Introduction

The purpose of this report is to investigate the relationship between different products in the market basket. The data used for this analysis was obtained from Kaggle, a popular data science community website that provides a variety of datasets to work with. The dataset consists of 7501 transactions or rows, each representing a shopping transaction carried out by a customer in a market.

There are a total of 119 columns in the dataset, representing 119 different products such as groceries and cleaning supplies. The most commonly purchased products include mineral water, eggs, spaghetti, french fries, and many more.

Upon analyzing the data, it was discovered that most of the transactions consisted of small baskets containing 1, 2, or 3 products, which occurred 1787, 1358, and 1306 times, respectively, adding up to 51.41% of the total transactions. The median transaction consisted of the purchase of 3 products, with the first and third quartile of transactions containing 2 and 5 products, respectively. This means that most baskets had no more than 5 products.

If every basket was filled with all possible products, a total of 892,619 purchases could have been made. However, with a density of only 3.29%, only 29,358 purchases were made.

library(knitr)
library(arules)
## Loading required package: Matrix
## 
## Attaching package: 'arules'
## The following objects are masked from 'package:base':
## 
##     abbreviate, write
library(arulesViz)
library(kableExtra)
## Warning in !is.null(rmarkdown::metadata$output) && rmarkdown::metadata$output
## %in% : 'length(x) = 2 > 1' in coercion to 'logical(1)'
data <- read.transactions("Market_Basket_Optimisation.csv",  sep=",", header=TRUE)
## Warning in asMethod(object): removing duplicated items in transactions

To develop a better understanding of the dataset, I created graphical representations in the form of plots, which depicted the frequency of occurrence of each item in the data set. The plots showed both the absolute number of times an item appeared in the transactions as well as the percentage of total transactions that included that item. This allowed me to easily identify the most popular items in the dataset and gain insight into the overall distribution of items sold. Analyzing item frequency can help identify patterns in customer behavior, preferences and inform strategic business decisions.

itemFrequencyPlot(data, topN = 10, type = "absolute", main = "Item frequency", cex.names = 0.75 , support = 0.2, popCol = "black",
  popLwd = 1,
  lift = FALSE,
  horiz = FALSE,
  names = TRUE,col = rainbow(4))

Upon analyzing the item frequency in the Market Basket data, it has been found that Mineral water and eggs are the most frequently purchased products. This discovery can provide valuable insights into the transactional behavior of customers and the factors influencing their purchasing decisions.

This information can be leveraged by businesses to tailor their marketing strategies and improve the overall customer experience. For instance, promoting these popular products more effectively or expanding their product offerings in related categories can drive sales and improve customer satisfaction.

By understanding the item frequency distribution, businesses can also gain insights into customer preferences and identify potential opportunities for cross-selling or upselling. This can enable businesses to create more effective promotional campaigns and drive revenue growth.

In conclusion, analyzing the item frequency in Market Basket data can provide businesses with valuable insights that can be used to optimize their marketing strategies, improve customer experience and drive sales growth.

Association Rule

Association rules are used in market basket analysis to identify relationships between two or more products that frequently occur together in transactions. These rules are characterized by a few parameters that are used to measure the strength and significance of the relationships between products.

The support level of a rule measures how often the rule appears in the dataset compared to the total number of transactions. This parameter is used to determine how frequently the rule occurs and how significant the relationship between the products is.

The confidence level of a rule measures the percentage of times when both the consequent product(s) and antecedent product(s) appear in a transaction, in comparison to all the times when the antecedent product(s) appear in a transaction. In other words, it is a ratio of the support level of both the consequent and antecedent items to the support level of the antecedent item(s). This parameter is used to determine how often the consequent product(s) occur when the antecedent product(s) are present, and how strong the relationship between the products is.

