Association Rules
Menali
April 15, 2019
Introduction
Association Rules is a popular and well researched method for discovering interesting relations between variables in large databases. arules package in R provides a basic infrastructure for creating and manipulating input data sets and for analyzing the resulting item sets and rules.
Apriori Algorithm is used to find all rules (the default association type for apriori()) with a minimum support of 0.3% and a confidence of 0.5. Example of Apriori algorithm is market basket analysis. It provides insights into which products tend to be purchased together and which are most amenable to promotion. The drawback of Apriori algorithm is that it is slow and can generate lot of rules which might be difficult to understand, although visualization, filtering techniques might help.
Data
The data used here is ‘Groceries’. The Groceries 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 data set is provided for arules by Michael Hahsler, Kurt Hornik and Thomas Reutterer.
Libraries
Before proceeding, the important libraries that will be used for the analysis are
library(arules)
library(arulesViz)
library(tidyverse)Importing the data
Importing the data and summary of the data
data("Groceries")
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 sausageCouple of insights that can be derived from the summary :
- Density of 0.026 means 2.6 % are non-zero matrix cells.
- Dimensions: 9835 * 169
- Whole milk was purchased 2513 times which is 26% of the transactions
- 2519 transactions contained 1 item , while only 1 transaction had 32 items
- First quartile and median is 2 and 3 , which means that 25% of the transactions had 2 items and about half contained 3 items
Let’s see what Grocery data has in store for us:
grocery <- as(Groceries, 'data.frame')
head(grocery)## items
## 1 {citrus fruit,semi-finished bread,margarine,ready soups}
## 2 {tropical fruit,yogurt,coffee}
## 3 {whole milk}
## 4 {pip fruit,yogurt,cream cheese ,meat spreads}
## 5 {other vegetables,whole milk,condensed milk,long life bakery product}
## 6 {whole milk,butter,yogurt,rice,abrasive cleaner}Frequency of the first five items:
itemFrequency(Groceries[,1:5])## frankfurter sausage liver loaf ham meat
## 0.058973055 0.093950178 0.005083884 0.026029487 0.025826131Items with a support of atleast 10%
itemFrequencyPlot(Groceries, support= 0.10)
Items with a support of atleast 5%
itemFrequencyPlot(Groceries, support= 0.05)
Relative frequency of top 20 items
itemFrequencyPlot(Groceries, topN = 20)
Visualizing first 5 transactions
image(Groceries[1:5])
100 random transactions
image(sample(Groceries, 100))
Apriori algorithm
Finding items that are sold three times a day, therefore for a month, support = 90/9835
basket <- apriori(Groceries, parameter = list(support = 0.009, 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 0.009 2
## 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: 88
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [93 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [224 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].basket## set of 224 rulessummary(basket)## set of 224 rules
##
## rule length distribution (lhs + rhs):sizes
## 2 3
## 111 113
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.000 2.000 3.000 2.504 3.000 3.000
##
## summary of quality measures:
## support confidence lift count
## Min. :0.009049 Min. :0.2513 Min. :0.9932 Min. : 89.0
## 1st Qu.:0.010066 1st Qu.:0.2974 1st Qu.:1.5767 1st Qu.: 99.0
## Median :0.012303 Median :0.3603 Median :1.8592 Median :121.0
## Mean :0.016111 Mean :0.3730 Mean :1.9402 Mean :158.5
## 3rd Qu.:0.018480 3rd Qu.:0.4349 3rd Qu.:2.2038 3rd Qu.:181.8
## Max. :0.074835 Max. :0.6389 Max. :3.7969 Max. :736.0
##
## mining info:
## data ntransactions support confidence
## Groceries 9835 0.009 0.25Couple of insights from the summary are as follows:
- Gave a set of 224 rules , rule length distribution gives us how many items are present in how many rules
- 2 items are present in 111 rules
- 3 items are present in 113 rules
inspect(basket[1:10])## lhs rhs support confidence lift
## [1] {baking powder} => {whole milk} 0.009252669 0.5229885 2.046793
## [2] {grapes} => {other vegetables} 0.009049314 0.4045455 2.090754
## [3] {meat} => {other vegetables} 0.009964413 0.3858268 1.994013
## [4] {meat} => {whole milk} 0.009964413 0.3858268 1.509991
## [5] {frozen meals} => {whole milk} 0.009862735 0.3476703 1.360659
## [6] {hard cheese} => {other vegetables} 0.009456024 0.3858921 1.994350
## [7] {hard cheese} => {whole milk} 0.010066090 0.4107884 1.607682
## [8] {butter milk} => {other vegetables} 0.010371124 0.3709091 1.916916
## [9] {butter milk} => {whole milk} 0.011591256 0.4145455 1.622385
## [10] {ham} => {other vegetables} 0.009150991 0.3515625 1.816930
## count
## [1] 91
## [2] 89
## [3] 98
## [4] 98
## [5] 97
## [6] 93
## [7] 99
## [8] 102
## [9] 114
## [10] 90The first five rules are seen here. Also, we can see support for the top 10 most frequent items. We can see the lift column along with support and confidence. The lift of a rule measures how much likely an item or itemset is purchased relative to its typical rate of purchase, given that you know another item or itemsethas been purchased.
