Association Analysis
Bradley Agwa
2022-04-04
Association Analysis
Context
Create association rules that will allow us to identify relationships between variables in the dataset. We have been provided with a dataset that comprises of groups of items that will be associated with others.
# We first we install the required arules library
#install.packages("arules")# Loading the arules library
library(arules, warn.conflicts = FALSE)## Warning: package 'arules' was built under R version 4.1.3## Loading required package: MatrixLoad data
path <- "http://bit.ly/SupermarketDatasetII"
super <- read.transactions(path, sep = ",")## Warning in asMethod(object): removing duplicated items in transactionssuper## transactions in sparse format with
## 7501 transactions (rows) and
## 119 items (columns)# Verifying the object's class
# This should show us transactions as the type of data that we will need
class(super)## [1] "transactions"
## attr(,"package")
## [1] "arules"# Previewing our first 5 transactions
inspect(super[1:5])## items
## [1] {almonds,
## antioxydant juice,
## avocado,
## cottage cheese,
## energy drink,
## frozen smoothie,
## green grapes,
## green tea,
## honey,
## low fat yogurt,
## mineral water,
## olive oil,
## salad,
## salmon,
## shrimp,
## spinach,
## tomato juice,
## vegetables mix,
## whole weat flour,
## yams}
## [2] {burgers,
## eggs,
## meatballs}
## [3] {chutney}
## [4] {avocado,
## turkey}
## [5] {energy bar,
## green tea,
## milk,
## mineral water,
## whole wheat rice}# Generating a summary of the supermarket dataset
# This would give us some information such as the most purchased items,
# distribution of the item sets (no. of items purchased in each transaction), etc.
summary(super)## transactions as itemMatrix in sparse format with
## 7501 rows (elements/itemsets/transactions) and
## 119 columns (items) and a density of 0.03288973
##
## most frequent items:
## mineral water eggs spaghetti french fries chocolate
## 1788 1348 1306 1282 1229
## (Other)
## 22405
##
## element (itemset/transaction) length distribution:
## sizes
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 1754 1358 1044 816 667 493 391 324 259 139 102 67 40 22 17 4
## 18 19 20
## 1 2 1
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 3.914 5.000 20.000
##
## includes extended item information - examples:
## labels
## 1 almonds
## 2 antioxydant juice
## 3 asparagusWe can see that mineral water leads in sales followed by eggs,sphagetti,french fries and chocolate.
# Exploring the frequency of some articles
# i.e. transacations ranging from 8 to 10 and performing
# some operation in percentage terms of the total transactions
itemFrequency(super[, 8:10],type = "absolute")## black tea blueberries body spray
## 107 69 86round(itemFrequency(super[, 8:10],type = "relative")*100,2)## black tea blueberries body spray
## 1.43 0.92 1.15# Displaying top 10 most common items in the transactions dataset
# and the items whose relative importance is at least 10%
#
par(mfrow = c(1, 2))
# plot the frequency of items
itemFrequencyPlot(super, topN = 10,col="darkgreen")
itemFrequencyPlot(super, support = 0.1,col="darkred")
# Building a model based on association rules
# using the apriori function
# We use Min Support as 0.001 and confidence as 0.8
rules <- apriori (super, parameter = list(supp = 0.001, conf = 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 TRUE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 7
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[119 item(s), 7501 transaction(s)] done [0.01s].
## sorting and recoding items ... [116 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 ... [74 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].rules## set of 74 rulesSince we built the model using 0.001 Min support and confidence as 0.8 we obtained 74 rules.
# we will see what happens if we increase the support or lower the confidence level
# Building a apriori model with Min Support as 0.002 and confidence as 0.8.
rules2 <- apriori (super,parameter = list(supp = 0.002, conf = 0.8)) ## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 0.002 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: 15
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[119 item(s), 7501 transaction(s)] done [0.00s].
## sorting and recoding items ... [115 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 done [0.00s].
## writing ... [2 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].rules2## set of 2 rulesThis gives us 2 rules which is too little.
# Building apriori model with Min Support as 0.002 and confidence as 0.6.
rules3 <- apriori (super, parameter = list(supp = 0.001, conf = 0.6)) ## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.6 0.1 1 none FALSE TRUE 5 0.001 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: 7
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[119 item(s), 7501 transaction(s)] done [0.00s].
## sorting and recoding items ... [116 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 ... [545 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].rules3## set of 545 rulesThis gives us 545 rules which is okay but we will use rules.