The lift level of a rule measures the ratio of the confidence level of the rule to the support level of the consequent product(s) from the rule. It can also be described as the probability of the consequent product(s) occurring in the transaction where the antecedent product(s) occur, compared to the probability of the consequent product(s) occurring in the whole set of transactions. Lift values higher than one indicate a positive relationship between two products (or sets of products), while values lower than one indicate a negative relationship. If the lift level is equal to one, the products are independent, and the rule has no significance.

These parameters are used to identify the most significant association rules between products in the dataset. By analyzing these rules, businesses can gain insights into customer behavior and preferences, and use this information to optimize their product offerings and marketing strategies.

Apriori Algorithm

Apriori is a widely used algorithm for association rule mining in market basket analysis. It helps identify frequent item sets in a large dataset that can be used to generate association rules between items.

To use the algorithm, a database of transactions is needed. Apriori works by iteratively reducing the number of items in the frequent item sets until only frequent items remain. This is done using a “bottom-up” approach, starting with single items and then combining items to create larger item sets. The algorithm prunes candidate item sets that are not frequent enough based on a support threshold. The algorithm then generates all frequent item sets and selects the rules that meet a minimum confidence threshold.

Apriori’s time complexity is O(2^n), which can make it computationally expensive for large datasets. However, its simplicity and ability to identify frequent patterns in large datasets make it a widely used algorithm.

To start the algorithm, item sets of size 1, called candidates, are generated. Each candidate is then checked against the data to determine its support. If a candidate item set has sufficient support, it is considered a frequent item set and added to a set of frequent item sets. Next, the algorithm generates new candidates by combining the frequent item sets, and the process is repeated. The algorithm continues to generate new candidates and check their support until no more frequent item sets can be found.

Finally, association rules can be generated by computing the confidence of each frequent item set. Confidence is defined as the proportion of transactions that contain the antecedent (left-hand side) also containing the consequent (right-hand side). By using Apriori to generate association rules, businesses can better understand customer purchasing behavior and make informed decisions about product offerings and promotions.

rules_apriori_algorithm<-apriori(data, parameter=list(supp=0.02, conf=0.3))
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.3    0.1    1 none FALSE            TRUE       5    0.02      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: 150 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[119 item(s), 7500 transaction(s)] done [0.00s].
## sorting and recoding items ... [53 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 done [0.00s].
## writing ... [20 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
rules_apriori_algorithm_i <-  inspect(head(sort(rules_apriori_algorithm, by = "support", decreasing = TRUE),10))
##      lhs                    rhs             support    confidence coverage  
## [1]  {spaghetti}         => {mineral water} 0.05973333 0.3430322  0.17413333
## [2]  {chocolate}         => {mineral water} 0.05266667 0.3213995  0.16386667
## [3]  {milk}              => {mineral water} 0.04800000 0.3703704  0.12960000
## [4]  {ground beef}       => {mineral water} 0.04093333 0.4165536  0.09826667
## [5]  {ground beef}       => {spaghetti}     0.03920000 0.3989145  0.09826667
## [6]  {frozen vegetables} => {mineral water} 0.03573333 0.3748252  0.09533333
## [7]  {pancakes}          => {mineral water} 0.03373333 0.3548387  0.09506667
## [8]  {burgers}           => {eggs}          0.02880000 0.3302752  0.08720000
## [9]  {olive oil}         => {mineral water} 0.02746667 0.4178499  0.06573333
## [10] {cake}              => {mineral water} 0.02746667 0.3388158  0.08106667
##      lift     count
## [1]  1.439698 448  
## [2]  1.348907 395  
## [3]  1.554436 360  
## [4]  1.748266 307  
## [5]  2.290857 294  
## [6]  1.573133 268  
## [7]  1.489250 253  
## [8]  1.837585 216  
## [9]  1.753707 206  
## [10] 1.422002 206

The table shows the top 10 association rules generated by the Apriori algorithm, sorted in descending order by confidence. Each rule is characterized by the left-hand side (lhs) and right-hand side (rhs) itemsets, along with their support, confidence, coverage, lift, and count values.