Sorting according to lift
inspect(sort(basket, by = "lift")[1:5]) ## lhs rhs support confidence lift count
## [1] {berries} => {whipped/sour cream} 0.009049314 0.2721713 3.796886 89
## [2] {tropical fruit,
## other vegetables} => {pip fruit} 0.009456024 0.2634561 3.482649 93
## [3] {pip fruit,
## other vegetables} => {tropical fruit} 0.009456024 0.3618677 3.448613 93
## [4] {citrus fruit,
## other vegetables} => {root vegetables} 0.010371124 0.3591549 3.295045 102
## [5] {tropical fruit,
## other vegetables} => {root vegetables} 0.012302999 0.3427762 3.144780 121- People who buy berries have 4 times tendency to buy whipped/sour cream than other customers
Taking subsets of Arules
Sometimes the marketing team requires to promote a specific product, say they want to promote berries, and want to find out how often and with which items the berries are purchased. The subset function enables one to find subsets of transactions, items or rules. The %in% operator is used for exact matching
Suppose I want to see it for berries:
berries <- subset(basket, items %in% "berries")
inspect(berries)## lhs rhs support confidence lift
## [1] {berries} => {whipped/sour cream} 0.009049314 0.2721713 3.796886
## [2] {berries} => {yogurt} 0.010574479 0.3180428 2.279848
## [3] {berries} => {other vegetables} 0.010269446 0.3088685 1.596280
## [4] {berries} => {whole milk} 0.011794611 0.3547401 1.388328
## count
## [1] 89
## [2] 104
## [3] 101
## [4] 116- Yoghurt and whipped/sour cream turned up with which Berries is purchased
Scatter Plot for 224 rules
plot(basket)## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
plot(basket, measure=c("support", "lift"), shading="confidence")## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
Shading by order (number of items contained in the rule)
plot(basket, shading="order", control=list(main = "Two-key plot"))## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
Interactive Scatter Plot
plot(basket, measure=c("support", "lift"), shading="confidence", interactive=TRUE)Group-based visualization
plot(basket, method="grouped")
Graph-based visualization
plot(basket, method="graph", control=list(type="items"))## Available control parameters (with default values):
