Homework 6

Association Rules with Grocery Data

Author

Byeong-Hak Choe

Published

April 27, 2026

Modified

May 10, 2026

Direction

  • Please submit one Quarto Document of Homework 6 to Brightspace using the following file naming convention:

  • Example:

    • danl-320-hw6-choe-byeonghak.qmd

  • Due: May 6, 2026, 11:59 P.M. (ET)

  • Please send Byeong-Hak an email (bchoe@geneseo.edu) if you have any questions.


Setup

library(tidyverse)
library(rmarkdown)

library(arules)
library(arulesViz)
library(plotly)


πŸ“₯ Load the Grocery Transaction Data

The data are stored in a single transaction format, where each row represents one item purchased in one transaction.

grocery <- read.transactions(
  "https://bcdanl.github.io/data/market_basket.tsv",
  format = "single",
  header = TRUE,
  cols = c(1, 2),
  rm.duplicates = TRUE
)

Question 1. 🏷️ Transaction and Item Labels

What do the labels for the column and the row of grocery represent?

In the transaction matrix:

  • The columns represent grocery item categories.
  • The rows represent individual grocery transactions.
colnames(grocery)[1:10]
 [1] "abrasive cleaner" "artif. sweetener" "baby cosmetics"   "baby food"       
 [5] "bags"             "baking powder"    "bathroom cleaner" "beef"            
 [9] "berries"          "beverages"       
rownames(grocery)[1:10]
 [1] "1"    "10"   "100"  "1000" "1001" "1002" "1003" "1004" "1005" "1006"
itemLabels(grocery)[1:20]
 [1] "abrasive cleaner" "artif. sweetener" "baby cosmetics"   "baby food"       
 [5] "bags"             "baking powder"    "bathroom cleaner" "beef"            
 [9] "berries"          "beverages"        "bottled beer"     "bottled water"   
[13] "brandy"           "brown bread"      "butter"           "butter milk"     
[17] "cake bar"         "candles"          "candy"            "canned beer"

The first few column labels show item categories, such as grocery product names. The row labels identify individual transactions.

A transaction matrix is a sparse binary matrix. A value of TRUE or 1 means that a given item appeared in a given transaction, while a value of FALSE or 0 means that it did not.

summary(grocery)
transactions as itemMatrix in sparse format with
 9835 rows (elements/itemsets/transactions) and
 169 columns (items) and a density of 0.02609085 

most frequent items:
      whole milk other vegetables       rolls/buns             soda 
            2513             1903             1809             1715 
          yogurt          (Other) 
            1372            34054 

element (itemset/transaction) length distribution:
sizes
   1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
2159 1643 1300 1004  855  645  545  438  350  246  182  117   78   77   55   46 
  17   18   19   20   21   22   23   24   26   27   28   29   32 
  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
1 abrasive cleaner
2 artif. sweetener
3   baby cosmetics

includes extended transaction information - examples:
  transactionID
1             1
2            10
3           100


Question 2. πŸ“¦ Transaction Size Distribution

What are the first quartile, median, third quartile, and maximum of transaction sizes in grocery? Visualize the distribution of transaction sizes.

The transaction size is the number of items purchased in each transaction.

basket_sizes <- size(grocery)

summary(basket_sizes)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   2.000   3.000   4.409   6.000  32.000

A tidy summary table is shown below.

transaction_size_summary <- tibble(
  statistic = c("Minimum", "First quartile", "Median", "Mean", "Third quartile", "Maximum"),
  value = as.numeric(summary(basket_sizes))
)

transaction_size_summary
# A tibble: 6 Γ— 2
  statistic      value
  <chr>          <dbl>
1 Minimum         1   
2 First quartile  2   
3 Median          3   
4 Mean            4.41
5 Third quartile  6   
6 Maximum        32

πŸ“Š Density Plot of Transaction Sizes

basket_sizes_df <- tibble(
  transaction_id = rownames(grocery),
  transaction_size = basket_sizes
)

basket_sizes_df |>
  ggplot(aes(x = transaction_size)) +
  geom_density(fill = "gray80", color = "black") +
  labs(
    title = "Distribution of Grocery Transaction Sizes",
    x = "Number of items in transaction",
    y = "Density"
  ) +
  theme_minimal()

Most transactions contain a relatively small number of items, while a smaller number of transactions contain many items.


