27 min read

Practical Introduction to Market Basket Analysis - Asociation Rules

Introduction

Ever wondered why items are displayed in a particular way in retail/online stores. Why certain items are suggested to you based on what you have added to the cart? Blame it on market basket analysis or association rule mining.

Resources

Below are the links to all the resources related to this post:

What?

Market basket analysis uses association rule mining under the hood to identify products frequently bought together. Before we get into the nitty gritty of market basket analysis, let us get a basic understanding of association rule mining. It finds association between different objects in a set. In the case of market basket analysis, the objects are the products purchased by a cusomter and the set is the transaction. In short, market basket analysis

  • is a unsupervised data mining technique
  • that uncovers products frequently bought together
  • and creates if-then scenario rules

Why ?

Market basket analysis creates actionable insights for:

  • designing store layout
  • online recommendation engines
  • targeted marketing campaign/sales promotion/email campaign
  • cross/up selling
  • catalogue design

Advantages

Market basket analysisis is cost effective as data required is readily available through electronic point of sale systems. It generates actionable insights for product placement, cross/up selling strategies, targeted marketing campaigns, catalogue design, pricing strategies, inventory control etc.

Use Cases

Association rule mining has applications in several industries including retail, telecommunications, banking, insurance, manufacturing and medical. Let us look at its applications in more detail in the following industries:

Retail

The introduction of electronic point of sale systems have allowed the collection of immense amounts of data and retail organizations make prolifc use of market basket analysis for

  • designing store layout so that consumers can more easily find items that are frequently purchased together
  • recommending associated products that are frequently bought together, “Customers who purchased this product also viewed this product…”
  • emailing customers who bought products specific products with other products and offers on those products that are likely to be interesting to them.
  • grouping products that customers purchase frequently together in the store’s product placement
  • designing special promotions that combine or discount certain products
  • optimizing the layout of the catalog of an eCommerce site
  • controlling inventory based on product demands and what products sell better together

Banks

Banks and financial institutions use market basket analysis to analyze credit card purchases for fraud detection and cross sell insurance products, investment products (mutual funds etc.), tax preparation, retirement planning, wealth management etc. It can also be used for next best offer, sequence and seasonal offers.

Telecommunications

The telecommunications industry is characterized by high volatility and low customer loyalty due to lucrative offers for new customers from other service providers. The more services a customer uses from a particular operator, the harder it gets for him/her to switch to another operator. Market basket analysis is used to bundle mobile, landline, TV and internet services to customers to increase stickiness and reduce churn.

course ad

Simple Example

Before we move on to the case study, let us use a simple example to understand the important terminologies that we will come across in the rest of the tutorial. In the example, the transactions include the following products:

  • mobile phones
  • ear phones
  • USB cable
  • power bank
  • screen guard
  • mobile case cover
  • modem/router
  • mouse
  • external hard drive

Steps

The two important steps in market basket analysis are:

  • frequent itemset generation
  • rules generation

We will discuss these steps in more detail in the case study.

Itemset

Itemset is the collection of items purchased by a customer. In our example, mobile phone and screen guard are a frequent intemset. They are present in 3 out of 5 transactions.

Antecedent & Consequent

Antecedent is the items of the left hand side of the rule and consequent is the right hand side of the rule. In our example, mobile phone is the antecedent and screen guard is the consequent.

Support

Support is the probability of the antecedent event occuring. It is the relative frequency of the itemset. If it is less than 50% then the association is considered less fruitful. In our example, support is the relative frequency of transactions that include both mobile phone and screen guard.

Confidence

Confidence is the probability the consequent will co-occur with the antecedent. It expresses the operational efficiency of the rule. In our example, it is the probability that a customer will purchase screen guard provided that he has already bought the mobile phone.

Lift

The lift ratio calculates the efficiency of the rule in finding consequences, compared to a random selection of transactions. Generally, a Lift ratio of greater than one suggests some applicability of the rule.To compute the lift for a rule, divide the support of the itemset by the product of the support for antecedent and consequent. Now, let us understand how to interpret lift.

Interpretation

  • Lift = 1: implies no relationship between mobile phone and screen guard (i.e., mobile phone and screen guard occur together only by chance)
  • Lift > 1: implies that there is a positive relationship between mobile phone and screen guard (i.e., mobile phone and screen guard occur together more often than random)
  • Lift < 1: implies that there is a negative relationship between mobile phone and screen guard (i.e., mobile phone and screen guard occur together less often than random)

youtube ad

Data

Two public data sets are available for users to explore and learn market basket analysis:

The groceries data set is available in the arules package as well. In this tutorial, we will use the UCI data set as it closely resembles real world data sets giving us a chance to reshape the data and restructure it in format required by the arules package.

