Market analysis of products and baskets - Rule Association

Finding correlations between items purchased.
Rule mining
machine learning
R
Author

Dan A. Tshisungu

Published

August 21, 2024

Introduction

Also called Frequent itemset analysis, association analysis, association rule learning, it is one of the most popular data mining methods.

It is typically applied in the analysis of consumer buying trends in supermarkets and chain stores as it models a many-to-many relationships between items and baskets (also transactions).

Using data from a groceries store, we will try to investigate it to discover patterns and/or correlations between items purchased.

Data

library(here)
library(arules)
library(arulesViz)
library(tidyverse)
library(reshape2)
library(ggplot2)
library(plotly)
library(dplyr)
library(DT)

data <- read_csv(here("data", "basketAnalysis.csv")) %>% 
  janitor::clean_names()

DT::datatable(data)

Our dataset has 999 observations or transactions and 17 variables including the index variable representing the transaction or basket number.

Data cleaning

data <- data %>% 
  rename(transaction = x1) %>% 
  mutate(transaction= transaction + 1)

DT::datatable(data)

Data Exploration

skimr::skim(data)
Data summary
Name data
Number of rows 999
Number of columns 17
_______________________
Column type frequency:
logical 16
numeric 1
________________________
Group variables None

Variable type: logical

skim_variable n_missing complete_rate mean count
apple 0 1 0.38 FAL: 616, TRU: 383
bread 0 1 0.38 FAL: 615, TRU: 384
butter 0 1 0.42 FAL: 579, TRU: 420
cheese 0 1 0.40 FAL: 595, TRU: 404
corn 0 1 0.41 FAL: 592, TRU: 407
dill 0 1 0.40 FAL: 601, TRU: 398
eggs 0 1 0.38 FAL: 615, TRU: 384
ice_cream 0 1 0.41 FAL: 589, TRU: 410
kidney_beans 0 1 0.41 FAL: 591, TRU: 408
milk 0 1 0.41 FAL: 594, TRU: 405
nutmeg 0 1 0.40 FAL: 598, TRU: 401
onion 0 1 0.40 FAL: 596, TRU: 403
sugar 0 1 0.41 FAL: 590, TRU: 409
unicorn 0 1 0.39 FAL: 610, TRU: 389
yogurt 0 1 0.42 FAL: 579, TRU: 420
chocolate 0 1 0.42 FAL: 578, TRU: 421

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
transaction 0 1 500 288.53 1 250.5 500 749.5 999 ▇▇▇▇▇

Notes:

  • We do not have missing values;

  • The mean represents the frequency of TRUE in each transaction, so it is the `support` measure, which tells us how frequently a set of items appear in transactions. apple for example has a support of 0.383% because it appears 383 times out of 999 transactions.

To help us extract the most relevant itemsets in our data, we will use measures: support, confidence, and lift.

  • support : is an indication of how frequently a set of items appear in baskets. \[ Support_(x) = \frac {frequency(X)}{n} \]

  • Confidence : is an indication of how often the support-rule has been found to be true. High is 50%, if less than that the rule has little practical effect. \[ Confidence(X⤑Y) = \frac {support(X ∪ Y)}{support(X)} = \frac {P(X ∩ Y)}{P(X)} = P(Y | X) \]

  • Lift : is a measure of association using both support and confidence. \(Lift(X-> Y) = \frac { P(X ∩ Y)} {P(X) ∗ P(Y)}\)

Let us visualize the frequency of each item to find out which items are most popular and which ones are the least popular:

p <- data %>% 
  melt(., id.vars = "transaction", 
       variable.name = "Item", 
       value.name = "Purchased") %>%
  group_by(Item) %>%
  summarise(Frequency = sum(Purchased)) %>% 
  ggplot( aes(x = reorder(Item, -Frequency), y = Frequency)) +
  geom_bar(stat = "identity", fill = "steelblue") +
  labs(title = "Item Distribution", x = "Item", y = "Frequency") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) 

ggplotly(p)

Chocolate seems to be the most purchased items closely followed by butter and yogurt while breads, eggs, and apple are less purchased.

Though less purchased compared others, there is not a major difference between the them.

Maybe we could visualize which pairs of items are usually bought together:

# Generate all possible item pairs
generate_pairs <- function(items) {
  if (length(items) >= 2) {
    combn(items, 2, simplify = FALSE)
  } else {
    NULL
  }
}

# Create a co-occurrence matrix
item_pairs <- do.call(rbind, lapply(1:nrow(data), function(i) {
  row <- data[i, -1]
  items <- names(row)[row == TRUE]
  pairs <- generate_pairs(items)
  if (!is.null(pairs)) {
    do.call(rbind, lapply(pairs, function(pair) data.frame(Item1 = pair[1], Item2 = pair[2])))
  } else {
    NULL
  }
}))

# Count the frequency of each item pair
pair_counts <- item_pairs %>%
  group_by(Item1, Item2) %>%
  summarise(Frequency = n()) %>%
  ungroup()

# Create a bubble chart using ggplot2
p2 <- ggplot(pair_counts, aes(x = Item1, y = Item2, size = Frequency, color = Frequency)) +
  geom_point(alpha = 0.7) +
  labs(title = "Items Frequently Bought Together", x = "Item 1", y = "Item 2") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  scale_color_gradientn(colors = c("steelblue","yellow"))

# Make the plot interactive using plotly
DT::datatable(pair_counts)
ggplotly(p2)

We see that while some products are never bought together (i.e. bread and ice-cream, eggs and onions), some pairs seems to be frequently bought together (i.e. milk and chocolate 211 times, ice-cream and butter 207 times, or even ice-cream and chocolate 202 times).