Question 3. πŸ” Top 50 Most Frequently Purchased Items

Find the top 50 most frequently occurring items in grocery. Also, visualize the distribution of top 50 item occurrences in grocery.

We first calculate the absolute frequency of each item and convert the result into a tidy data frame.

grocery_count <- itemFrequency(grocery, type = "absolute")

grocery_count_df <- tibble(
  item = names(grocery_count),
  count = as.numeric(grocery_count)
) |>
  arrange(desc(count))

grocery_top50 <- grocery_count_df |>
  slice_head(n = 50)

grocery_top50
# A tibble: 50 Γ— 2
   item             count
   <chr>            <dbl>
 1 whole milk        2513
 2 other vegetables  1903
 3 rolls/buns        1809
 4 soda              1715
 5 yogurt            1372
 6 bottled water     1087
 7 root vegetables   1072
 8 tropical fruit    1032
 9 shopping bags      969
10 sausage            924
# β„Ή 40 more rows

πŸ“Š arules Frequency Plot

The itemFrequencyPlot() function gives a quick visualization directly from the transaction object.

itemFrequencyPlot(
  grocery,
  type = "absolute",
  topN = 50,
  cex.names = 0.75
)

πŸ“Š Alternative ggplot Bar Chart of Top 50 Items

grocery_top50 |>
  mutate(item = fct_reorder(item, count)) |>
  ggplot(aes(x = item, y = count)) +
  geom_col(color = "black", fill = "gray75") +
  coord_flip() +
  labs(
    title = "Top 50 Most Frequently Purchased Grocery Items",
    x = "Item",
    y = "Number of transactions"
  ) +
  theme_minimal()

The most frequently purchased items are the items that appear in the largest number of transactions.


Question 4. ⛏️ Association Rules from Grocery Transactions

From the subset of grocery whose transaction size is greater than 1, find association rules with:

  • minimum support = 0.01,
  • minimum confidence = 0.25, and
  • minimum rule length = 2.

Find the top 10 rules in terms of lift values.

We first keep only transactions with more than one item because association rules require relationships across items.

grocery_use <- grocery[basket_sizes > 1]

summary(grocery_use)
transactions as itemMatrix in sparse format with
 7676 rows (elements/itemsets/transactions) and
 169 columns (items) and a density of 0.03176503 

most frequent items:
      whole milk other vegetables       rolls/buns             soda 
            2392             1841             1700             1559 
          yogurt          (Other) 
            1332            32383 

element (itemset/transaction) length distribution:
sizes
   2    3    4    5    6    7    8    9   10   11   12   13   14   15   16   17 
1643 1300 1004  855  645  545  438  350  246  182  117   78   77   55   46   29 
  18   19   20   21   22   23   24   26   27   28   29   32 
  14   14    9   11    4    6    1    1    1    1    3    1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   3.000   4.000   5.368   7.000  32.000 

includes extended item information - examples:
            labels
1 abrasive cleaner
2 artif. sweetener
3   baby cosmetics

includes extended transaction information - examples:
  transactionID
1             1
2            10
3           100

Now we run the Apriori algorithm.

rules <- apriori(
  grocery_use,
  parameter = list(
    support = 0.01,
    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    0.01      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: 76 

set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[169 item(s), 7676 transaction(s)] done [0.00s].
sorting and recoding items ... [98 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 4 done [0.00s].
writing ... [310 rule(s)] done [0.00s].
creating S4 object  ... done [0.00s].
summary(rules)
set of 310 rules

rule length distribution (lhs + rhs):sizes
  2   3   4 
134 172   4 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   2.000   3.000   2.581   3.000   4.000 

summary of quality measures:
    support          confidence        coverage            lift      
 Min.   :0.01003   Min.   :0.2508   Min.   :0.01655   Min.   :0.811  
 1st Qu.:0.01159   1st Qu.:0.2973   1st Qu.:0.03114   1st Qu.:1.323  
 Median :0.01381   Median :0.3577   Median :0.04123   Median :1.542  
 Mean   :0.01858   Mean   :0.3740   Mean   :0.05294   Mean   :1.612  
 3rd Qu.:0.02084   3rd Qu.:0.4371   3rd Qu.:0.06217   3rd Qu.:1.856  
 Max.   :0.09588   Max.   :0.6389   Max.   :0.31162   Max.   :3.174  
     count      
 Min.   : 77.0  
 1st Qu.: 89.0  
 Median :106.0  
 Mean   :142.6  
 3rd Qu.:160.0  
 Max.   :736.0  

mining info:
        data ntransactions support confidence
 grocery_use          7676    0.01       0.25
                                                                                         call
 apriori(data = grocery_use, parameter = list(support = 0.01, confidence = 0.25, minlen = 2))