## main = Graph for 100 rules
## nodeColors = c("#66CC6680", "#9999CC80")
## nodeCol = c("#EE0000FF", "#EE0303FF", "#EE0606FF", "#EE0909FF", "#EE0C0CFF", "#EE0F0FFF", "#EE1212FF", "#EE1515FF", "#EE1818FF", "#EE1B1BFF", "#EE1E1EFF", "#EE2222FF", "#EE2525FF", "#EE2828FF", "#EE2B2BFF", "#EE2E2EFF", "#EE3131FF", "#EE3434FF", "#EE3737FF", "#EE3A3AFF", "#EE3D3DFF", "#EE4040FF", "#EE4444FF", "#EE4747FF", "#EE4A4AFF", "#EE4D4DFF", "#EE5050FF", "#EE5353FF", "#EE5656FF", "#EE5959FF", "#EE5C5CFF", "#EE5F5FFF", "#EE6262FF", "#EE6666FF", "#EE6969FF", "#EE6C6CFF", "#EE6F6FFF", "#EE7272FF", "#EE7575FF", "#EE7878FF", "#EE7B7BFF", "#EE7E7EFF", "#EE8181FF", "#EE8484FF", "#EE8888FF", "#EE8B8BFF", "#EE8E8EFF", "#EE9191FF", "#EE9494FF", "#EE9797FF", "#EE9999FF", "#EE9B9BFF", "#EE9D9DFF", "#EE9F9FFF", "#EEA0A0FF", "#EEA2A2FF", "#EEA4A4FF", "#EEA5A5FF", "#EEA7A7FF", "#EEA9A9FF", "#EEABABFF", "#EEACACFF", "#EEAEAEFF", "#EEB0B0FF", "#EEB1B1FF", "#EEB3B3FF", "#EEB5B5FF", "#EEB7B7FF", "#EEB8B8FF", "#EEBABAFF", "#EEBCBCFF", "#EEBDBDFF", "#EEBFBFFF", "#EEC1C1FF", "#EEC3C3FF", "#EEC4C4FF", "#EEC6C6FF", "#EEC8C8FF", "#EEC9C9FF", "#EECBCBFF", "#EECDCDFF", "#EECFCFFF", "#EED0D0FF", "#EED2D2FF", "#EED4D4FF", "#EED5D5FF", "#EED7D7FF", "#EED9D9FF", "#EEDBDBFF", "#EEDCDCFF", "#EEDEDEFF", "#EEE0E0FF", "#EEE1E1FF", "#EEE3E3FF", "#EEE5E5FF", "#EEE7E7FF", "#EEE8E8FF", "#EEEAEAFF", "#EEECECFF", "#EEEEEEFF")
## edgeCol = c("#474747FF", "#494949FF", "#4B4B4BFF", "#4D4D4DFF", "#4F4F4FFF", "#515151FF", "#535353FF", "#555555FF", "#575757FF", "#595959FF", "#5B5B5BFF", "#5E5E5EFF", "#606060FF", "#626262FF", "#646464FF", "#666666FF", "#686868FF", "#6A6A6AFF", "#6C6C6CFF", "#6E6E6EFF", "#707070FF", "#727272FF", "#747474FF", "#767676FF", "#787878FF", "#7A7A7AFF", "#7C7C7CFF", "#7E7E7EFF", "#808080FF", "#828282FF", "#848484FF", "#868686FF", "#888888FF", "#8A8A8AFF", "#8C8C8CFF", "#8D8D8DFF", "#8F8F8FFF", "#919191FF", "#939393FF", "#959595FF", "#979797FF", "#999999FF", "#9A9A9AFF", "#9C9C9CFF", "#9E9E9EFF", "#A0A0A0FF", "#A2A2A2FF", "#A3A3A3FF", "#A5A5A5FF", "#A7A7A7FF", "#A9A9A9FF", "#AAAAAAFF", "#ACACACFF", "#AEAEAEFF", "#AFAFAFFF", "#B1B1B1FF", "#B3B3B3FF", "#B4B4B4FF", "#B6B6B6FF", "#B7B7B7FF", "#B9B9B9FF", "#BBBBBBFF", "#BCBCBCFF", "#BEBEBEFF", "#BFBFBFFF", "#C1C1C1FF", "#C2C2C2FF", "#C3C3C4FF", "#C5C5C5FF", "#C6C6C6FF", "#C8C8C8FF", "#C9C9C9FF", "#CACACAFF", "#CCCCCCFF", "#CDCDCDFF", "#CECECEFF", "#CFCFCFFF", "#D1D1D1FF", "#D2D2D2FF", "#D3D3D3FF", "#D4D4D4FF", "#D5D5D5FF", "#D6D6D6FF", "#D7D7D7FF", "#D8D8D8FF", "#D9D9D9FF", "#DADADAFF", "#DBDBDBFF", "#DCDCDCFF", "#DDDDDDFF", "#DEDEDEFF", "#DEDEDEFF", "#DFDFDFFF", "#E0E0E0FF", "#E0E0E0FF", "#E1E1E1FF", "#E1E1E1FF", "#E2E2E2FF", "#E2E2E2FF", "#E2E2E2FF")
## alpha = 0.5
## cex = 1
## itemLabels = TRUE
## labelCol = #000000B3
## measureLabels = FALSE
## precision = 3
## layout = NULL
## layoutParams = list()
## arrowSize = 0.5
## engine = igraph
## plot = TRUE
## plot_options = list()
## max = 100
## verbose = FALSE