We just observed pairs of products frequently bought together, what is the average number of items in a transaction?

p3 <- data %>% 
  rowwise() %>% 
  mutate(item_count = sum(c_across(-transaction))) %>%
  ungroup() %>% 
  group_by(item_count) %>% 
  summarise(Frequency = n()) %>%
  ungroup %>% 
  ggplot(aes(item_count, Frequency)) +
  geom_bar(stat = "identity", fill = "steelblue") +
  labs(title = "Distribution of the Number of Items per Transaction", 
       x = "Number of Items", 
       y = "Frequency") +
  theme_minimal()

ggplotly(p3)

Most transactions contain on average 7 to 9 items in them.

Modelling

While there are many algorithms we could use, we will focus on the A-priori algorithm because it is the most popular and easy to implement. Furthermore, it uses the measures we mentioned above in the process of generating itemsets.

Data transformation

Our dataset only contains boolen values and does not need further pre-processing which are required when dealing with numerical features.

However, we do need to transform our tibble into a set of transactions:

trans <- data %>% 
  select(-transaction) %>% 
  transactions()

trans
transactions in sparse format with
 999 transactions (rows) and
 16 items (columns)

We have 999 transactions and 16 unique items which are:

 [1] "apple"        "bread"        "butter"       "cheese"       "corn"        
 [6] "dill"         "eggs"         "ice_cream"    "kidney_beans" "milk"        
[11] "nutmeg"       "onion"        "sugar"        "unicorn"      "yogurt"      
[16] "chocolate"

Let us have a look at the first 2 transactions:

    items        transactionID
[1] {bread,                   
     corn,                    
     dill,                    
     ice_cream,               
     sugar,                   
     yogurt,                  
     chocolate}              1
[2] {milk}                   2

A summary can be made about all the transactions:

transactions as itemMatrix in sparse format with
 999 rows (elements/itemsets/transactions) and
 16 columns (items) and a density of 0.4032783 

most frequent items:
chocolate    butter    yogurt ice_cream     sugar   (Other) 
      421       420       420       410       409      4366 

element (itemset/transaction) length distribution:
sizes
  1   2   3   4   5   6   7   8   9  10  11  12  13 
 59  63  72  81  99  99 132 115 115  82  55  23   4 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   4.000   7.000   6.452   9.000  13.000 

includes extended item information - examples:
  labels variables levels
1  apple     apple   TRUE
2  bread     bread   TRUE
3 butter    butter   TRUE

includes extended transaction information - examples:
  transactionID
1             1
2             2
3             3

We have a sparse matrix, the most frequent items, as well as a more detailed length distribution of the transactions (i.e 59 transactions only have 1 item in them).

Now we model the algorithm but before we have to set the parameters values of our support and confidence:

Rules generation

Based on our EDA, the items frequencies are relatively the same, and setting a moderate support could help extract rules of those runner-items. Furthermore, setting the confidence high (50%) will strengthen our believe about the rules found.

support-threshold: 15%

confidence : 50%

rules <- apriori(trans,
                 parameter = list(supp=0.15,
                                  conf= 0.5,
                                  maxlen=10, 
                                  target= "rules"))
Apriori

Parameter specification:
 confidence minval smax arem  aval originalSupport maxtime support minlen
        0.5    0.1    1 none FALSE            TRUE       5    0.15      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: 149 

set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[16 item(s), 999 transaction(s)] done [0.00s].
sorting and recoding items ... [16 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 done [0.00s].
writing ... [5 rule(s)] done [0.00s].
creating S4 object  ... done [0.00s].
inspect(rules) %>% 
  DT::datatable()
    lhs            rhs         support   confidence coverage  lift     count
[1] {bread}     => {yogurt}    0.1931932 0.5026042  0.3843844 1.195480 193  
[2] {dill}      => {chocolate} 0.1991992 0.5000000  0.3983984 1.186461 199  
[3] {milk}      => {chocolate} 0.2112112 0.5209877  0.4054054 1.236263 211  
[4] {chocolate} => {milk}      0.2112112 0.5011876  0.4214214 1.236263 211  
[5] {ice_cream} => {butter}    0.2072072 0.5048780  0.4104104 1.200889 207

Based on our parameters, we extracted the above 5 rules:

