Homework 10 DATA624
Mehreen Ali Gillani
2026-05-06
Introduction:
Imagine 10000 receipts sitting on your table. Each receipt represents a transaction with items that were purchased. The receipt is a representation of stuff that went into a customer’s basket - and therefore ‘Market Basket Analysis’.
That is exactly what the Groceries Data Set contains: a collection of receipts with each line representing 1 receipt and the items purchased. Each line is called a transaction and each column in a row represents an item. The data set is attached.
Your assignment is to use R to mine the data for association rules. You should report support, confidence and lift and your top 10 rules by lift.
Extra credit: do a simple cluster analysis on the data as well. Use whichever packages you like.
1. Load the Groceres dataset
# ================================
# Market Basket Analysis & Clustering
# Groceries Dataset
# ================================
# 1. Load required packages and dataset
# install.packages(c("arules", "arulesViz", "factoextra", "cluster", "pheatmap"))
library(arules) # For association rules## Loading required package: Matrix##
## Attaching package: 'arules'## The following objects are masked from 'package:base':
##
## abbreviate, writelibrary(arulesViz) # For visualizing rules (optional)
library(cluster) # For clustering
library(factoextra) # For visualizing clusters## Loading required package: ggplot2## Welcome to factoextra!## Want to learn more? See two factoextra-related books at https://www.datanovia.com/en/product/practical-guide-to-principal-component-methods-in-r/library(pheatmap)
data("Groceries")
summary(Groceries)## transactions as itemMatrix in sparse format with
## 9835 rows (elements/itemsets/transactions) and
## 169 columns (items) and a density of 0.02609146
##
## most frequent items:
## whole milk other vegetables rolls/buns soda
## 2513 1903 1809 1715
## yogurt (Other)
## 1372 34055
##
## element (itemset/transaction) length distribution:
## sizes
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 2159 1643 1299 1005 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 level2 level1
## 1 frankfurter sausage meat and sausage
## 2 sausage sausage meat and sausage
## 3 liver loaf sausage meat and sausageDataset overview:
This dataset has 9835 transactions (receipts) and 169 items
Average basket size is 4.4 items, with most baskets containing 1-6 items (median = 3 items).
The most frequently purchased item is “whole milk” (appearing in 2,513 baskets, 25.6% of transactions), followed by other vegetables, rolls/buns, soda, and yogurt.
2. Mine association rules
# Use Apriori algorithm with reasonable thresholds
# (adjust support/confidence for meaningful rules)
rules <- apriori(Groceries,
parameter = list(supp = 0.001, # support threshold (0.1%)
conf = 0.5, # confidence threshold (50%)
target = "rules",
minlen = 2)) # at least 2 items per rule## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.5 0.1 1 none FALSE TRUE 5 0.001 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: 9
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [157 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 5 6 done [0.00s].
## writing ... [5668 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].# 4. Sort rules by lift (highest first)
rules_by_lift <- sort(rules, by = "lift", decreasing = TRUE)Apriori algorithm Output:
The Apriori algorithm generated 5,668 association rules using minimum support of 0.001 (at least 9 transactions) and confidence of 0.5.
The algorithm successfully processed all 9,835 transactions with 169 items, reducing to 157 items after recoding (excluding items too rare to meet the support threshold).
Rules include itemsets from size 2 up to size 6 as specified by maxlen=10.
3. Display top 10 rules by lift with support, confidence, lift
# ========== TOP 10 RULES BY LIFT ==========
inspect(rules_by_lift[1:10])## lhs rhs support confidence coverage lift count
## [1] {Instant food products,
## soda} => {hamburger meat} 0.001220132 0.6315789 0.001931876 18.99565 12
## [2] {soda,
## popcorn} => {salty snack} 0.001220132 0.6315789 0.001931876 16.69779 12
## [3] {flour,
## baking powder} => {sugar} 0.001016777 0.5555556 0.001830198 16.40807 10
## [4] {ham,
## processed cheese} => {white bread} 0.001931876 0.6333333 0.003050330 15.04549 19
## [5] {whole milk,
## Instant food products} => {hamburger meat} 0.001525165 0.5000000 0.003050330 15.03823 15
## [6] {other vegetables,
## curd,
## yogurt,
## whipped/sour cream} => {cream cheese } 0.001016777 0.5882353 0.001728521 14.83409 10
## [7] {processed cheese,
## domestic eggs} => {white bread} 0.001118454 0.5238095 0.002135231 12.44364 11
## [8] {tropical fruit,
## other vegetables,
## yogurt,
## white bread} => {butter} 0.001016777 0.6666667 0.001525165 12.03058 10
## [9] {hamburger meat,
## yogurt,
## whipped/sour cream} => {butter} 0.001016777 0.6250000 0.001626843 11.27867 10
## [10] {tropical fruit,
## other vegetables,
## whole milk,
## yogurt,
## domestic eggs} => {butter} 0.001016777 0.6250000 0.001626843 11.27867 10TOP 10 RULES BY LIFT, Observation
The highest lift rule (18.99) shows that buying “Instant food products” and “soda” together makes customers 19 times more likely to buy “hamburger meat” than buying it randomly.
