K-means Clustering

Introduction

• Customer segmentation is a key strategy in e-commerce that helps businesses classify customers based on their purchasing behavior.
• It enables targeted marketing efforts and supports customer retention strategies.
• Traditionally, segmentation was based on demographic attributes.
• With the rise of machine learning, data-driven methods like K-Means clustering have become more prevalent.
• This study uses K-Means clustering to analyze an online retail dataset and identify customer groups based on purchase behaviors.
• Recent research emphasizes the effectiveness of clustering algorithms for customer segmentation.

Introduction

• K-Means clustering is favored for its efficiency and ease of implementation (Paramita and Hariguna 2024).
• The study adopts K-Means clustering using R to enable a data-driven approach for customer analysis and business decision-making.

Selection of k (Number of Clusters)

The optimal number of clusters k is determined using the Elbow Method, which plots WCSS against k values. The elbow point—where the rate of decrease in WCSS (Within-Cluster Sum of Squares (WCSS) is a measure of the variance within clusters. The elbow point—where the curve bends—indicates the optimal number of clusters.) diminishes—indicates the optimal k.

\[ \text{WCSS} = \sum_{x_k \in Z_1^{(I)}} \text{distance}(x_k^{(j)}, z_1^{(I)})^2 + \sum_{x_k \in Z_2^{(I)}} \text{distance}(x_k^{(j)}, z_2^{(I)})^2 + \sum_{x_k \in Z_3^{(I)}} \text{distance}(x_k^{(j)}, z_3^{(I)})^2 + \cdots \]

Elbow Method (Image Source: Soumo Chatterjee)

Proximity Measures

K-Means clustering assigns points to clusters based on distance metrics. The most commonly used metrics are:

• Euclidean Distance (Most Common in K-Means):

\[ D_{euclidean}(x_1, x_2) = \sqrt{ \sum_{i=1}^{n} ((x_{1})_{i} - (x_{2})_{i})^2 } \]

• Manhattan Distance (Useful for Grid-Based Data):

\[ D_{manhattan}(x_1, x_2) = \sum_{i=1}^{n} |((x_{1})_{i} - (x_{2})_{i})| \]

Choosing an appropriate distance metric affects cluster shape and performance (Bradley, Bennett, and Demiriz 2000).

Data Exploration and Visualization

Exploratory Data Analysis

Data Cleaning and Transformation

# Data Cleaning
df <- df %>%
  filter(!is.na(CustomerID)) %>%
  filter(!grepl("^C", InvoiceNo)) %>%
  filter(Quantity > 0, UnitPrice > 0) %>%
  mutate(TotalSpending = Quantity * UnitPrice) %>%
  mutate(InvoiceDate = as.Date(InvoiceDate)) %>%
  mutate(Description = replace_na(Description, "Unknown"))

This reduces the dataset to valid transactions, removing 135,080 rows with missing CustomerID, cancelled transactions (starting with “C”), and entries with non-positive Quantity or UnitPrice.

Modeling and Results

RFM Analysis and Data Preparation

RFM analysis quantifies customer behavior using three metrics:

• Recency: Days since the last purchase (relative to December 10, 2011).
• Frequency: Number of transactions per customer.
• Monetary: Total spending per customer.

# Outlier Removal Function
remove_outliers <- function(data, column) {
  Q1 <- quantile(data[[column]], 0.25)
  Q3 <- quantile(data[[column]], 0.75)
  IQR_value <- Q3 - Q1
  lower_bound <- Q1 - 1.5 * IQR_value
  upper_bound <- Q3 + 1.5 * IQR_value
  data %>% filter(data[[column]] >= lower_bound & data[[column]] <= upper_bound)
}

# Removing Outliers
df <- df %>%
  remove_outliers("Quantity") %>%
  remove_outliers("UnitPrice")

# RFM Analysis Data Preparation
customer_data <- df %>%
  group_by(CustomerID) %>%
  summarise(
    Recency = as.numeric(as.Date("2011-12-10") - max(InvoiceDate)),
    Frequency = n(),
    Monetary = sum(TotalSpending)
  )

# Log Transformation
customer_data_log <- customer_data %>%
  mutate(
    Frequency = log1p(Frequency),
    Monetary = log1p(Monetary)
  )

# Standardizing Data for K-Means Clustering
customer_data_scaled <- customer_data_log %>%
  select(-CustomerID) %>%
  scale()

• Outliers in Recency, Frequency, and Monetary are removed using the IQR method.
• Log transformation (log1p) reduces skewness in the RFM metrics.
• Data is scaled to ensure equal weighting of features during clustering.

The boxplots show that after transformation, the distributions are more symmetric, though some outliers remain (e.g., high Monetary values).

K-Means Clustering Analysis

Determining Optimal k

In this step, we are using the Elbow Method to determine the optimal number of clusters (k) for K-Means clustering. The plot displays the Total Within Sum of Squares (WSS) for different values of k, and we observe how the WSS decreases as the number of clusters increases. In our case, the elbow clearly appears at k = 3, meaning that three clusters provide the best segmentation of the data without overfitting. Choosing more than three clusters would result in only marginal improvement while increasing complexity unnecessarily.

Applying K-Means Clustering

The visualization illustrates the results of a K-Means clustering algorithm applied to customer data, projected onto two principal components—Dim1 and Dim2—which together capture approximately 95.6% of the total variance (Dim1: 73.3%, Dim2: 22.3%). The plot reveals three distinct customer segments, each represented by a unique color and shape: Cluster 1 (blue circles), Cluster 2 (yellow triangles), and Cluster 3 (grey squares). The separation between clusters is generally clear, indicating well-defined groupings; however, there is a slight overlap between Clusters 2 and 3, suggesting the possibility of similar behaviors or characteristics among customers near the boundary. This dimensionality reduction has proven effective, as most of the important information in the dataset is retained in just two dimensions, allowing for clear interpretation and visual segmentation of the customer base. These insights can be valuable for targeted marketing, personalized services, or strategic business decisions.

Dim1 and Dim2 are principal components resulting from a dimensionality reduction technique

Cluster Profiling

Cluster Profiling is the process of analyzing the characteristics of different customer segments after applying a clustering algorithm (like K-means). It helps us understand the behavior and value of each group, making it easier to tailor marketing strategies and business decisions. In this analysis, we’ve grouped customers into three clusters based on their Recency, Frequency, and Monetary values (RFM analysis). We then calculated the average values of these metrics for each cluster to interpret their purchasing behavior. By visualizing these summaries, we can clearly identify which clusters contain loyal customers, occasional buyers, or those at risk of churn—allowing businesses to take targeted actions accordingly.

Insights

• Cluster 1 (Green): Moderate recency (~57 days), low frequency (~3 transactions), and moderate spending (~5.56 log units). These are occasional buyers.
• Cluster 2 (Yellow): Low recency (~37 days), high frequency (~4.78 transactions), and high spending (~7.33 log units). These are loyal, high-value customers.
• Cluster 3 (Blue): High recency (~256 days), low frequency (~2.60 transactions), and low spending (~5.13 log units). These are inactive customers at risk of churn.