Data Dictionary

  • invoice number
  • stock code
  • description
  • quantity
  • invoice date
  • unit price
  • customer id
  • country

Libraries

library(readxl)
library(readr)
library(arules)
library(arulesViz)
library(magrittr)
library(dplyr)
library(lubridate)
library(forcats)
library(ggplot2)

Preprocessing

This section is optional. You can skip to the Read Data section without any loss of continuity.

As shown above, the data set has one row per item. We have created a tiny R package mbar,
for data pre-processing. It can be installed from GitHub as shown below:

# install.packages("devtools")
devtools::install_github("rsquaredacademy/mbar")

We will use mbar_prep_data() from the mbar package to reshape the data so that there is one row per transaction with items across columns excluding the column names.

library(mbar)
mba_data     <- read_excel("online-retail.xlsx")
transactions <- mbar_prep_data(mba_data, InvoiceNo, Description)
head(transactions)
## # A tibble: 6 x 1,114
##   item_1 item_2 item_3 item_4 item_5 item_6 item_7 item_8 item_9 item_10
##   <chr>  <chr>  <chr>  <chr>  <chr>  <chr>  <chr>  <chr>  <chr>  <chr>  
## 1 WHITE~ WHITE~ CREAM~ KNITT~ RED W~ SET 7~ GLASS~ ""     ""     ""     
## 2 HAND ~ HAND ~ ""     ""     ""     ""     ""     ""     ""     ""     
## 3 ASSOR~ POPPY~ POPPY~ FELTC~ IVORY~ BOX O~ BOX O~ BOX O~ HOME ~ LOVE B~
## 4 JAM M~ RED C~ YELLO~ BLUE ~ ""     ""     ""     ""     ""     ""     
## 5 BATH ~ ""     ""     ""     ""     ""     ""     ""     ""     ""     
## 6 ALARM~ ALARM~ ALARM~ PANDA~ STARS~ INFLA~ VINTA~ SET/2~ ROUND~ SPACEB~
## # ... with 1,104 more variables: item_11 <chr>, item_12 <chr>,
## #   item_13 <chr>, item_14 <chr>, item_15 <chr>, item_16 <chr>,
## #   item_17 <chr>, item_18 <chr>, item_19 <chr>, item_20 <chr>,
## #   item_21 <chr>, item_22 <chr>, item_23 <chr>, item_24 <chr>,
## #   item_25 <chr>, item_26 <chr>, item_27 <chr>, item_28 <chr>,
## #   item_29 <chr>, item_30 <chr>, item_31 <chr>, item_32 <chr>,
## #   item_33 <chr>, item_34 <chr>, item_35 <chr>, item_36 <chr>,
## #   item_37 <chr>, item_38 <chr>, item_39 <chr>, item_40 <chr>,
## #   item_41 <chr>, item_42 <chr>, item_43 <chr>, item_44 <chr>,
## #   item_45 <chr>, item_46 <chr>, item_47 <chr>, item_48 <chr>,
## #   item_49 <chr>, item_50 <chr>, item_51 <chr>, item_52 <chr>,
## #   item_53 <chr>, item_54 <chr>, item_55 <chr>, item_56 <chr>,
## #   item_57 <chr>, item_58 <chr>, item_59 <chr>, item_60 <chr>,
## #   item_61 <chr>, item_62 <chr>, item_63 <chr>, item_64 <chr>,
## #   item_65 <chr>, item_66 <chr>, item_67 <chr>, item_68 <chr>,
## #   item_69 <chr>, item_70 <chr>, item_71 <chr>, item_72 <chr>,
## #   item_73 <chr>, item_74 <chr>, item_75 <chr>, item_76 <chr>,
## #   item_77 <chr>, item_78 <chr>, item_79 <chr>, item_80 <chr>,
## #   item_81 <chr>, item_82 <chr>, item_83 <chr>, item_84 <chr>,
## #   item_85 <chr>, item_86 <chr>, item_87 <chr>, item_88 <chr>,
## #   item_89 <chr>, item_90 <chr>, item_91 <chr>, item_92 <chr>,
## #   item_93 <chr>, item_94 <chr>, item_95 <chr>, item_96 <chr>,
## #   item_97 <chr>, item_98 <chr>, item_99 <chr>, item_100 <chr>,
## #   item_101 <chr>, item_102 <chr>, item_103 <chr>, item_104 <chr>,
## #   item_105 <chr>, item_106 <chr>, item_107 <chr>, item_108 <chr>,
## #   item_109 <chr>, item_110 <chr>, ...

EDA

Before we generate the rules using the arules package, let us explore the data set a bit.

