Market Basket analysis of Cosmetics
seetharam annepu 71710036
8 September 2017
ifelse(require(arules),{library("arules")},install.packages("arules"))## Loading required package: arules## Warning: package 'arules' was built under R version 3.5.3## Loading required package: Matrix##
## Attaching package: 'arules'## The following objects are masked from 'package:base':
##
## abbreviate, write## [1] "arules"ifelse(require(readxl),{library("readxl")},install.packages("readxl"))## Loading required package: readxl## Warning: package 'readxl' was built under R version 3.5.3## [1] "readxl"ifelse(require(Matrix),{library("Matrix")},install.packages("Matrix"))## [1] "readxl"ifelse(require(arulesViz),{library("arulesViz")},install.packages("arulesViz"))## Loading required package: arulesViz## Warning: package 'arulesViz' was built under R version 3.5.3## Loading required package: grid## [1] "arulesViz"mydata<-read_excel(file.choose(),sheet =2,col_names = T)## New names:
## * `` -> `..2`mydata<-mydata[-2]
mydata<-mydata[-1]
cosmetics<-as.matrix(mydata)
nrow(cosmetics)## [1] 1000we need to convert the data frame into transactions type data. transaction matrix is a sparce matrix and acccepts only trasaction type data which is of the form citrus fruit, semi-finished bread, margarine, ready soups tropical fruit, yogurt, coffee
whole milk
pip fruit, yogurt, cream cheese, meat spreads
but what we have is a logical matrix Bag Blush Nail Polish Brushes Concealer Eyebrow Pencils Bronzer Lip liner Mascara Eye shadow Foundation Lip Gloss Lipstick Eyeliner 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0
hence we need to convert logical matrix into transaction type matrix
cosmetics <-apply(cosmetics,2,as.logical)
cosmetics <- as(cosmetics, "transactions")most purchased items
itemFrequency(cosmetics)## Bag Blush Nail Polish Brushes
## 0.054 0.363 0.280 0.149
## Concealer Eyebrow Pencils Bronzer Lip liner
## 0.442 0.042 0.279 0.234
## Mascara Eye shadow Foundation Lip Gloss
## 0.357 0.381 0.536 0.490
## Lipstick Eyeliner
## 0.322 0.457itemFrequencyPlot(cosmetics, support = 0.1)
image(cosmetics[1:10])
Now the building blocks of the association rule mining are
Support: percentage of transactions in antecedent and consequent co-occur Confidence: this is a conditional probability. given the probability of occurance of antecedent what is the probability of occurence of consequent and Lift:actual confidence divided by confidence of the pair assuming they are independent. in other words, lift is used to determine that the association is not random and the consequent is really dependent on the antecedent
enough of theory time to dig these rules out of the data
rules = apriori(cosmetics, parameter=list(support=0.1, confidence=0.8,minlen=1,maxlen=5))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 0.1 1
## maxlen target ext
## 5 rules FALSE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 100
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[14 item(s), 1000 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 ... [26 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].rules## set of 26 rulesinspect(head(sort(rules, by="lift"),15))## lhs rhs support confidence
## [1] {Brushes} => {Nail Polish} 0.149 1.0000000
## [2] {Blush,Concealer,Eye shadow} => {Mascara} 0.119 0.9596774
## [3] {Blush,Eye shadow} => {Mascara} 0.169 0.9285714
## [4] {Nail Polish,Eye shadow} => {Mascara} 0.119 0.9083969
## [5] {Concealer,Eye shadow} => {Mascara} 0.179 0.8905473
## [6] {Bronzer,Eye shadow} => {Mascara} 0.124 0.8794326
## [7] {Concealer,Eye shadow,Eyeliner} => {Mascara} 0.114 0.8769231
## [8] {Blush,Mascara} => {Eye shadow} 0.169 0.9184783
## [9] {Eye shadow,Lipstick} => {Mascara} 0.110 0.8527132
## [10] {Mascara,Lipstick} => {Eye shadow} 0.110 0.9090909
## [11] {Blush,Concealer,Mascara} => {Eye shadow} 0.119 0.9083969
## [12] {Bronzer,Mascara} => {Eye shadow} 0.124 0.9051095
## [13] {Mascara} => {Eye shadow} 0.321 0.8991597
## [14] {Eye shadow} => {Mascara} 0.321 0.8425197
## [15] {Nail Polish,Mascara} => {Eye shadow} 0.119 0.8880597
## lift count
## [1] 3.571429 149
## [2] 2.688172 119
## [3] 2.601040 169
## [4] 2.544529 119
## [5] 2.494530 179
## [6] 2.463397 124
## [7] 2.456367 114
## [8] 2.410704 169
## [9] 2.388552 110
## [10] 2.386065 110
## [11] 2.384244 119
## [12] 2.375615 124
## [13] 2.359999 321
## [14] 2.359999 321
## [15] 2.330865 119rules.sorted<-head(sort(rules, by="lift"),15)
inspect(head(sort(rules, by="lift"),1))## lhs rhs support confidence lift count
## [1] {Brushes} => {Nail Polish} 0.149 1 3.571429 149df.nail.brush<-data.frame(`nail polish`=mydata[,3],`Brushes`=mydata[,4])
table(df.nail.brush)## Brushes
## Nail.Polish 0 1
## 0 720 0
## 1 131 149hence Support for first rule: {Brushes} => {Nail Polish} is ((total people who bought both Brushes and nail polish together)/(total transactions)) = 149/1000 = 0.149 similarly Confidence(Brushes, Nail Polish) = P(Nail Polish/Brushes) = P(Brushes & Nail.Polish) / P(Brushes) = 0.149 / 0.149 = 1 = 100 % all the people who bought brushes bought nail polish. Lift Ratio = 1(from above)/0.28 = 3.5714 it is 3.5 times likely that brushes are bought with nail polish.