πŸ“‹ Tidy Rule Table

The as("data.frame") function converts the rules into a data frame, which makes it easier to use tidyverse tools.

rules_lift <- rules |>
  sort(by = "lift", decreasing = TRUE) |>
  head(n = 5)

rules_df <- rules_lift |> 
  as("data.frame") |>
  separate(
    col = rules,
    into = c("lhs", "rhs"),
    sep = " => "
  ) |> 
  arrange(-lift)

rules_df
                                lhs                  rhs    support confidence
1                         {berries} {whipped/sour cream} 0.01159458  0.2807571
2           {beef,other vegetables}    {root vegetables} 0.01016154  0.4020619
3 {other vegetables,tropical fruit}          {pip fruit} 0.01211569  0.2634561
4                 {beef,whole milk}    {root vegetables} 0.01029182  0.3779904
5      {other vegetables,pip fruit}     {tropical fruit} 0.01211569  0.3618677
    coverage     lift count
1 0.04129755 3.173920    89
2 0.02527358 2.947686    78
3 0.04598749 2.824426    93
4 0.02722772 2.771208    79
5 0.03348098 2.752920    93

πŸ” Top 10 Rules by Lift

top10_lift_rules <- rules_df |>
  slice_max(lift, n = 10)

top10_lift_rules
                                lhs                  rhs    support confidence
1                         {berries} {whipped/sour cream} 0.01159458  0.2807571
2           {beef,other vegetables}    {root vegetables} 0.01016154  0.4020619
3 {other vegetables,tropical fruit}          {pip fruit} 0.01211569  0.2634561
4                 {beef,whole milk}    {root vegetables} 0.01029182  0.3779904
5      {other vegetables,pip fruit}     {tropical fruit} 0.01211569  0.3618677
    coverage     lift count
1 0.04129755 3.173920    89
2 0.02527358 2.947686    78
3 0.04598749 2.824426    93
4 0.02722772 2.771208    79
5 0.03348098 2.752920    93

The top rules by lift identify item combinations that occur together much more often than expected under independence.

πŸ“ˆ Rule Plot

plot(
  rules,
  measure = c("support", "confidence"),
  shading = "lift",
  interactive = FALSE
)

πŸ•ΈοΈ Rule Graph

pinterac <- plot(rules, method = "graph", engine = "htmlwidget")

The graph plot is useful for exploring relationships among items, but it can be visually crowded when there are many rules.

πŸ” Top 10 Rules by Confidence

top10_confidence_rules <- rules_df |>
  slice_max(confidence, n = 10)

top10_confidence_rules
                                lhs                  rhs    support confidence
1           {beef,other vegetables}    {root vegetables} 0.01016154  0.4020619
2                 {beef,whole milk}    {root vegetables} 0.01029182  0.3779904
3      {other vegetables,pip fruit}     {tropical fruit} 0.01211569  0.3618677
4                         {berries} {whipped/sour cream} 0.01159458  0.2807571
5 {other vegetables,tropical fruit}          {pip fruit} 0.01211569  0.2634561
    coverage     lift count
1 0.02527358 2.947686    78
2 0.02722772 2.771208    79
3 0.03348098 2.752920    93
4 0.04129755 3.173920    89
5 0.04598749 2.824426    93


Question 5. 🧠 Interpret the Rule with the Highest Lift

Interpret the following qualities of the rule with the highest lift:

  1. confidence,
  2. coverage, and
  3. lift.

We identify the rule with the highest lift.

highest_lift_rule <- rules_df |>
  slice_max(lift, n = 1)

highest_lift_rule
        lhs                  rhs    support confidence   coverage    lift count
1 {berries} {whipped/sour cream} 0.01159458  0.2807571 0.04129755 3.17392    89

Let the rule be written as:

\[ X \Rightarrow Y \]

where \(X\) is the item or set of items on the left-hand side and \(Y\) is the item or set of items on the right-hand side.

Interpretation

The rule found here is:

{berries} => {whipped/sour cream}

This means that customers who bought berries were also likely to buy whipped/sour cream.