What time of day do people purchase?

purchase_time <-
  mba_data %>%
  group_by(InvoiceDate) %>%
  slice(1) %>%
  mutate(time_of_day = hour(InvoiceDate)) %>%
  pull(time_of_day) %>%
  as.factor() %>%
  fct_count()

purchase_time %>%
  ggplot() +
  geom_col(aes(x = f, y = n), fill = "blue") +
  xlab("Hour of Day") + ylab("Transactions") +
  ggtitle("Hourly Transaction Distribution")  

How many items are purchased on an average?

items <- 
  mba_data %>%
  group_by(InvoiceNo) %>%
  summarize(count = n()) %>%
  pull(count) 

mean(items)
## [1] 20.92313
median(items)
## [1] 10

Most Purchased Items

mba_data %>%
  group_by(Description) %>%
  summarize(count = n()) %>%
  arrange(desc(count))
## # A tibble: 4,212 x 2
##    Description                        count
##    <chr>                              <int>
##  1 WHITE HANGING HEART T-LIGHT HOLDER  2369
##  2 REGENCY CAKESTAND 3 TIER            2200
##  3 JUMBO BAG RED RETROSPOT             2159
##  4 PARTY BUNTING                       1727
##  5 LUNCH BAG RED RETROSPOT             1638
##  6 ASSORTED COLOUR BIRD ORNAMENT       1501
##  7 SET OF 3 CAKE TINS PANTRY DESIGN    1473
##  8 <NA>                                1454
##  9 PACK OF 72 RETROSPOT CAKE CASES     1385
## 10 LUNCH BAG  BLACK SKULL.             1350
## # ... with 4,202 more rows

Average Order Value

total_revenue <- 
  mba_data %>%
  group_by(InvoiceNo) %>%
  summarize(order_sum = sum(UnitPrice)) %>%
  pull(order_sum) %>%
  sum()

total_transactions <- 
  mba_data %>%
  group_by(InvoiceNo) %>%
  summarize(n()) %>%
  nrow()

total_revenue / total_transactions
## [1] 96.47892

Read Data

It is now time to read data into R. We will use read.transactions() from arules package. The data cannot be read using read.csv() or read_csv() owing to the way it is structured. We will read the transaction_data.csv file as it contains the data we had modified in the previous step. We need to specify the following in order to read the data set:

  • name of the data set within quotes (single or double)
  • the format of the data, if each line represnts a transaction, use basket, and if each line represents an item in the transaction, use single
  • the separator used to separate the items in a transaction

In our data set, each line represents a transaction and the items in the transaction are separated by a ,.

basket_data <- read.transactions("transaction_data.csv", format = "basket", 
  sep = ",")
basket_data
## transactions in sparse format with
##  25901 transactions (rows) and
##  10085 items (columns)

The read.transactions() function allows you to read data where each row represents a item and not a transaction. In that case, the format argument should be set to the value single and the cols argument should specify the names or positions of the columns that represent the transaction id and item id. We tried to read data in this way as well but failed to do so. However, the code is available below for other users to try and let us know if you find a way to get it to work or spot any mistakes we may have made.

get_data <- read.transactions("retail.csv", 
  format = "single",
  sep = ",",
  cols = c("InvoiceNo", "item"))

We were able to read the data when we removed the sep argument from the above code, but the result from the summary() function was way different than what we see in the next section i.e. it showed higher number of transactions and items.

Data Summary

To get a quick overview of the data, use summary(). It will return the following:

  • number of transactions
  • number of items
  • most frequent items
  • distribution of items
  • five number summary
summary(basket_data)
## transactions as itemMatrix in sparse format with
##  25901 rows (elements/itemsets/transactions) and
##  10085 columns (items) and a density of 0.001660018 
## 
## most frequent items:
## WHITE HANGING HEART T-LIGHT HOLDER           REGENCY CAKESTAND 3 TIER 
##                               1999                               1914 
##            JUMBO BAG RED RETROSPOT                      PARTY BUNTING 
##                               1806                               1488 
##            LUNCH BAG RED RETROSPOT                            (Other) 
##                               1404                             425005 
## 
## element (itemset/transaction) length distribution:
## sizes
##    0    1    2    3    4    5    6    7    8    9   10   11   12   13   14 
## 1454 4578 1727 1208  942  891  781  715  696  683  612  642  547  530  543 
##   15   16   17   18   19   20   21   22   23   24   25   26   27   28   29 
##  555  537  479  459  491  428  405  328  311  280  248  261  235  221  233 
##   30   31   32   33   34   35   36   37   38   39   40   41   42   43   44 
##  224  175  174  145  149  139  122  119  100  117   98   94  102   93   72 
##   45   46   47   48   49   50   51   52   53   54   55   56   57   58   59 
##   73   74   71   69   68   59   70   49   49   54   57   42   32   42   39 
##   60   61   62   63   64   65   66   67   68   69   70   71   72   73   74 
##   34   40   22   27   30   24   34   28   25   21   23   26   14   17   24 
##   75   76   77   78   79   80   81   82   83   84   85   86   87   88   89 
##   11   18   14   13   10   16   18   15   10    9   16   13   16   13    7 
##   90   91   92   93   94   95   96   97   98   99  100  101  102  103  104 
##    8   12   12    8    7    7    4    7    9    5    8    8    4    5    7 
##  105  106  107  108  109  110  111  112  113  114  115  116  117  118  119 
##    2    3    7    9    4    7    4    2    7    1    1    4    7    6    2 
##  120  121  122  123  124  125  126  127  129  130  131  132  133  134  135 
##    3    5    4    4    2    5    6    2    1    4    3    6    6    3    4 
##  136  137  138  139  140  141  142  143  144  145  146  147  148  149  150 
##    3    2    1    1    3    8    5    3    4    4    6    2    3    1    4 
##  151  152  153  154  155  156  157  158  159  160  162  163  164  167  168 
##    3    2    4    7    3    3    5    2    4    5    1    2    1    3    5 
##  169  170  171  172  173  174  175  176  177  178  179  180  181  182  183 
##    2    2    4    3    1    3    5    1    2    2    2    2    1    2    1 
##  184  185  186  187  189  190  192  193  194  196  197  198  201  202  204 
##    2    1    1    2    2    1    1    5    1    2    3    2    1    1    2 
##  205  206  207  208  209  212  213  215  219  220  224  226  227  228  230 
##    2    1    3    3    2    1    2    2    7    1    3    3    1    1    2 
##  232  234  236  238  240  241  244  248  249  250  252  256  257  258  260 
##    1    2    1    2    2    2    1    1    2    2    1    1    1    1    2 
##  261  263  265  266  270  272  281  284  285  298  299  301  303  304  305 
##    1    2    1    1    1    1    1    1    2    1    2    1    1    1    3 
##  312  314  316  320  321  326  327  329  332  333  338  339  341  344  348 
##    2    1    1    2    1    1    1    1    1    1    1    1    1    2    1 
##  350  360  365  367  375  391  394  398  400  402  405  411  419  422  429 
##    1    2    1    1    3    1    1    1    1    1    1    1    2    1    1 
##  431  442  447  460  468  471  477  509  514  530  587  627 1114 
##    2    1    1    1    1    1    1    1    1    1    1    1    1 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00    2.00    8.00   16.74   20.00 1114.00 
## 
## includes extended item information - examples:
##                    labels
## 1   *Boombox Ipod Classic
## 2 *USB Office Mirror Ball
## 3                       ?

Item Frequency Plot

The most frequent items in the data set can be plotted using itemFrequencyPlot(). We can specify the number of items to be plotted and whether the Y axis should represent the absolute or relative number of transactions that include the item.

The topN argument can be used to specify the number of items to be plotted and the type argument can be used to specify whether the Y axis represents absolute/relative frequency of the items.

itemFrequencyPlot(basket_data, topN = 10, type = 'absolute')

In the below plot, the Y axis represents the relative frequency of the items plotted.

itemFrequencyPlot(basket_data, topN = 10, type = 'relative')

apps ad

Generate Rules

Finally, to the part you all have been waiting for, rules generation. The apriori() function is used for generating the rules. We will first learn the different inputs that must be specified and later on play around with them and see how the rules generated change.

The first input is the data set, which in our case is basket_data. Next, we will supply the mining parameters using the parameter argument:

  • supp: minimum support for an itemset
  • conf: minimum confidence
  • maxlen: maximum number of items the antecedent may include
  • target: the type of association mined i.e. rules

The parameter argument takes several additional inputs but to get started, it is sufficient to know those mentioned above. All the inputs are supplied using a list().

For our case study, we will specify the following:

  • support: 0.009
  • confidence: 0.8
  • maxlen: 4

Keep in mind, mining association rules with very low values for support will result in a large number of rules being generated, resulting in long execution time and the process will eventually run out of memory.

rules <- apriori(basket_data, parameter = list(supp=0.009, conf=0.8, 
    target = "rules", maxlen = 4))
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.8    0.1    1 none FALSE            TRUE       5   0.009      1
##  maxlen target   ext
##       4  rules FALSE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 233 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[10085 item(s), 25901 transaction(s)] done [1.09s].
## sorting and recoding items ... [508 item(s)] done [0.05s].
## creating transaction tree ... done [0.08s].
## checking subsets of size 1 2 3 4
## Warning in apriori(basket_data, parameter = list(supp = 0.009, conf =
## 0.8, : Mining stopped (maxlen reached). Only patterns up to a length of 4
## returned!
##  done [0.08s].
## writing ... [22 rule(s)] done [0.00s].
## creating S4 object  ... done [0.03s].