All top 10 rules have lift values above 11, indicating strong positive associations, with 8 of the 10 rules involving dairy products (butter, cream cheese, yogurt) or meat items (hamburger meat, ham).
Most rules have low support (0.001-0.002 or 10-19 transactions) but high confidence (50-67%), meaning these are niche but reliable purchasing patterns.
4. Extra Credit: Cluster Analysis on Items
# Create binary matrix (items x transactions)
item_matrix <- t(as(Groceries, "matrix"))
# Jaccard distance & hierarchical clustering
item_dist <- dist(item_matrix, method = "binary")
hc_items <- hclust(item_dist, method = "average")
# Cut into 5 clusters
clusters <- cutree(hc_items, k = 5)
# Display results
cat("\n========== ITEM CLUSTERS (k=5) ==========\n")##
## ========== ITEM CLUSTERS (k=5) ==========for (i in 1:5) {
items_in_cluster <- names(clusters[clusters == i])
cat(paste0("\nCluster ", i, " (", length(items_in_cluster), " items):\n"))
cat(paste(items_in_cluster[1:min(10, length(items_in_cluster))], collapse = ", "))
if (length(items_in_cluster) > 10) cat(", ...")
cat("\n")
}##
## Cluster 1 (165 items):
## frankfurter, sausage, liver loaf, ham, meat, finished products, organic sausage, chicken, turkey, pork, ...
##
## Cluster 2 (1 items):
## frozen chicken
##
## Cluster 3 (1 items):
## liqueur
##
## Cluster 4 (1 items):
## make up remover
##
## Cluster 5 (1 items):
## sound storage medium# bar plot of cluster sizes
cluster_sizes <- table(clusters)
barplot(cluster_sizes,
main = "Item Cluster Sizes (k=5)",
xlab = "Cluster",
ylab = "Number of Items",
col = 2:6,
names.arg = paste("Cluster", 1:5),
ylim = c(0, max(cluster_sizes) + 10))
# Add count labels on bars
text(x = 1:5, y = cluster_sizes + 5,
labels = cluster_sizes, cex = 1.2)
Interesting observation: cluster 1 has 165 items whereas cluster 2-5 has one item each.
Lets check those items frequency and figure out why its happening?
# Check frequency of singleton items
itemFrequency(Groceries)[c("frozen chicken", "liqueur",
"make up remover", "sound storage medium")]## frozen chicken liqueur make up remover
## 0.0006100661 0.0009150991 0.0008134215
## sound storage medium
## 0.0001016777Why 1 cluster has 165 items, others have 1 each
Frequencies of the 4 “singleton” items:
frozen chicken → appears in 6 receipts (0.06%)
liqueur → appears in 9 receipts (0.09%)
make up remover → appears in 8 receipts (0.08%)
sound storage medium → appears in 1 receipt (0.01%) The math: For Jaccard distance:
If an item appears in only 1-9 transactions out of 9835
It almost never co-occurs with any other item
Intersection with any other item = 0 (or very tiny)
Jaccard similarity = 0 → distance = 1 (maximum)
These items are statistical orphans - they don’t cluster because they don’t share baskets with others.
Filter out rare items:
# Function to get cluster summary with different threshold
cluster_summary <- function(min_support, n_clusters = 4) {
# Filter items
keep_items <- itemFrequency(Groceries) >= min_support
data_filt <- Groceries[, keep_items]
# Cluster
mat <- t(as(data_filt, "matrix"))
dist_mat <- dist(mat, method = "binary")
hc <- hclust(dist_mat, method = "average")
clusters <- cutree(hc, k = n_clusters)
# Return clean results
list(
threshold = paste0(min_support * 100, "%"),
transactions = paste0(min_support * 9835, "+"),
items = ncol(data_filt),
cluster_sizes = as.vector(table(clusters)),
clusters = clusters
)
}
# Test different thresholds
thresholds <- c(0.01, 0.005, 0.001) # 1%, 0.5%, 0.1%
n_transactions <- c(98, 49, 10)
# output
for(i in 1:3) {
result <- cluster_summary(thresholds[i])
cat("Threshold:", result$threshold,
"| Min transactions:", n_transactions[i],
"| Items kept:", result$items, "\n")
cat(" Cluster sizes:", paste(result$cluster_sizes, collapse = ", "), "\n\n")
}## Threshold: 1% | Min transactions: 98 | Items kept: 88
## Cluster sizes: 81, 2, 3, 2
##
## Threshold: 0.5% | Min transactions: 49 | Items kept: 120
## Cluster sizes: 117, 1, 1, 1
##
## Threshold: 0.1% | Min transactions: 10 | Items kept: 157
## Cluster sizes: 150, 3, 2, 2Key insight:
1% threshold (98+ transactions) → Most balanced (81 items in main cluster, small outliers)
0.5% or 0.1% → Highly skewed because rare items become singletons
Recommendation: Use min_support = 0.005 (49+ transactions) for meaningful clusters without too many outliers.