  • Yogurt is likely to be bought if bread is bought

  • chocolate is likely to be bought if dill is bought

Should we want a more invasive marketing approach, we could lessen our confidence but increasing the support in order to extract more rules from our data:

Support-threshold: 15%

confidence: 40%

rules <- apriori(trans,
                 parameter = list(supp=0.15,
                                  conf= 0.4,
                                  maxlen=10, 
                                  minlen= 2,
                                  target= "rules")
                 )
Apriori

Parameter specification:
 confidence minval smax arem  aval originalSupport maxtime support minlen
        0.4    0.1    1 none FALSE            TRUE       5    0.15      2
 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: 149 

set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[16 item(s), 999 transaction(s)] done [0.00s].
sorting and recoding items ... [16 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 done [0.00s].
writing ... [238 rule(s)] done [0.00s].
creating S4 object  ... done [0.00s].
inspect(rules) %>% 
  DT::datatable()
      lhs               rhs            support   confidence coverage  lift     
[1]   {eggs}         => {bread}        0.1571572 0.4088542  0.3843844 1.0636597
[2]   {bread}        => {eggs}         0.1571572 0.4088542  0.3843844 1.0636597
[3]   {eggs}         => {apple}        0.1561562 0.4062500  0.3843844 1.0596443
[4]   {apple}        => {eggs}         0.1561562 0.4073107  0.3833834 1.0596443
[5]   {eggs}         => {unicorn}      0.1681682 0.4375000  0.3843844 1.1235540
[6]   {unicorn}      => {eggs}         0.1681682 0.4318766  0.3893894 1.1235540
[7]   {eggs}         => {dill}         0.1571572 0.4088542  0.3843844 1.0262445
[8]   {eggs}         => {cheese}       0.1691692 0.4401042  0.3843844 1.0882774
[9]   {cheese}       => {eggs}         0.1691692 0.4183168  0.4044044 1.0882774
[10]  {eggs}         => {nutmeg}       0.1721722 0.4479167  0.3843844 1.1158822
[11]  {nutmeg}       => {eggs}         0.1721722 0.4289277  0.4014014 1.1158822
[12]  {eggs}         => {onion}        0.1741742 0.4531250  0.3843844 1.1232553
[13]  {onion}        => {eggs}         0.1741742 0.4317618  0.4034034 1.1232553
[14]  {eggs}         => {corn}         0.1801802 0.4687500  0.3843844 1.1505682
[15]  {corn}         => {eggs}         0.1801802 0.4422604  0.4074074 1.1505682
[16]  {eggs}         => {kidney_beans} 0.1691692 0.4401042  0.3843844 1.0776080
[17]  {kidney_beans} => {eggs}         0.1691692 0.4142157  0.4084084 1.0776080
[18]  {eggs}         => {sugar}        0.1701702 0.4427083  0.3843844 1.0813340
[19]  {sugar}        => {eggs}         0.1701702 0.4156479  0.4094094 1.0813340
[20]  {eggs}         => {milk}         0.1761762 0.4583333  0.3843844 1.1305556
[21]  {milk}         => {eggs}         0.1761762 0.4345679  0.4054054 1.1305556
[22]  {eggs}         => {ice_cream}    0.1571572 0.4088542  0.3843844 0.9962081
[23]  {eggs}         => {yogurt}       0.1861862 0.4843750  0.3843844 1.1521205
[24]  {yogurt}       => {eggs}         0.1861862 0.4428571  0.4204204 1.1521205
[25]  {eggs}         => {butter}       0.1731732 0.4505208  0.3843844 1.0715960
[26]  {butter}       => {eggs}         0.1731732 0.4119048  0.4204204 1.0715960
[27]  {eggs}         => {chocolate}    0.1821822 0.4739583  0.3843844 1.1246660
[28]  {chocolate}    => {eggs}         0.1821822 0.4323040  0.4214214 1.1246660
[29]  {bread}        => {apple}        0.1541542 0.4010417  0.3843844 1.0460591
[30]  {apple}        => {bread}        0.1541542 0.4020888  0.3833834 1.0460591
[31]  {bread}        => {unicorn}      0.1681682 0.4375000  0.3843844 1.1235540
[32]  {unicorn}      => {bread}        0.1681682 0.4318766  0.3893894 1.1235540
[33]  {bread}        => {dill}         0.1601602 0.4166667  0.3843844 1.0458543
[34]  {dill}         => {bread}        0.1601602 0.4020101  0.3983984 1.0458543