Change the values of supp, conf and maxlen, and observe how the rules generated change.

Rules Summary

Once the rules have been generated by apriori(), we can use summary() to get some basic information such as rule length distribution.

summary(rules)
## set of 22 rules
## 
## rule length distribution (lhs + rhs):sizes
##  2  3  4 
## 11  9  2 
## 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.000   2.000   2.500   2.591   3.000   4.000 
## 
## summary of quality measures:
##     support           confidence          lift           count      
##  Min.   :0.009034   Min.   :0.8035   Min.   :22.59   Min.   :234.0  
##  1st Qu.:0.010453   1st Qu.:0.8530   1st Qu.:25.02   1st Qu.:270.8  
##  Median :0.013223   Median :0.8868   Median :55.94   Median :342.5  
##  Mean   :0.012760   Mean   :0.9120   Mean   :48.55   Mean   :330.5  
##  3rd Qu.:0.014362   3rd Qu.:1.0000   3rd Qu.:61.23   3rd Qu.:372.0  
##  Max.   :0.018339   Max.   :1.0000   Max.   :71.30   Max.   :475.0  
## 
## mining info:
##         data ntransactions support confidence
##  basket_data         25901   0.009        0.8

The output from summary() does not display the rules though. To view the rules, we have to use inspect().

Inspect Rules

The inspect() function will display the rules along with:

  • support
  • confidence
  • lift
  • count

Before you inspect the rules, you can sort it by support, confidence or lift. In the below, output, we sort the rules by confidence in descending order before inspecting them.

basket_rules <- sort(rules, by = 'confidence', decreasing = TRUE)
inspect(basket_rules[1:10])
##      lhs                                  rhs                                   support confidence     lift count
## [1]  {BACK DOOR}                       => {KEY FOB}                         0.009613528  1.0000000 61.23168   249
## [2]  {SET 3 RETROSPOT TEA}             => {SUGAR}                           0.014362380  1.0000000 69.62634   372
## [3]  {SUGAR}                           => {SET 3 RETROSPOT TEA}             0.014362380  1.0000000 69.62634   372
## [4]  {SET 3 RETROSPOT TEA}             => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [5]  {SUGAR}                           => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [6]  {SHED}                            => {KEY FOB}                         0.011273696  1.0000000 61.23168   292
## [7]  {SET 3 RETROSPOT TEA,                                                                                       
##       SUGAR}                           => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [8]  {COFFEE,                                                                                                    
##       SET 3 RETROSPOT TEA}             => {SUGAR}                           0.014362380  1.0000000 69.62634   372
## [9]  {COFFEE,                                                                                                    
##       SUGAR}                           => {SET 3 RETROSPOT TEA}             0.014362380  1.0000000 69.62634   372
## [10] {PINK REGENCY TEACUP AND SAUCER,                                                                            
##       REGENCY CAKESTAND 3 TIER,                                                                                  
##       ROSES REGENCY TEACUP AND SAUCER} => {GREEN REGENCY TEACUP AND SAUCER} 0.009999614  0.8900344 25.16679   259

Redundant & Non Redundant Rules

Redundant Rules

A rule is redundant if a more general rules with the same or a higher confidence exists. That is, a more specific rule is redundant if it is only equally or even less predictive than a more general rule. A rule is more general if it has the same RHS but one or more items removed from the LHS.

Example 1

In the above example, the first rule has the same support, condifence and lift as the next two rules. The second item in the left hand side of the rule is not adding any value and as such makes the rule redundant.

Example 2

In the above example, the first two rules have the same support, condifence and lift. The third rule differs only with respect to lift.

Example 3

In the above example, the first and third rule have the same support, condifence and lift. The second rule is different with respect to confidence and lift.

Now that we have understood what redundant rules are and how to identify them, let us use the below R code to inspect them.

inspect(rules[is.redundant(rules)])
##     lhs                             rhs                   support   
## [1] {SET 3 RETROSPOT TEA,SUGAR}  => {COFFEE}              0.01436238
## [2] {COFFEE,SET 3 RETROSPOT TEA} => {SUGAR}               0.01436238
## [3] {COFFEE,SUGAR}               => {SET 3 RETROSPOT TEA} 0.01436238
##     confidence lift     count
## [1] 1          55.94168 372  
## [2] 1          69.62634 372  
## [3] 1          69.62634 372

Non-redundant Rules

Now let us look at the non-redundant rules.

