Association Rules
Unsupervised Learning - Association Rules
Daria Ivanushenko
Review of the Data set
Dataset is taken form the dataset repository. It contains information on conducted transactions and items that were purchased. Data set contains 1862 transactions and 12 unique items to purchase.
library(arules)
transactions = read.transactions("transaction_data.csv", sep = ",", header = T, skip = 0, format = "basket")
transactions## transactions in sparse format with
## 1862 transactions (rows) and
## 12 items (columns)inspect(head(transactions))## items
## [1] {abrasive cleaner,
## coffee,
## fish,
## frozen meals,
## ice cream}
## [2] {baking powder,
## butter,
## coffee,
## frozen meals,
## ice cream}
## [3] {abrasive cleaner,
## butter,
## coffee,
## frozen vegetables,
## ice cream}
## [4] {baking powder,
## butter,
## frozen meals,
## ice cream}
## [5] {cake bar,
## coffee,
## frozen meals,
## frozen vegetables,
## ice cream}
## [6] {abrasive cleaner,
## domestic eggs,
## fish,
## honey}length(transactions)## [1] 1862itemFrequency(transactions, type="absolute")## abrasive cleaner baking powder butter cake bar
## 360 662 839 386
## coffee domestic eggs fish frozen meals
## 605 430 563 1001
## frozen vegetables grapes honey ice cream
## 541 445 355 554itemFrequencyPlot(transactions, topN=12, type="relative", main="Item Frequency") 
From the above graph we can say that frozen meals, butter and baking powder creating top 3 purchased products.
Association Rules
We are creating rules in our datasets with Apriori Algorithm.
rules.trans = apriori(transactions, parameter=list(supp=0.1, conf=0.5))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.5 0.1 1 none FALSE TRUE 5 0.1 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: 186
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[12 item(s), 1862 transaction(s)] done [0.00s].
## sorting and recoding items ... [12 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [31 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].rules.trans## set of 31 rulesHere we can see that 31 rules were created.
rules.trans2 = apriori(transactions, parameter=list(supp=0.05, conf=0.5))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.5 0.1 1 none FALSE TRUE 5 0.05 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: 93
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[12 item(s), 1862 transaction(s)] done [0.00s].
## sorting and recoding items ... [12 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [70 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].rules.trans2## set of 70 rulesWe can imply that the lower the support the higher number of rules to analyze we have to.I deciedd to stick with 31 rules.
rules.by.conf = sort(rules.trans, by="confidence", decreasing=TRUE)
inspect(head(rules.by.conf))## lhs rhs support confidence
## [1] {coffee} => {frozen meals} 0.3114930 0.9586777
## [2] {baking powder,coffee} => {frozen meals} 0.1331901 0.9575290
## [3] {baking powder,butter,coffee} => {frozen meals} 0.1015038 0.9450000
## [4] {coffee,fish} => {frozen meals} 0.1143931 0.9424779
## [5] {butter,coffee} => {frozen meals} 0.1552095 0.9322581
## [6] {baking powder,coffee} => {butter} 0.1074114 0.7722008
## coverage lift count
## [1] 0.3249194 1.783275 580
## [2] 0.1390977 1.781138 248
## [3] 0.1074114 1.757832 189
## [4] 0.1213749 1.753141 213
## [5] 0.1664876 1.734130 289
## [6] 0.1390977 1.713752 200Confidence is telling us the frequency of appearing item rhs in customer basket given the fact that item lhs is already there. The highest value confidence can take is 1 means that customer will always purchase item rhs together with item lhs. We can say that most probably customer will buy frozen meals having coffee, baking powder, fish and butter.