[35]  {bread}        => {cheese}       0.1731732 0.4505208  0.3843844 1.1140354
[36]  {cheese}       => {bread}        0.1731732 0.4282178  0.4044044 1.1140354
[37]  {bread}        => {nutmeg}       0.1711712 0.4453125  0.3843844 1.1093945
[38]  {nutmeg}       => {bread}        0.1711712 0.4264339  0.4014014 1.1093945
[39]  {bread}        => {onion}        0.1781782 0.4635417  0.3843844 1.1490772
[40]  {onion}        => {bread}        0.1781782 0.4416873  0.4034034 1.1490772
[41]  {bread}        => {corn}         0.1741742 0.4531250  0.3843844 1.1122159
[42]  {corn}         => {bread}        0.1741742 0.4275184  0.4074074 1.1122159
[43]  {bread}        => {kidney_beans} 0.1671672 0.4348958  0.3843844 1.0648552
[44]  {kidney_beans} => {bread}        0.1671672 0.4093137  0.4084084 1.0648552
[45]  {bread}        => {sugar}        0.1791792 0.4661458  0.3843844 1.1385811
[46]  {sugar}        => {bread}        0.1791792 0.4376528  0.4094094 1.1385811
[47]  {bread}        => {milk}         0.1741742 0.4531250  0.3843844 1.1177083
[48]  {milk}         => {bread}        0.1741742 0.4296296  0.4054054 1.1177083
[49]  {bread}        => {ice_cream}    0.1811812 0.4713542  0.3843844 1.1484947
[50]  {ice_cream}    => {bread}        0.1811812 0.4414634  0.4104104 1.1484947
[51]  {bread}        => {yogurt}       0.1931932 0.5026042  0.3843844 1.1954799
[52]  {yogurt}       => {bread}        0.1931932 0.4595238  0.4204204 1.1954799
[53]  {bread}        => {butter}       0.1801802 0.4687500  0.3843844 1.1149554
[54]  {butter}       => {bread}        0.1801802 0.4285714  0.4204204 1.1149554
[55]  {bread}        => {chocolate}    0.1851852 0.4817708  0.3843844 1.1432044
[56]  {chocolate}    => {bread}        0.1851852 0.4394299  0.4214214 1.1432044
[57]  {apple}        => {unicorn}      0.1661662 0.4334204  0.3833834 1.1130770
[58]  {unicorn}      => {apple}        0.1661662 0.4267352  0.3893894 1.1130770
[59]  {apple}        => {dill}         0.1791792 0.4673629  0.3833834 1.1731044
[60]  {dill}         => {apple}        0.1791792 0.4497487  0.3983984 1.1731044
[61]  {apple}        => {cheese}       0.1621622 0.4229765  0.3833834 1.0459246
[62]  {cheese}       => {apple}        0.1621622 0.4009901  0.4044044 1.0459246
[63]  {apple}        => {nutmeg}       0.1721722 0.4490862  0.3833834 1.1187957
[64]  {nutmeg}       => {apple}        0.1721722 0.4289277  0.4014014 1.1187957
[65]  {apple}        => {onion}        0.1671672 0.4360313  0.3833834 1.0808816
[66]  {onion}        => {apple}        0.1671672 0.4143921  0.4034034 1.0808816
[67]  {apple}        => {corn}         0.1861862 0.4856397  0.3833834 1.1920247
[68]  {corn}         => {apple}        0.1861862 0.4570025  0.4074074 1.1920247
[69]  {apple}        => {kidney_beans} 0.1761762 0.4595300  0.3833834 1.1251728
[70]  {kidney_beans} => {apple}        0.1761762 0.4313725  0.4084084 1.1251728
[71]  {apple}        => {sugar}        0.1821822 0.4751958  0.3833834 1.1606861
[72]  {sugar}        => {apple}        0.1821822 0.4449878  0.4094094 1.1606861
[73]  {apple}        => {milk}         0.1841842 0.4804178  0.3833834 1.1850305
[74]  {milk}         => {apple}        0.1841842 0.4543210  0.4054054 1.1850305
[75]  {apple}        => {ice_cream}    0.1721722 0.4490862  0.3833834 1.0942368
[76]  {ice_cream}    => {apple}        0.1721722 0.4195122  0.4104104 1.0942368
[77]  {apple}        => {yogurt}       0.1871872 0.4882507  0.3833834 1.1613391
[78]  {yogurt}       => {apple}        0.1871872 0.4452381  0.4204204 1.1613391
[79]  {apple}        => {butter}       0.1881882 0.4908616  0.3833834 1.1675494
[80]  {butter}       => {apple}        0.1881882 0.4476190  0.4204204 1.1675494
[81]  {apple}        => {chocolate}    0.1831832 0.4778068  0.3833834 1.1337981
[82]  {chocolate}    => {apple}        0.1831832 0.4346793  0.4214214 1.1337981
[83]  {unicorn}      => {dill}         0.1681682 0.4318766  0.3893894 1.0840320