inspect(rules[!is.redundant(rules)])
##      lhs                                     rhs                                   support confidence     lift count
## [1]  {REGENCY TEA PLATE PINK}             => {REGENCY TEA PLATE GREEN}         0.009034400  0.8863636 71.29722   234
## [2]  {BACK DOOR}                          => {KEY FOB}                         0.009613528  1.0000000 61.23168   249
## [3]  {SET 3 RETROSPOT TEA}                => {SUGAR}                           0.014362380  1.0000000 69.62634   372
## [4]  {SUGAR}                              => {SET 3 RETROSPOT TEA}             0.014362380  1.0000000 69.62634   372
## [5]  {SET 3 RETROSPOT TEA}                => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [6]  {COFFEE}                             => {SET 3 RETROSPOT TEA}             0.014362380  0.8034557 55.94168   372
## [7]  {SUGAR}                              => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [8]  {COFFEE}                             => {SUGAR}                           0.014362380  0.8034557 55.94168   372
## [9]  {REGENCY TEA PLATE GREEN}            => {REGENCY TEA PLATE ROSES}         0.010347091  0.8322981 55.99313   268
## [10] {SHED}                               => {KEY FOB}                         0.011273696  1.0000000 61.23168   292
## [11] {SET/6 RED SPOTTY PAPER CUPS}        => {SET/6 RED SPOTTY PAPER PLATES}   0.012084476  0.8087855 44.38211   313
## [12] {SET/20 RED RETROSPOT PAPER NAPKINS,                                                                           
##       SET/6 RED SPOTTY PAPER CUPS}        => {SET/6 RED SPOTTY PAPER PLATES}   0.009111617  0.8872180 48.68609   236
## [13] {PINK REGENCY TEACUP AND SAUCER,                                                                               
##       ROSES REGENCY TEACUP AND SAUCER}    => {GREEN REGENCY TEACUP AND SAUCER} 0.018339060  0.8828996 24.96505   475
## [14] {GREEN REGENCY TEACUP AND SAUCER,                                                                              
##       PINK REGENCY TEACUP AND SAUCER}     => {ROSES REGENCY TEACUP AND SAUCER} 0.018339060  0.8512545 22.59051   475
## [15] {PINK REGENCY TEACUP AND SAUCER,                                                                               
##       REGENCY CAKESTAND 3 TIER}           => {ROSES REGENCY TEACUP AND SAUCER} 0.011235087  0.8584071 22.78033   291
## [16] {PINK REGENCY TEACUP AND SAUCER,                                                                               
##       REGENCY CAKESTAND 3 TIER}           => {GREEN REGENCY TEACUP AND SAUCER} 0.011312305  0.8643068 24.43931   293
## [17] {STRAWBERRY CHARLOTTE BAG,                                                                                     
##       WOODLAND CHARLOTTE BAG}             => {RED RETROSPOT CHARLOTTE BAG}     0.010771785  0.8110465 23.65644   279
## [18] {PINK REGENCY TEACUP AND SAUCER,                                                                               
##       REGENCY CAKESTAND 3 TIER,                                                                                     
##       ROSES REGENCY TEACUP AND SAUCER}    => {GREEN REGENCY TEACUP AND SAUCER} 0.009999614  0.8900344 25.16679   259
## [19] {GREEN REGENCY TEACUP AND SAUCER,                                                                              
##       PINK REGENCY TEACUP AND SAUCER,                                                                               
##       REGENCY CAKESTAND 3 TIER}           => {ROSES REGENCY TEACUP AND SAUCER} 0.009999614  0.8839590 23.45843   259

What influenced purchase of product X?

So far, we have learnt how to generate, inspect and prune rules. Now, how do we use these rules? To make business sense, we need to come up with a set of rules that can be used either for product placement in physical stores or as recommendations in an online store or for targeted marketing via email campaigns etc. To achieve that, we need to know 2 things:

  • what products influenced the purchase of product X?
  • what purchases did product X influence?

For our case study, we can modify the above questions as:

What influenced the purchase of sugar?

To view the products which influenced the purchase of sugar, we will continue to use the apriori() function but add one more argument, appearance. It restricts the appearance of the items. Since we want the right hand side of the rules to have only one value, sugar, we will set the rhs argument to sugar. The left hand side of the rules should include all the products that influenced the purchase of sugar i.e. it will exclude sugar. We will use the default argument and supply it the value lhs i.e. all items excluding sugar can appear on the left hand side of the rule by default.