plot(rules)## To reduce overplotting, jitter is added! Use jitter = 0 to prevent jitter.
#plot(rules, method="matrix", measure="lift", control=list(reorder="support"))
plot(rules, method="paracoord",measure="lift", control=list(reorder=TRUE))
plot(rules, method="graph")
## igraph layout generators can be used (see ? igraph::layout_)
#plot(rules, method="graph", control=list(layout=igraph::in_circle()))
plot(rules, method="graph", control=list(type="itemsets"))## Warning: Unknown control parameters: type## Available control parameters (with default values):
## main = Graph for 26 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
Redundant rules can be found out by putting the antecedant and consequent in the same basket and building a matrix based on these rules. the matrix represents all rules created from same item set. the redundant rules are
subset.matrix <- is.subset(rules.sorted, rules.sorted)
subset.matrix<-subset.matrix*1
subset.matrix[lower.tri(subset.matrix, diag=T)] <- NA
redundant <- colSums(subset.matrix, na.rm=T) >= 1
which(redundant)## {Concealer,Mascara,Eye shadow,Eyeliner}
## 7
## {Blush,Mascara,Eye shadow}
## 8
## {Mascara,Eye shadow,Lipstick}
## 10
## {Blush,Concealer,Mascara,Eye shadow}
## 11
## {Bronzer,Mascara,Eye shadow}
## 12
## {Mascara,Eye shadow}
## 14
## {Nail Polish,Mascara,Eye shadow}
## 15The distinct rules with minimum basket length are
nonredundant <- colSums(subset.matrix, na.rm=T) <= 1
which(nonredundant)## {Nail Polish,Brushes}
## 1
## {Blush,Concealer,Mascara,Eye shadow}
## 2
## {Blush,Mascara,Eye shadow}
## 3
## {Nail Polish,Mascara,Eye shadow}
## 4
## {Concealer,Mascara,Eye shadow}
## 5
## {Bronzer,Mascara,Eye shadow}
## 6
## {Concealer,Mascara,Eye shadow,Eyeliner}
## 7
## {Blush,Mascara,Eye shadow}
## 8
## {Mascara,Eye shadow,Lipstick}
## 9
## {Mascara,Eye shadow,Lipstick}
## 10
## {Bronzer,Mascara,Eye shadow}
## 12
## {Mascara,Eye shadow}
## 13
## {Mascara,Eye shadow}
## 14rules.pruned <- rules.sorted[!redundant]
inspect(rules.pruned)## lhs rhs support confidence
## [1] {Brushes} => {Nail Polish} 0.149 1.0000000
## [2] {Blush,Concealer,Eye shadow} => {Mascara} 0.119 0.9596774
## [3] {Blush,Eye shadow} => {Mascara} 0.169 0.9285714
## [4] {Nail Polish,Eye shadow} => {Mascara} 0.119 0.9083969
## [5] {Concealer,Eye shadow} => {Mascara} 0.179 0.8905473
## [6] {Bronzer,Eye shadow} => {Mascara} 0.124 0.8794326
## [7] {Eye shadow,Lipstick} => {Mascara} 0.110 0.8527132
## [8] {Mascara} => {Eye shadow} 0.321 0.8991597
## lift count
## [1] 3.571429 149
## [2] 2.688172 119
## [3] 2.601040 169
## [4] 2.544529 119
## [5] 2.494530 179
## [6] 2.463397 124
## [7] 2.388552 110
## [8] 2.359999 321plot(rules.pruned, method="paracoord",measure="lift", control=list(reorder=TRUE))
plot(rules.pruned, method="graph")
Inferences and interpretation
From distinct rules we can infer that mascara and eye shadow has high association. hence we can recommend the retailer to place them together. Also, we can see that the blush is frequently purchased by customers who buy multiple items such as concealer, eye shadow and mascara, hence these can be offered as a special bundle. as expected brush has high correlation with nail polish.
Rule mining could also be used to build recommendation systems such as the very popular netflix recommendation system (rules can be formed from cast and directors along with genre). cosine similarity is another algorithm used to build recommendation system.