  • Confidence = 0.2808 means that among customers who bought berries, about 28.1% also bought whipped/sour cream.

  • Coverage = 0.0413 means that about 4.1% of transactions contained berries. In other words, berries were not extremely common, but they appeared often enough to generate a meaningful rule.

  • Lift = 3.1739 means that customers who bought berries were about 3.17 times more likely to buy whipped/sour cream than an average customer. Because the lift is greater than 1, berries and whipped/sour cream are purchased together more often than we would expect by chance.

Overall, this rule suggests a strong positive association between berries and whipped/sour cream. This makes intuitive sense because customers may buy berries and whipped or sour cream together for desserts, toppings, or fruit-based snacks.


Question 6. πŸ₯› What Did Customers Buy Before Buying Whole Milk?

What item(s) did customers buy before buying whole milk?

For this milk rule, use:

  • minimum support = 0.01,
  • minimum confidence = 0.25, and
  • minimum rule length = 2.

To answer this question, we place whole milk on the right-hand side of the rule. This means we are looking for rules of the form:

\[ X \Rightarrow \{\text{whole milk}\} \]

milk_rules_rhs <- apriori(
  grocery_use,
  parameter = list(
    support = 0.01,
    confidence = 0.25,
    minlen = 2
  ),
  appearance = list(
    default = "lhs",
    rhs = "whole milk"
  )
)
Apriori

Parameter specification:
 confidence minval smax arem  aval originalSupport maxtime support minlen
       0.25    0.1    1 none FALSE            TRUE       5    0.01      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: 76 

set item appearances ...[1 item(s)] done [0.00s].
set transactions ...[169 item(s), 7676 transaction(s)] done [0.00s].
sorting and recoding items ... [98 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 4 done [0.00s].
writing ... [110 rule(s)] done [0.00s].
creating S4 object  ... done [0.00s].
summary(milk_rules_rhs)
set of 110 rules

rule length distribution (lhs + rhs):sizes
 2  3  4 
53 56  1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.000   2.000   3.000   2.527   3.000   4.000 

summary of quality measures:
    support          confidence        coverage            lift      
 Min.   :0.01003   Min.   :0.2527   Min.   :0.01655   Min.   :0.811  
 1st Qu.:0.01186   1st Qu.:0.3905   1st Qu.:0.02534   1st Qu.:1.253  
 Median :0.01472   Median :0.4371   Median :0.03439   Median :1.403  
 Mean   :0.02086   Mean   :0.4452   Mean   :0.05055   Mean   :1.429  
 3rd Qu.:0.02495   3rd Qu.:0.5041   3rd Qu.:0.05970   3rd Qu.:1.618  
 Max.   :0.09588   Max.   :0.6389   Max.   :0.23984   Max.   :2.050  
     count      
 Min.   : 77.0  
 1st Qu.: 91.0  
 Median :113.0  
 Mean   :160.1  
 3rd Qu.:191.5  
 Max.   :736.0  

mining info:
        data ntransactions support confidence
 grocery_use          7676    0.01       0.25
                                                                                                                                                 call
 apriori(data = grocery_use, parameter = list(support = 0.01, confidence = 0.25, minlen = 2), appearance = list(default = "lhs", rhs = "whole milk"))
milk_rules_rhs_df <- DATAFRAME(milk_rules_rhs, separate = TRUE) |>
  as_tibble() |>
  arrange(desc(lift))

milk_rules_rhs_df |> 
  paged_table()

These rules show which items are associated with customers also buying whole milk.


Question 7. πŸ›οΈ What Are Customers Who Bought Whole Milk Also Likely to Buy?

Find item(s) that customers who bought whole milk are also likely to buy.

To answer this question, we place whole milk on the left-hand side of the rule. This means we are looking for rules of the form:

\[ \{\text{whole milk}\} \Rightarrow Y \]

milk_rules_lhs <- apriori(
  grocery_use,
  parameter = list(
    support = 0.01,
    confidence = 0.30,
    minlen = 2
  ),
  appearance = list(
    lhs = "whole milk",
    default = "rhs"
  )
)
Apriori