  • default
  • rhs
sugar_rules <- apriori(basket_data, parameter = list(supp = 0.009, conf = 0.8), 
  appearance = list(default = "lhs", rhs = "SUGAR")) 
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.8    0.1    1 none FALSE            TRUE       5   0.009      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: 233 
## 
## set item appearances ...[1 item(s)] done [0.00s].
## set transactions ...[10085 item(s), 25901 transaction(s)] done [1.45s].
## sorting and recoding items ... [508 item(s)] done [0.03s].
## creating transaction tree ... done [0.05s].
## checking subsets of size 1 2 3 4 done [0.17s].
## writing ... [3 rule(s)] done [0.00s].
## creating S4 object  ... done [0.02s].
rules_sugar <- sort(sugar_rules, by = "confidence", decreasing = TRUE)
inspect(rules_sugar)
##     lhs                             rhs     support    confidence lift    
## [1] {SET 3 RETROSPOT TEA}        => {SUGAR} 0.01436238 1.0000000  69.62634
## [2] {COFFEE,SET 3 RETROSPOT TEA} => {SUGAR} 0.01436238 1.0000000  69.62634
## [3] {COFFEE}                     => {SUGAR} 0.01436238 0.8034557  55.94168
##     count
## [1] 372  
## [2] 372  
## [3] 372

For the support and confidence we have mentioned, we know the following products influenced the purchase of sugar:

  • COFFEE
  • SET 3 RETROSPOT TEA

What purchases did product X influence?

Now that we know what products influenced the purchase of sugar, let us answer the second question.

What purchases did sugar influence?

In this case, we want sugar to be on the left hand side of the rule and all the products it influenced to be on the right hand side. We set the lhs argument to sugar and the default argument to rhs as all the products, the purchase of which was influenced by sugar should appear on the left hand side of the rule by default.

sugar_rules <- apriori(basket_data, parameter = list(supp = 0.009, conf = 0.8), 
  appearance = list(default = "rhs", lhs = "SUGAR")) 
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.8    0.1    1 none FALSE            TRUE       5   0.009      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: 233 
## 
## set item appearances ...[1 item(s)] done [0.00s].
## set transactions ...[10085 item(s), 25901 transaction(s)] done [1.65s].
## sorting and recoding items ... [508 item(s)] done [0.03s].
## creating transaction tree ... done [0.05s].
## checking subsets of size 1 2 done [0.03s].
## writing ... [2 rule(s)] done [0.00s].
## creating S4 object  ... done [0.02s].
rules_sugar <- sort(sugar_rules, by = "confidence", decreasing = TRUE)
inspect(rules_sugar)
##     lhs        rhs                   support    confidence lift     count
## [1] {SUGAR} => {SET 3 RETROSPOT TEA} 0.01436238 1          69.62634 372  
## [2] {SUGAR} => {COFFEE}              0.01436238 1          55.94168 372

For the support and confidence we have mentioned, we know the purchase of the following products were influenced by sugar:

  • COFFEE
  • SET 3 RETROSPOT TEA

Top Rules

Let us take a look at the top rules by

Support

supp_rules <- sort(rules, by = 'support', decreasing = TRUE)
top_rules <- supp_rules[1:10]
inspect(top_rules)
##      lhs                                  rhs                                  support confidence     lift count
## [1]  {PINK REGENCY TEACUP AND SAUCER,                                                                           
##       ROSES REGENCY TEACUP AND SAUCER} => {GREEN REGENCY TEACUP AND SAUCER} 0.01833906  0.8828996 24.96505   475
## [2]  {GREEN REGENCY TEACUP AND SAUCER,                                                                          
##       PINK REGENCY TEACUP AND SAUCER}  => {ROSES REGENCY TEACUP AND SAUCER} 0.01833906  0.8512545 22.59051   475
## [3]  {SET 3 RETROSPOT TEA}             => {SUGAR}                           0.01436238  1.0000000 69.62634   372
## [4]  {SUGAR}                           => {SET 3 RETROSPOT TEA}             0.01436238  1.0000000 69.62634   372
## [5]  {SET 3 RETROSPOT TEA}             => {COFFEE}                          0.01436238  1.0000000 55.94168   372
## [6]  {COFFEE}                          => {SET 3 RETROSPOT TEA}             0.01436238  0.8034557 55.94168   372
## [7]  {SUGAR}                           => {COFFEE}                          0.01436238  1.0000000 55.94168   372
## [8]  {COFFEE}                          => {SUGAR}                           0.01436238  0.8034557 55.94168   372
## [9]  {SET 3 RETROSPOT TEA,                                                                                      
##       SUGAR}                           => {COFFEE}                          0.01436238  1.0000000 55.94168   372
## [10] {COFFEE,                                                                                                   
##       SET 3 RETROSPOT TEA}             => {SUGAR}                           0.01436238  1.0000000 69.62634   372

