#load packages
set.seed(123)
knitr::opts_chunk$set(message = FALSE, warning = FALSE, fig.width = 7, fig.height = 5)

# Load packages
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.3
library(data.table)
library(ggrepel)

1 Load the Data

filename <- "customer_clustering_data.csv"

#TODO: use fread to load the data into a data.table called df
df = ...

2 Quick EDA (Scatter & Distributions)

Let’s plot the scatter plot of Online (x axis) vs In-Store Spend (y axis), income, and age distribution

# TODO: Create the three plots: (1) online vs offline spend, (2) income distribution, (3) age distribution
p1 = ggplot(df, ...)

p2 = ggplot(df, ...)

p3 = ggplot(df, ...)

p1
p2
p3
  • Do you see natural groupings by spend/income/age (e.g., online-heavy, in-store-heavy, omni-channel (i.e., customer who spend in both channels))?

3 Choose features for clustering and scale them

The features we will use are Online_Spend, InStore_Spend, Age, Income.

# This is done for you 

features <- df[, .(Online_Spend, InStore_Spend, Age, Income)]
X <- scale(features)  # mean=0, sd=1
summary(X)
  • Why do we scale before k-means?

4 Choose k: Elbow Method (WSS)

# this code computes the within-cluster sum of squares (wss) for k=2 to k=10
wss <- sapply(2:10, function(k){
  kmeans(X, centers = k, nstart = 25)$tot.withinss
})

# TODO: plot the within-cluster sum of squares (wss vs number of clusters)
elbow_plot <- data.frame(k = 2:10, wss = wss)
ggplot(elbow_plot, ...)
  • Inspect the plot. Where is the “elbow”? Propose a k.

5 Fit K-means with the optimal K identified above

# TODO: set K and run kmeans
k = ...

# run kmeans
km = 
  
#add cluster label to df as a new variable called "cluster"

6 Cluster Profiling (Means by Cluster)

# TODO: compute means of features by cluster
  • What business personas do these clusters represent?

7 PCA Projection

7.1 Run PCA

# This is done for you

# run PCA on scaled data
pca_result <- prcomp(X, center = FALSE, scale. = FALSE)
# check variance explained
summary(pca_result)
  • How many PCs explain >80% of variance?

7.2 Extract PCA Loadings

# This is done for you

# Keep first two principal components (scores) and add cluster labels
pca_data <- data.frame(pca_result$x[, 1:2], cluster = df$cluster)

# Extract loadings which tell you how each original variable contributes to each PC.
pca_loadings <- as.data.frame(pca_result$rotation[, 1:2]) # 2 columns: PC1, PC2
pca_loadings$variable <- rownames(pca_loadings)           # keep var names for plotting
pca_loadings[,1:2]
  • What do the loadings tell you about how each original variable contributes to each PC?

7.3 Plot PCA loadings

# This is done for you

# Scale arrows for better visibility in plots
arrow_scale <- 10   # tweak if arrows are too short/long

# Plot loadings alone (annotated with variables names)
p_loadings <- ggplot(pca_loadings, aes(x = PC1 * arrow_scale, y = PC2 * arrow_scale, label = variable)) +
  geom_segment(aes(x = 0, y = 0, xend = PC1 * arrow_scale, yend = PC2 * arrow_scale),
               arrow = arrow(length = unit(0.3, "cm")), color = "blue") +
  geom_text(size = 5) +
  labs(
    title = "PCA Loadings: Store attributes",
    x = "\nPrincipal Component 1",
    y = "Principal Component 2\n"
  ) +
  geom_vline(xintercept = 0, linetype = "dashed", color = "gray") +
  geom_hline(yintercept = 0, linetype = "dashed", color = "gray") +
  theme_minimal() +
  coord_cartesian(xlim = c(-2, 8), ylim = c(-10, 4))  # adjust as needed
p_loadings
  • Do the directions of the arrow align with you previous description of the PCs? (Interpretation tip: A long arrow toward PC1+ means that variable increases as you move right; toward PC2+ means it increases as you move up. Opposite directions imply negative association with that PC.)

7.4 Plot PCA scores with clusters

# TODO: plot the PCA scores (i.e, the value of PC1 and PC2 for each row of the dataset) and color them by cluster
ggplot(pca_data, ...)
  • Do clusters separate cleanly in the first two PCs?

7.5 PCA Biplot (Scores + Loadings)

# This is done for you

arrow_scale <- 2   # tweak if arrows are too short/long

biplot <- ggplot() +
  geom_point(data = pca_data, aes(x = PC1, y = PC2, color = cluster), size = 2, alpha = 0.8) +
  geom_segment(data = pca_loadings,
               aes(x = 0, y = 0, xend = PC1*arrow_scale, yend = PC2*arrow_scale),
               arrow = arrow(length = unit(0.2, "cm")),
               color = "blue") +
  geom_text(data = pca_loadings,
            aes(x = PC1 * 1.4, y = PC2 * 1.4, label = variable),
            size = 4) +
  labs(
    title = "Biplot of PCA",
    x = "\nPrincipal Component 1",
    y = "Principal Component 2\n"
  ) +
  geom_vline(xintercept = 0, linetype = "dashed", color = "gray") +
  geom_hline(yintercept = 0, linetype = "dashed", color = "gray") +
  theme_minimal()
biplot

  • How do the clusters relate to the original features based on the biplot? Do you see a correspondence with the clustering means table above (part 6)?

  • Now that you performed the whole clustering analysis, answer the following questions:

    • Which cluster looks most valuable?
    • What marketing actions would you take for each segment? (e.g., how would you target them? how? what offers?)