Parameter specification:
 confidence minval smax arem  aval originalSupport maxtime support minlen
        0.3    0.1    1 none FALSE            TRUE       5    0.01      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: 76 

set item appearances ...[1 item(s)] done [0.00s].
set transactions ...[169 item(s), 7676 transaction(s)] done [0.00s].
sorting and recoding items ... [98 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 done [0.00s].
writing ... [1 rule(s)] done [0.00s].
creating S4 object  ... done [0.00s].
summary(milk_rules_lhs)
set of 1 rules

rule length distribution (lhs + rhs):sizes
2 
1 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      2       2       2       2       2       2 

summary of quality measures:
    support          confidence        coverage           lift      
 Min.   :0.09588   Min.   :0.3077   Min.   :0.3116   Min.   :1.283  
 1st Qu.:0.09588   1st Qu.:0.3077   1st Qu.:0.3116   1st Qu.:1.283  
 Median :0.09588   Median :0.3077   Median :0.3116   Median :1.283  
 Mean   :0.09588   Mean   :0.3077   Mean   :0.3116   Mean   :1.283  
 3rd Qu.:0.09588   3rd Qu.:0.3077   3rd Qu.:0.3116   3rd Qu.:1.283  
 Max.   :0.09588   Max.   :0.3077   Max.   :0.3116   Max.   :1.283  
     count    
 Min.   :736  
 1st Qu.:736  
 Median :736  
 Mean   :736  
 3rd Qu.:736  
 Max.   :736  

mining info:
        data ntransactions support confidence
 grocery_use          7676    0.01        0.3
                                                                                                                                                call
 apriori(data = grocery_use, parameter = list(support = 0.01, confidence = 0.3, minlen = 2), appearance = list(lhs = "whole milk", default = "rhs"))
milk_rules_lhs_df <- DATAFRAME(milk_rules_lhs, separate = TRUE) |>
  as_tibble() |>
  arrange(desc(lift))

milk_rules_lhs_df
# A tibble: 1 Γ— 7
  LHS          RHS                support confidence coverage  lift count
  <fct>        <fct>                <dbl>      <dbl>    <dbl> <dbl> <int>
1 {whole milk} {other vegetables}  0.0959      0.308    0.312  1.28   736

The resulting rules describe items that are likely to appear in the same basket after whole milk appears on the left-hand side.


Question 8. πŸ“‰ Items Customers Are Less Likely to Buy Before Buying Whole Milk

Using the result of association rule mining in Question 4, find item(s) that customers are less likely to buy before buying whole milk. Why do you think those items are less likely to be purchased when customers buy whole milk?

A rule with lift less than 1 indicates a negative association. In this context, the left-hand-side item and whole milk appear together less often than expected under independence.

We first filter the rules from Question 4 to rules where whole milk is on the right-hand side and the lift is less than 1.

less_likely_milk_rules <- rules_df |>
  filter(str_detect(rhs, "whole milk")) |>
  filter(lift < 1) |>
  arrange(lift)

less_likely_milk_rules
[1] lhs        rhs        support    confidence coverage   lift       count     
<0 rows> (or 0-length row.names)

This table is empty. It means that within the rules generated using the Question 4 thresholds, there are no rules with whole milk on the right-hand side and lift less than 1.

We can also inspect the lowest-lift rules overall.

lowest_lift_rules <- rules_df |>
  arrange(lift) |>
  slice_head(n = 10)

lowest_lift_rules
                                lhs                  rhs    support confidence
1      {other vegetables,pip fruit}     {tropical fruit} 0.01211569  0.3618677
2                 {beef,whole milk}    {root vegetables} 0.01029182  0.3779904
3 {other vegetables,tropical fruit}          {pip fruit} 0.01211569  0.2634561
4           {beef,other vegetables}    {root vegetables} 0.01016154  0.4020619
5                         {berries} {whipped/sour cream} 0.01159458  0.2807571
    coverage     lift count
1 0.03348098 2.752920    93
2 0.02722772 2.771208    79
3 0.04598749 2.824426    93
4 0.02527358 2.947686    78
5 0.04129755 3.173920    89

Interpretation

Rules with lift less than 1 suggest that the items appear together less often than expected. For example, if a rule involving bottled beer and whole milk has lift below 1, it means customers who buy bottled beer are less likely than the average customer to also buy whole milk.

One possible explanation is that these products may belong to different shopping occasions. For example, customers buying beer may be shopping for entertainment, parties, or beverages, while customers buying whole milk may be shopping for regular household groceries, breakfast items, or cooking ingredients.

This does not mean that customers never buy the items together. It only means that the items occur together less often than expected based on their individual frequencies.


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