] {root vegetables,
## whipped/sour cream,
## flour} => {whole milk} 0.001728521 1 3.913649 17
## [5] {butter,
## soft cheese,
## domestic eggs} => {whole milk} 0.001016777 1 3.913649 10
## [6] {citrus fruit,
## root vegetables,
## soft cheese} => {other vegetables} 0.001016777 1 5.168156 10
## [7] {pip fruit,
## butter,
## hygiene articles} => {whole milk} 0.001016777 1 3.913649 10
## [8] {root vegetables,
## whipped/sour cream,
## hygiene articles} => {whole milk} 0.001016777 1 3.913649 10
## [9] {pip fruit,
## root vegetables,
## hygiene articles} => {whole milk} 0.001016777 1 3.913649 10
## [10] {cream cheese ,
## domestic eggs,
## sugar} => {whole milk} 0.001118454 1 3.913649 11
All five rules have the same item listed on the right-hand side; whole milk, which is predictable given that it is the most frequently purchased item. They all have a confidence of 1 which means that a customer who buys the products listed on the right-hand side have a 100% probability of buying whole milk as well. However, all five rules have around average support and lift. The top rule states that a customer who buys rice and sugar is going to also buy milk.
When instead the data set is sorted by support (likelihood all the items will appear in the same transaction) there is one new addition to the right-hand side.
inspect(sort(rules, by = "support")[1:10])
## lhs rhs support confidence lift count
## [1] {citrus fruit,
## tropical fruit,
## root vegetables,
## whole milk} => {other vegetables} 0.003152008 0.8857143 4.577509 31
## [2] {other vegetables,
## curd,
## domestic eggs} => {whole milk} 0.002846975 0.8235294 3.223005 28
## [3] {hamburger meat,
## curd} => {whole milk} 0.002541942 0.8064516 3.156169 25
## [4] {herbs,
## rolls/buns} => {whole milk} 0.002440264 0.8000000 3.130919 24
## [5] {tropical fruit,
## herbs} => {whole milk} 0.002338587 0.8214286 3.214783 23
## [6] {citrus fruit,
## root vegetables,
## other vegetables,
## yogurt} => {whole milk} 0.002338587 0.8214286 3.214783 23
## [7] {pork,
## other vegetables,
## butter} => {whole milk} 0.002236909 0.8461538 3.311549 22
## [8] {tropical fruit,
## root vegetables,
## yogurt,
## rolls/buns} => {whole milk} 0.002236909 0.8148148 3.188899 22
## [9] {tropical fruit,
## grapes,
## whole milk} => {other vegetables} 0.002033554 0.8000000 4.134524 20
## [10] {root vegetables,
## other vegetables,
## yogurt,
## fruit/vegetable juice} => {whole milk} 0.002033554 0.8333333 3.261374 20
Other vegetables are the second most frequently purchased item so it is no surprise that it has shown up in our top 5 rules sorted by support.
To take a closer look and pinpoint rules involving the sale of whole milk the following code is run.
#What are customers likely to buy that would predict that they would buy milk?
rulesWholeMilk<-subset(rules, subset = rhs %in% "whole milk" & lift> 1.2)
inspect(sort(rulesWholeMilk, by = "confidence", decreasing = TRUE)[1:5])
## lhs rhs support confidence lift count
## [1] {rice,
## sugar} => {whole milk} 0.001220132 1 3.913649 12
## [2] {canned fish,
## hygiene articles} => {whole milk} 0.001118454 1 3.913649 11
## [3] {root vegetables,
## butter,
## rice} => {whole milk} 0.001016777 1 3.913649 10
## [4] {root vegetables,
## whipped/sour cream,
## flour} => {whole milk} 0.001728521 1 3.913649 17
## [5] {butter,
## soft cheese,
## domestic eggs} => {whole milk} 0.001016777 1 3.913649 10
#If a customer is buying milk what other item are they then likely to purchase?
rulesWholeMilk<-subset(rules, subset = lhs %in% "whole milk" & lift> 1.2)
inspect(sort(rulesWholeMilk, by = "confidence", decreasing = TRUE)[1:5])
## lhs rhs support confidence lift count
## [1] {tropical fruit,
## grapes,
## whole milk,
## yogurt} => {other vegetables} 0.001016777 1.0000000 5.168156 10
## [2] {ham,
## tropical fruit,
## pip fruit,
## whole milk} => {other vegetables} 0.001118454 1.0000000 5.168156 11
## [3] {whole milk,
## rolls/buns,
## soda,
## newspapers} => {other vegetables} 0.001016777 1.0000000 5.168156 10
## [4] {root vegetables,
## whole milk,
## yogurt,
## oil} => {other vegetables} 0.001423488 0.9333333 4.823612 14
## [5] {citrus fruit,
## tropical fruit,
## root vegetables,
## whole milk,
## yogurt} => {other vegetables} 0.001423488 0.9333333 4.823612 14
When whole milk is on the left-hand side we see that in the top five rules that other vegetables will be on the right-hand side. As previously stated this is unsurprising as other vegetables are a frequently purchased item. The second list (LHS) has above average lift and average to above average support which can be interpreted as the rules being relatively good.
If we were to pinpoint rules with other vegetables in it would be reasonable to expect to see other frequently purchase items in the transactions.
rulesOthrVeg<-subset(rules, subset = lhs %in% "other vegetables" & lift> 1.2)
inspect(sort(rulesOthrVeg, by = "confidence", decreasing = TRUE)[1:5])
## lhs rhs support confidence lift count
## [1] {root vegetables,
## other vegetables,
## yogurt,
## oil} => {whole milk} 0.001423488 1 3.913649 14
## [2] {root vegetables,
## other vegetables,
## butter,
## white bread} => {whole milk} 0.001016777 1 3.913649 10
## [3] {pork,
## other vegetables,
## butter,
## whipped/sour cream} => {whole milk} 0.001016777 1 3.913649 10
## [4] {other vegetables,
## butter,
## whipped/sour cream,
## domestic eggs} => {whole milk} 0.001220132 1 3.913649 12
## [5] {pip fruit,
## root vegetables,
## other vegetables,
## bottled water} => {whole milk} 0.001118454 1 3.913649 11
Sure enough, the right-hand side is populated with whole milk. The pattern that is showing up indicates that the best evaluation of customer behavior we can make using this analysis method is that customers buying more than one frequently purchased item is likely. This of course is common sense and probably did not require a market basket analysis to discover. People are likely to buy products that are part of a weekly grocery list and are generally considered dietary staples.
If we take the third most frequently purchased item, bread and rolls, we see that it follows this pattern.
rulesRollsBums<-subset(rules, subset = lhs %in% "rolls/buns" & lift> 1.2)
inspect(sort(rulesRollsBums, by = "confidence", decreasing = TRUE)[1:5])
## lhs rhs support confidence lift count
## [1] {whole milk,
## rolls/buns,
## soda,
## newspapers} => {other vegetables} 0.001016777 1.0000000 5.168156 10
## [2] {citrus fruit,
## whipped/sour cream,
## rolls/buns,
## pastry} => {whole milk} 0.001016777 1.0000000 3.913649 10
## [3] {sausage,
## tropical fruit,
## root vegetables,
## rolls/buns} => {whole milk} 0.001016777 1.0000000 3.913649 10
## [4] {beef,
## tropical fruit,
## yogurt,
## rolls/buns} => {whole milk} 0.001321810 0.9285714 3.634103 13
## [5] {tropical fruit,
## root vegetables,
## rolls/buns,
## bottled water} => {whole milk} 0.001118454 0.9166667 3.587512 11