[84]  {dill}         => {unicorn}      0.1681682 0.4221106  0.3983984 1.0840320
[85]  {unicorn}      => {cheese}       0.1701702 0.4370180  0.3893894 1.0806460
[86]  {cheese}       => {unicorn}      0.1701702 0.4207921  0.4044044 1.0806460
[87]  {unicorn}      => {nutmeg}       0.1651652 0.4241645  0.3893894 1.0567091
[88]  {nutmeg}       => {unicorn}      0.1651652 0.4114713  0.4014014 1.0567091
[89]  {unicorn}      => {onion}        0.1751752 0.4498715  0.3893894 1.1151901
[90]  {onion}        => {unicorn}      0.1751752 0.4342432  0.4034034 1.1151901
[91]  {unicorn}      => {corn}         0.1771772 0.4550129  0.3893894 1.1168497
[92]  {corn}         => {unicorn}      0.1771772 0.4348894  0.4074074 1.1168497
[93]  {unicorn}      => {kidney_beans} 0.1841842 0.4730077  0.3893894 1.1581733
[94]  {kidney_beans} => {unicorn}      0.1841842 0.4509804  0.4084084 1.1581733
[95]  {unicorn}      => {sugar}        0.1811812 0.4652956  0.3893894 1.1365045
[96]  {sugar}        => {unicorn}      0.1811812 0.4425428  0.4094094 1.1365045
[97]  {unicorn}      => {milk}         0.1831832 0.4704370  0.3893894 1.1604113
[98]  {milk}         => {unicorn}      0.1831832 0.4518519  0.4054054 1.1604113
[99]  {unicorn}      => {ice_cream}    0.1851852 0.4755784  0.3893894 1.1587874
[100] {ice_cream}    => {unicorn}      0.1851852 0.4512195  0.4104104 1.1587874
[101] {unicorn}      => {yogurt}       0.1841842 0.4730077  0.3893894 1.1250826
[102] {yogurt}       => {unicorn}      0.1841842 0.4380952  0.4204204 1.1250826
[103] {unicorn}      => {butter}       0.1821822 0.4678663  0.3893894 1.1128535
[104] {butter}       => {unicorn}      0.1821822 0.4333333  0.4204204 1.1128535
[105] {unicorn}      => {chocolate}    0.1861862 0.4781491  0.3893894 1.1346103
[106] {chocolate}    => {unicorn}      0.1861862 0.4418052  0.4214214 1.1346103
[107] {dill}         => {cheese}       0.1771772 0.4447236  0.3983984 1.0997002
[108] {cheese}       => {dill}         0.1771772 0.4381188  0.4044044 1.0997002
[109] {dill}         => {nutmeg}       0.1731732 0.4346734  0.3983984 1.0828895
[110] {nutmeg}       => {dill}         0.1731732 0.4314214  0.4014014 1.0828895
[111] {dill}         => {onion}        0.1921922 0.4824121  0.3983984 1.1958552
[112] {onion}        => {dill}         0.1921922 0.4764268  0.4034034 1.1958552
[113] {dill}         => {corn}         0.1801802 0.4522613  0.3983984 1.1100959
[114] {corn}         => {dill}         0.1801802 0.4422604  0.4074074 1.1100959
[115] {dill}         => {kidney_beans} 0.1721722 0.4321608  0.3983984 1.0581584
[116] {kidney_beans} => {dill}         0.1721722 0.4215686  0.4084084 1.0581584
[117] {dill}         => {sugar}        0.1791792 0.4497487  0.3983984 1.0985306
[118] {sugar}        => {dill}         0.1791792 0.4376528  0.4094094 1.0985306
[119] {dill}         => {milk}         0.1901902 0.4773869  0.3983984 1.1775544
[120] {milk}         => {dill}         0.1901902 0.4691358  0.4054054 1.1775544
[121] {dill}         => {ice_cream}    0.1851852 0.4648241  0.3983984 1.1325836
[122] {ice_cream}    => {dill}         0.1851852 0.4512195  0.4104104 1.1325836
[123] {dill}         => {yogurt}       0.1851852 0.4648241  0.3983984 1.1056174
[124] {yogurt}       => {dill}         0.1851852 0.4404762  0.4204204 1.1056174
[125] {dill}         => {butter}       0.1751752 0.4396985  0.3983984 1.0458543
[126] {butter}       => {dill}         0.1751752 0.4166667  0.4204204 1.0458543
[127] {dill}         => {chocolate}    0.1991992 0.5000000  0.3983984 1.1864608
[128] {chocolate}    => {dill}         0.1991992 0.4726841  0.4214214 1.1864608
[129] {cheese}       => {nutmeg}       0.1921922 0.4752475  0.4044044 1.1839708
[130] {nutmeg}       => {cheese}       0.1921922 0.4788030  0.4014014 1.1839708
[131] {cheese}       => {onion}        0.1851852 0.4579208  0.4044044 1.1351436
[132] {onion}        => {cheese}       0.1851852 0.4590571  0.4034034 1.1351436
[133] {cheese}       => {corn}         0.1821822 0.4504950  0.4044044 1.1057606