# More statistical information such as support, lift and confidence is also provided.
summary(rules)## set of 74 rules
##
## rule length distribution (lhs + rhs):sizes
## 3 4 5 6
## 15 42 16 1
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 4.000 4.000 4.041 4.000 6.000
##
## summary of quality measures:
## support confidence coverage lift
## Min. :0.001067 Min. :0.8000 Min. :0.001067 Min. : 3.356
## 1st Qu.:0.001067 1st Qu.:0.8000 1st Qu.:0.001333 1st Qu.: 3.432
## Median :0.001133 Median :0.8333 Median :0.001333 Median : 3.795
## Mean :0.001256 Mean :0.8504 Mean :0.001479 Mean : 4.823
## 3rd Qu.:0.001333 3rd Qu.:0.8889 3rd Qu.:0.001600 3rd Qu.: 4.877
## Max. :0.002533 Max. :1.0000 Max. :0.002666 Max. :12.722
## count
## Min. : 8.000
## 1st Qu.: 8.000
## Median : 8.500
## Mean : 9.419
## 3rd Qu.:10.000
## Max. :19.000
##
## mining info:
## data ntransactions support confidence
## super 7501 0.001 0.8
## call
## apriori(data = super, parameter = list(supp = 0.001, conf = 0.8))Most rules have 3 and 4 items though some rules do have upto 5 and 6.
# Observing rules built in our model i.e. first 5 model rules
inspect(rules[1:5])## lhs rhs support confidence
## [1] {frozen smoothie, spinach} => {mineral water} 0.001066524 0.8888889
## [2] {bacon, pancakes} => {spaghetti} 0.001733102 0.8125000
## [3] {nonfat milk, turkey} => {mineral water} 0.001199840 0.8181818
## [4] {ground beef, nonfat milk} => {mineral water} 0.001599787 0.8571429
## [5] {mushroom cream sauce, pasta} => {escalope} 0.002532996 0.9500000
## coverage lift count
## [1] 0.001199840 3.729058 8
## [2] 0.002133049 4.666587 13
## [3] 0.001466471 3.432428 9
## [4] 0.001866418 3.595877 12
## [5] 0.002666311 11.976387 19If someone buys frozen smoothie and spinach they are 89% likely to buy mineral water.
# Ordering the rules by a criteria such as the level of confidence
# then looking at the first five rules.
rules<-sort(rules, by="confidence", decreasing=TRUE)
inspect(rules[1:5])## lhs rhs support confidence coverage lift count
## [1] {french fries,
## mushroom cream sauce,
## pasta} => {escalope} 0.001066524 1.00 0.001066524 12.606723 8
## [2] {ground beef,
## light cream,
## olive oil} => {mineral water} 0.001199840 1.00 0.001199840 4.195190 9
## [3] {cake,
## meatballs,
## mineral water} => {milk} 0.001066524 1.00 0.001066524 7.717078 8
## [4] {cake,
## olive oil,
## shrimp} => {mineral water} 0.001199840 1.00 0.001199840 4.195190 9
## [5] {mushroom cream sauce,
## pasta} => {escalope} 0.002532996 0.95 0.002666311 11.976387 19The first four rules have a confidence of 100%.
# If we're interested in making a promotion relating to the sale of milk,
# we could create a subset of rules concerning these products
# This would tell us the items that the customers bought before purchasing mineral
milk <- subset(rules, subset = rhs %pin% "milk")
# Then order by confidence
milk <-sort(milk, by="count", decreasing=TRUE)
inspect(milk[1:5])## lhs rhs support confidence
## [1] {meatballs, whole wheat pasta} => {milk} 0.001333156 0.8333333
## [2] {black tea, frozen smoothie} => {milk} 0.001199840 0.8181818
## [3] {cake, meatballs, mineral water} => {milk} 0.001066524 1.0000000
## [4] {escalope, hot dogs, mineral water} => {milk} 0.001066524 0.8888889
## [5] {burgers, ground beef, olive oil} => {milk} 0.001066524 0.8000000
## coverage lift count
## [1] 0.001599787 6.430898 10
## [2] 0.001466471 6.313973 9
## [3] 0.001066524 7.717078 8
## [4] 0.001199840 6.859625 8
## [5] 0.001333156 6.173663 8meatballs,whole wheat pasta had been in 10 baskets.
black tea,frozen smoothie had been in 9 baskets.
cake,meatballs,mineral water had been in 8 baskets.