The support of a rule represents the proportion of transactions that contain both the lhs and rhs itemsets. The confidence of a rule is the ratio of transactions that contain both the lhs and rhs itemsets to the total number of transactions that contain the lhs itemset. The coverage of a rule is the proportion of transactions that contain the lhs itemset. The lift of a rule represents the extent to which the lhs and rhs itemsets are dependent on each other, compared to if they were independent. A lift value greater than 1 indicates a positive relationship between the lhs and rhs itemsets, while a value less than 1 indicates a negative relationship.

From the table, we can observe that mineral water is a common rhs itemset in the top 10 rules, suggesting that it is frequently purchased with other items. For example, spaghetti is frequently purchased with mineral water, as indicated by the rule {spaghetti} => {mineral water} with a support of 0.0597 and a confidence of 0.3430. Similarly, milk, ground beef, and chocolate are also frequently purchased with mineral water.

The lift values in the table provide additional insights into the relationships between itemsets. For example, the lift value of 2.2908 for the rule {ground beef} => {spaghetti} indicates a strong positive relationship between ground beef and spaghetti, suggesting that these items are often purchased together. Conversely, the lift value of 0.9959 for the rule {olive oil} => {eggs} indicates a weak negative relationship between olive oil and eggs, suggesting that these items are less likely to be purchased together.

rules_apriori_algorithm_i <-  inspect(head(sort(rules_apriori_algorithm, by = "confidence", decreasing = TRUE),10))
##      lhs                    rhs             support    confidence coverage  
## [1]  {soup}              => {mineral water} 0.02306667 0.4564644  0.05053333
## [2]  {olive oil}         => {mineral water} 0.02746667 0.4178499  0.06573333
## [3]  {ground beef}       => {mineral water} 0.04093333 0.4165536  0.09826667
## [4]  {ground beef}       => {spaghetti}     0.03920000 0.3989145  0.09826667
## [5]  {cooking oil}       => {mineral water} 0.02013333 0.3942559  0.05106667
## [6]  {chicken}           => {mineral water} 0.02280000 0.3800000  0.06000000
## [7]  {frozen vegetables} => {mineral water} 0.03573333 0.3748252  0.09533333
## [8]  {milk}              => {mineral water} 0.04800000 0.3703704  0.12960000
## [9]  {tomatoes}          => {mineral water} 0.02440000 0.3567251  0.06840000
## [10] {pancakes}          => {mineral water} 0.03373333 0.3548387  0.09506667
##      lift     count
## [1]  1.915771 173  
## [2]  1.753707 206  
## [3]  1.748266 307  
## [4]  2.290857 294  
## [5]  1.654683 151  
## [6]  1.594852 171  
## [7]  1.573133 268  
## [8]  1.554436 360  
## [9]  1.497168 183  
## [10] 1.489250 253

Above table showing the list of top 10 items based on its confidence. Observing the table, it can be concluded that mineral water is a popular item that is commonly associated with various other items such as soup, olive oil, ground beef, spaghetti, cooking oil, chicken, frozen vegetables, milk, tomatoes, and pancakes. This indicates that the presence of mineral water in a customer’s basket increases the likelihood of them buying these other items as well. Retailers could use this information to create marketing strategies to promote these items together or provide discounts when purchased together to increase their sales.

Conclusion

In conclusion, the analysis of the dataset using the Apriori algorithm for association rule mining revealed several interesting insights about the customers’ purchasing behavior. The analysis identified frequent item sets and association rules based on support, confidence, and lift metrics. The top 10 association rules with the highest confidence levels showed that customers tend to buy mineral water along with other items such as spaghetti, milk, ground beef, and chocolate.

The lift metric revealed that the association between the antecedent and consequent items was positive, indicating that customers tend to buy these items together more often than expected by chance. This information can be used by the grocery store to optimize their product placement and marketing strategies to increase sales and customer satisfaction.

Reference