[134] {corn}         => {cheese}       0.1821822 0.4471744  0.4074074 1.1057606
[135] {cheese}       => {kidney_beans} 0.2002002 0.4950495  0.4044044 1.2121433
[136] {kidney_beans} => {cheese}       0.2002002 0.4901961  0.4084084 1.2121433
[137] {cheese}       => {sugar}        0.1871872 0.4628713  0.4044044 1.1305829
[138] {sugar}        => {cheese}       0.1871872 0.4572127  0.4094094 1.1305829
[139] {cheese}       => {milk}         0.1721722 0.4257426  0.4044044 1.0501650
[140] {milk}         => {cheese}       0.1721722 0.4246914  0.4054054 1.0501650
[141] {cheese}       => {ice_cream}    0.1871872 0.4628713  0.4044044 1.1278254
[142] {ice_cream}    => {cheese}       0.1871872 0.4560976  0.4104104 1.1278254
[143] {cheese}       => {yogurt}       0.1811812 0.4480198  0.4044044 1.0656471
[144] {yogurt}       => {cheese}       0.1811812 0.4309524  0.4204204 1.0656471
[145] {cheese}       => {butter}       0.1821822 0.4504950  0.4044044 1.0715347
[146] {butter}       => {cheese}       0.1821822 0.4333333  0.4204204 1.0715347
[147] {cheese}       => {chocolate}    0.1861862 0.4603960  0.4044044 1.0924837
[148] {chocolate}    => {cheese}       0.1861862 0.4418052  0.4214214 1.0924837
[149] {nutmeg}       => {onion}        0.1951952 0.4862843  0.4014014 1.2054541
[150] {onion}        => {nutmeg}       0.1951952 0.4838710  0.4034034 1.2054541
[151] {nutmeg}       => {corn}         0.1811812 0.4513716  0.4014014 1.1079120
[152] {corn}         => {nutmeg}       0.1811812 0.4447174  0.4074074 1.1079120
[153] {nutmeg}       => {kidney_beans} 0.1891892 0.4713217  0.4014014 1.1540450
[154] {kidney_beans} => {nutmeg}       0.1891892 0.4632353  0.4084084 1.1540450
[155] {nutmeg}       => {sugar}        0.1931932 0.4812968  0.4014014 1.1755879
[156] {sugar}        => {nutmeg}       0.1931932 0.4718826  0.4094094 1.1755879
[157] {nutmeg}       => {milk}         0.1821822 0.4538653  0.4014014 1.1195345
[158] {milk}         => {nutmeg}       0.1821822 0.4493827  0.4054054 1.1195345
[159] {nutmeg}       => {ice_cream}    0.1871872 0.4663342  0.4014014 1.1362630
[160] {ice_cream}    => {nutmeg}       0.1871872 0.4560976  0.4104104 1.1362630
[161] {nutmeg}       => {yogurt}       0.1921922 0.4788030  0.4014014 1.1388671
[162] {yogurt}       => {nutmeg}       0.1921922 0.4571429  0.4204204 1.1388671
[163] {nutmeg}       => {butter}       0.1981982 0.4937656  0.4014014 1.1744567
[164] {butter}       => {nutmeg}       0.1981982 0.4714286  0.4204204 1.1744567
[165] {nutmeg}       => {chocolate}    0.1861862 0.4638404  0.4014014 1.1006569
[166] {chocolate}    => {nutmeg}       0.1861862 0.4418052  0.4214214 1.1006569
[167] {onion}        => {corn}         0.1841842 0.4565757  0.4034034 1.1206858
[168] {corn}         => {onion}        0.1841842 0.4520885  0.4074074 1.1206858
[169] {onion}        => {kidney_beans} 0.1701702 0.4218362  0.4034034 1.0328784
[170] {kidney_beans} => {onion}        0.1701702 0.4166667  0.4084084 1.0328784
[171] {onion}        => {sugar}        0.1901902 0.4714640  0.4034034 1.1515710
[172] {sugar}        => {onion}        0.1901902 0.4645477  0.4094094 1.1515710
[173] {onion}        => {milk}         0.1821822 0.4516129  0.4034034 1.1139785
[174] {milk}         => {onion}        0.1821822 0.4493827  0.4054054 1.1139785
[175] {onion}        => {ice_cream}    0.1921922 0.4764268  0.4034034 1.1608546
[176] {ice_cream}    => {onion}        0.1921922 0.4682927  0.4104104 1.1608546
[177] {onion}        => {yogurt}       0.1921922 0.4764268  0.4034034 1.1332152
[178] {yogurt}       => {onion}        0.1921922 0.4571429  0.4204204 1.1332152
[179] {onion}        => {butter}       0.1971972 0.4888337  0.4034034 1.1627260
[180] {butter}       => {onion}        0.1971972 0.4690476  0.4204204 1.1627260
[181] {onion}        => {chocolate}    0.1961962 0.4863524  0.4034034 1.1540760
[182] {chocolate}    => {onion}        0.1961962 0.4655582  0.4214214 1.1540760