rules.by.lift = sort(rules.trans, by="lift", decreasing=TRUE)
inspect(head(rules.by.lift))## lhs rhs support confidence
## [1] {fish,frozen meals} => {coffee} 0.1143931 0.6339286
## [2] {baking powder,butter,frozen meals} => {coffee} 0.1015038 0.6096774
## [3] {baking powder,frozen meals} => {coffee} 0.1331901 0.6063570
## [4] {butter,coffee,frozen meals} => {baking powder} 0.1015038 0.6539792
## [5] {butter,coffee} => {baking powder} 0.1074114 0.6451613
## [6] {coffee} => {frozen meals} 0.3114930 0.9586777
## coverage lift count
## [1] 0.1804511 1.951033 213
## [2] 0.1664876 1.876396 189
## [3] 0.2196563 1.866176 248
## [4] 0.1552095 1.839440 189
## [5] 0.1664876 1.814638 200
## [6] 0.3249194 1.783275 580Lift is telling us about the frequency of purchasing product lhs and rhs together that separately. From the output we can say that fish, frozen meals and coffee are twice (lift is equal for 1.951) likely to be purchased together than separately. Value of lift higher than 1 implies that products are more likely to be purchased together that separately, value of lift less that 1 means that products are more likely to be bought separately.
rules.by.count = sort(rules.trans, by="count", decreasing=TRUE)
inspect(head(rules.by.count))## lhs rhs support confidence coverage lift
## [1] {} => {frozen meals} 0.5375940 0.5375940 1.0000000 1.000000
## [2] {coffee} => {frozen meals} 0.3114930 0.9586777 0.3249194 1.783275
## [3] {frozen meals} => {coffee} 0.3114930 0.5794206 0.5375940 1.783275
## [4] {butter} => {frozen meals} 0.2696026 0.5983313 0.4505908 1.112980
## [5] {frozen meals} => {butter} 0.2696026 0.5014985 0.5375940 1.112980
## [6] {baking powder} => {butter} 0.2658432 0.7477341 0.3555317 1.659453
## count
## [1] 1001
## [2] 580
## [3] 580
## [4] 502
## [5] 502
## [6] 495Count shows the number of transactions for each fo the combinations of the items. The most purchased are frozen meals and combination of frozen meals and coffee.
rules.by.supp = sort(rules.trans, by="support", decreasing=TRUE)
inspect(head(rules.by.supp))## lhs rhs support confidence coverage lift
## [1] {} => {frozen meals} 0.5375940 0.5375940 1.0000000 1.000000
## [2] {coffee} => {frozen meals} 0.3114930 0.9586777 0.3249194 1.783275
## [3] {frozen meals} => {coffee} 0.3114930 0.5794206 0.5375940 1.783275
## [4] {butter} => {frozen meals} 0.2696026 0.5983313 0.4505908 1.112980
## [5] {frozen meals} => {butter} 0.2696026 0.5014985 0.5375940 1.112980
## [6] {baking powder} => {butter} 0.2658432 0.7477341 0.3555317 1.659453
## count
## [1] 1001
## [2] 580
## [3] 580
## [4] 502
## [5] 502
## [6] 495Support is telling us how many times certain set of items appeared in out dataset. The highest support is around 54% for frozen meals meaning that only frozen meals were bought around 1000 times. We can notice that frozen meals appears in all transactions with the highest score of the support.
Graphical Ilustration
With the help of arulesViz package I will produce graphical illustration of the rules. I decided to create a smaller sample of rules with top 5 rules for the highest lift and provided graphical analysis. Idea of cutting the sample provided easier understanding of the graphs.
rules_5 <- head(rules.trans, n = 5, by = "lift")library(arulesViz)
plot(rules_5, method="graph")
This graph illustrates rules we produced with apriori algorithm with support equal to 10%. Graphs shows the relationships of the items in our dataset. Size of the circle represents support and color shows the lift.
plot(rules.trans, method = "paracoord")
Parallel coordinates plots is another variation of the graphical representation of the association rules. Color intensity is confidence and width of the arrow is support. Source.
Another great way of plotting association rules was found at Data Camp. Its an interactive version of previous plots and I think its great for plotting big numbers of rules. You can use dropdown list to filter be association rule, item name and item id. Also, you can zoom in the plot which helps to understand better the relationships.
plot(rules.trans, method = "graph", engine = "htmlwidget")