Confidence

conf_rules <- sort(rules, by = 'confidence', decreasing = TRUE)
top_rules <- conf_rules[1:10]
inspect(top_rules)
##      lhs                                  rhs                                   support confidence     lift count
## [1]  {BACK DOOR}                       => {KEY FOB}                         0.009613528  1.0000000 61.23168   249
## [2]  {SET 3 RETROSPOT TEA}             => {SUGAR}                           0.014362380  1.0000000 69.62634   372
## [3]  {SUGAR}                           => {SET 3 RETROSPOT TEA}             0.014362380  1.0000000 69.62634   372
## [4]  {SET 3 RETROSPOT TEA}             => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [5]  {SUGAR}                           => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [6]  {SHED}                            => {KEY FOB}                         0.011273696  1.0000000 61.23168   292
## [7]  {SET 3 RETROSPOT TEA,                                                                                       
##       SUGAR}                           => {COFFEE}                          0.014362380  1.0000000 55.94168   372
## [8]  {COFFEE,                                                                                                    
##       SET 3 RETROSPOT TEA}             => {SUGAR}                           0.014362380  1.0000000 69.62634   372
## [9]  {COFFEE,                                                                                                    
##       SUGAR}                           => {SET 3 RETROSPOT TEA}             0.014362380  1.0000000 69.62634   372
## [10] {PINK REGENCY TEACUP AND SAUCER,                                                                            
##       REGENCY CAKESTAND 3 TIER,                                                                                  
##       ROSES REGENCY TEACUP AND SAUCER} => {GREEN REGENCY TEACUP AND SAUCER} 0.009999614  0.8900344 25.16679   259

Lift

lift_rules <- sort(rules, by = 'lift', decreasing = TRUE)
top_rules <- lift_rules[1:10]
inspect(top_rules)
##      lhs                          rhs                           support confidence     lift count
## [1]  {REGENCY TEA PLATE PINK}  => {REGENCY TEA PLATE GREEN} 0.009034400  0.8863636 71.29722   234
## [2]  {SET 3 RETROSPOT TEA}     => {SUGAR}                   0.014362380  1.0000000 69.62634   372
## [3]  {SUGAR}                   => {SET 3 RETROSPOT TEA}     0.014362380  1.0000000 69.62634   372
## [4]  {COFFEE,                                                                                    
##       SET 3 RETROSPOT TEA}     => {SUGAR}                   0.014362380  1.0000000 69.62634   372
## [5]  {COFFEE,                                                                                    
##       SUGAR}                   => {SET 3 RETROSPOT TEA}     0.014362380  1.0000000 69.62634   372
## [6]  {BACK DOOR}               => {KEY FOB}                 0.009613528  1.0000000 61.23168   249
## [7]  {SHED}                    => {KEY FOB}                 0.011273696  1.0000000 61.23168   292
## [8]  {REGENCY TEA PLATE GREEN} => {REGENCY TEA PLATE ROSES} 0.010347091  0.8322981 55.99313   268
## [9]  {SET 3 RETROSPOT TEA}     => {COFFEE}                  0.014362380  1.0000000 55.94168   372
## [10] {COFFEE}                  => {SET 3 RETROSPOT TEA}     0.014362380  0.8034557 55.94168   372

packages ad

Visualization

To visualize the rules, the authors of arules have created a companion package, arulesViz. It offers several options for visualizing the rules generated by apriori().

Scatter Plot

We can use the default plot() method to create a scatter plot. It will plot the support on the X axis, the confidence on the Y axis and the lift is represented by the opaqueness/alpha of the color of the points.

plot(basket_rules)

Network Plot

We can create a network plot using the method argument and supplying it the value graph. You can see the directionality of the rule in the below plot. For example, people who buy shed also buy key fob and similarly, people who buy back door also buy key fob. It will be difficult to identify the directionality of the rules when we are trying to plot too many rules. The method argument takes several other values as well.

plot(top_rules, method = 'graph')

Things to keep in mind..

Directionality of rule is lost while using lift

The directionality of a rule is lost while using lift. In the below example, the lift is same for both the following rules:

  • {Mobile Phone} => {Screen Guard}
  • {Screen Guard} => {Mobile Phone}

It is clear that the lift is the same irrespective of the direction of the rule.

Confidence as a measure can be misleading

If you look at the below example, the confidence for the second rule, {Screen Guard} => {Mobile Phone}, is greater than the first rule, {Mobile Phone} => {Screen Guard}. It does not mean that we can recommend a mobile phone to a customer who is purchasing a screen guard. It is important to ensure that we do not use rules just because they have high confidence associated with them.

Summary

  • market basket analysis is an unsupervised data mining technique
  • uncovers products frequently bought together
  • creates if-then scenario rules
  • cost-effective, insightful and actionable
  • association rule mining has applications in several industries
  • directionality of rule is lost while using lift
  • confidence as a measure can be misleading

Your knowledge of the domain/business matters a lot when you are trying to use market basket analysis. Especially, when you are trying to select or shortlist rules and use them for product placement in a store or for recommending products online. It is a good practice to critically review the rules before implementing them.