[183] {corn}         => {kidney_beans} 0.1951952 0.4791155  0.4074074 1.1731283
[184] {kidney_beans} => {corn}         0.1951952 0.4779412  0.4084084 1.1731283
[185] {corn}         => {sugar}        0.1871872 0.4594595  0.4074074 1.1222494
[186] {sugar}        => {corn}         0.1871872 0.4572127  0.4094094 1.1222494
[187] {corn}         => {milk}         0.1931932 0.4742015  0.4074074 1.1696970
[188] {milk}         => {corn}         0.1931932 0.4765432  0.4054054 1.1696970
[189] {corn}         => {ice_cream}    0.1921922 0.4717445  0.4074074 1.1494457
[190] {ice_cream}    => {corn}         0.1921922 0.4682927  0.4104104 1.1494457
[191] {corn}         => {yogurt}       0.1901902 0.4668305  0.4074074 1.1103896
[192] {yogurt}       => {corn}         0.1901902 0.4523810  0.4204204 1.1103896
[193] {corn}         => {butter}       0.1911912 0.4692875  0.4074074 1.1162338
[194] {butter}       => {corn}         0.1911912 0.4547619  0.4204204 1.1162338
[195] {corn}         => {chocolate}    0.1921922 0.4717445  0.4074074 1.1194127
[196] {chocolate}    => {corn}         0.1921922 0.4560570  0.4214214 1.1194127
[197] {kidney_beans} => {sugar}        0.1871872 0.4583333  0.4084084 1.1194988
[198] {sugar}        => {kidney_beans} 0.1871872 0.4572127  0.4094094 1.1194988
[199] {kidney_beans} => {milk}         0.1991992 0.4877451  0.4084084 1.2031046
[200] {milk}         => {kidney_beans} 0.1991992 0.4913580  0.4054054 1.2031046
[201] {kidney_beans} => {ice_cream}    0.1961962 0.4803922  0.4084084 1.1705165
[202] {ice_cream}    => {kidney_beans} 0.1961962 0.4780488  0.4104104 1.1705165
[203] {kidney_beans} => {yogurt}       0.1941942 0.4754902  0.4084084 1.1309874
[204] {yogurt}       => {kidney_beans} 0.1941942 0.4619048  0.4204204 1.1309874
[205] {kidney_beans} => {butter}       0.2022022 0.4950980  0.4084084 1.1776261
[206] {butter}       => {kidney_beans} 0.2022022 0.4809524  0.4204204 1.1776261
[207] {kidney_beans} => {chocolate}    0.1911912 0.4681373  0.4084084 1.1108530
[208] {chocolate}    => {kidney_beans} 0.1911912 0.4536817  0.4214214 1.1108530
[209] {sugar}        => {milk}         0.1861862 0.4547677  0.4094094 1.1217604
[210] {milk}         => {sugar}        0.1861862 0.4592593  0.4054054 1.1217604
[211] {sugar}        => {ice_cream}    0.1951952 0.4767726  0.4094094 1.1616972
[212] {ice_cream}    => {sugar}        0.1951952 0.4756098  0.4104104 1.1616972
[213] {sugar}        => {yogurt}       0.1911912 0.4669927  0.4094094 1.1107754
[214] {yogurt}       => {sugar}        0.1911912 0.4547619  0.4204204 1.1107754
[215] {sugar}        => {butter}       0.1961962 0.4792176  0.4094094 1.1398533
[216] {butter}       => {sugar}        0.1961962 0.4666667  0.4204204 1.1398533
[217] {sugar}        => {chocolate}    0.1881882 0.4596577  0.4094094 1.0907317
[218] {chocolate}    => {sugar}        0.1881882 0.4465558  0.4214214 1.0907317
[219] {milk}         => {ice_cream}    0.1771772 0.4370370  0.4054054 1.0648780
[220] {ice_cream}    => {milk}         0.1771772 0.4317073  0.4104104 1.0648780
[221] {milk}         => {yogurt}       0.1901902 0.4691358  0.4054054 1.1158730
[222] {yogurt}       => {milk}         0.1901902 0.4523810  0.4204204 1.1158730
[223] {milk}         => {butter}       0.1981982 0.4888889  0.4054054 1.1628571
[224] {butter}       => {milk}         0.1981982 0.4714286  0.4204204 1.1628571
[225] {milk}         => {chocolate}    0.2112112 0.5209877  0.4054054 1.2362629
[226] {chocolate}    => {milk}         0.2112112 0.5011876  0.4214214 1.2362629
[227] {ice_cream}    => {yogurt}       0.1821822 0.4439024  0.4104104 1.0558537
[228] {yogurt}       => {ice_cream}    0.1821822 0.4333333  0.4204204 1.0558537
[229] {ice_cream}    => {butter}       0.2072072 0.5048780  0.4104104 1.2008885
[230] {butter}       => {ice_cream}    0.2072072 0.4928571  0.4204204 1.2008885
[231] {ice_cream}    => {chocolate}    0.2022022 0.4926829  0.4104104 1.1690980
[232] {chocolate}    => {ice_cream}    0.2022022 0.4798100  0.4214214 1.1690980
[233] {yogurt}       => {butter}       0.1911912 0.4547619  0.4204204 1.0816837
[234] {butter}       => {yogurt}       0.1911912 0.4547619  0.4204204 1.0816837
[235] {yogurt}       => {chocolate}    0.1981982 0.4714286  0.4204204 1.1186630
[236] {chocolate}    => {yogurt}       0.1981982 0.4703088  0.4214214 1.1186630
[237] {butter}       => {chocolate}    0.2022022 0.4809524  0.4204204 1.1412623
[238] {chocolate}    => {butter}       0.2022022 0.4798100  0.4214214 1.1412623
      count
[1]   157  
[2]   157  
[3]   156  
[4]   156  
[5]   168  
[6]   168  
[7]   157  
[8]   169  
[9]   169  
[10]  172  
[11]  172  
[12]  174  
[13]  174  
[14]  180  
[15]  180  
[16]  169  
[17]  169  
[18]  170  
[19]  170  
[20]  176  
[21]  176  
[22]  157  
[23]  186  
[24]  186  
[25]  173  
[26]  173  
[27]  182  
[28]  182  
[29]  154  
[30]  154  
[31]  168  
[32]  168  
[33]  160  
[34]  160  
[35]  173  
[36]  173  
[37]  171  
[38]  171  
[39]  178  
[40]  178  
[41]  174  
[42]  174  
[43]  167  
[44]  167  
[45]  179  
[46]  179  
[47]  174  
[48]  174  
[49]  181  
[50]  181  
[51]  193  
[52]  193  
[53]  180  
[54]  180  
[55]  185  
[56]  185  
[57]  166  
[58]  166  
[59]  179  
[60]  179  
[61]  162  
[62]  162  
[63]  172  
[64]  172  
[65]  167  
[66]  167  
[67]  186  
[68]  186  
[69]  176  
[70]  176  
[71]  182  
[72]  182  
[73]  184  
[74]  184  
[75]  172  
[76]  172  
[77]  187  
[78]  187  
[79]  188  
[80]  188  
[81]  183  
[82]  183  
[83]  168  
[84]  168  
[85]  170  
[86]  170  
[87]  165  
[88]  165  
[89]  175  
[90]  175  
[91]  177  
[92]  177  
[93]  184  
[94]  184  
[95]  181  
[96]  181  
[97]  183  
[98]  183  
[99]  185  
[100] 185  
[101] 184  
[102] 184  
[103] 182  
[104] 182  
[105] 186  
[106] 186  
[107] 177  
[108] 177  
[109] 173  
[110] 173  
[111] 192  
[112] 192  
[113] 180  
[114] 180  
[115] 172  
[116] 172  
[117] 179  
[118] 179  
[119] 190  
[120] 190  
[121] 185  
[122] 185  
[123] 185  
[124] 185  
[125] 175  
[126] 175  
[127] 199  
[128] 199  
[129] 192  
[130] 192  
[131] 185  
[132] 185  
[133] 182  
[134] 182  
[135] 200  
[136] 200  
[137] 187  
[138] 187  
[139] 172  
[140] 172  
[141] 187  
[142] 187  
[143] 181  
[144] 181  
[145] 182  
[146] 182  
[147] 186  
[148] 186  
[149] 195  
[150] 195  
[151] 181  
[152] 181  
[153] 189  
[154] 189  
[155] 193  
[156] 193  
[157] 182  
[158] 182  
[159] 187  
[160] 187  
[161] 192  
[162] 192  
[163] 198  
[164] 198  
[165] 186  
[166] 186  
[167] 184  
[168] 184  
[169] 170  
[170] 170  
[171] 190  
[172] 190  
[173] 182  
[174] 182  
[175] 192  
[176] 192  
[177] 192  
[178] 192  
[179] 197  
[180] 197  
[181] 196  
[182] 196  
[183] 195  
[184] 195  
[185] 187  
[186] 187  
[187] 193  
[188] 193  
[189] 192  
[190] 192  
[191] 190  
[192] 190  
[193] 191  
[194] 191  
[195] 192  
[196] 192  
[197] 187  
[198] 187  
[199] 199  
[200] 199  
[201] 196  
[202] 196  
[203] 194  
[204] 194  
[205] 202  
[206] 202  
[207] 191  
[208] 191  
[209] 186  
[210] 186  
[211] 195  
[212] 195  
[213] 191  
[214] 191  
[215] 196  
[216] 196  
[217] 188  
[218] 188  
[219] 177  
[220] 177  
[221] 190  
[222] 190  
[223] 198  
[224] 198  
[225] 211  
[226] 211  
[227] 182  
[228] 182  
[229] 207  
[230] 207  
[231] 202  
[232] 202  
[233] 191  
[234] 191  
[235] 198  
[236] 198  
[237] 202  
[238] 202

Visualizations

Now let us visualize our rules:

plot(rules, engine = "html") %>% 
  layout(title = "Interactive visualization of rules")

Note that the higher (i.e. lift > 1) the lift score, the more likely item Y is to be purchased given item X is also purchased.

Interactive network plot of rules and items:

References

Michael Hahsler (2024). An R Companion for Introduction to Data Mining. figshare. DOI: 10.6084/m9.figshare.26750404 URL: https://mhahsler.github.io/Introduction_to_Data_Mining_R_Examples/book/

Jan Kirenz (2024). Introduction to Association Rule Mining in R.