Clustering Analysis of Wholesale Customers

ML Capstone Project — Group 4

Unsupervised customer segmentation using K-Means, Agglomerative Hierarchical Clustering, and DBSCAN, with and without PCA dimensionality reduction.

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Table of Contents

• Project Overview
• Dataset
• Repository Structure
• Pipeline
• Algorithms & Hyperparameter Tuning
• Results Summary
• Requirements
• How to Run
• Key Findings

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Project Overview

This project explores whether meaningful customer segments can be discovered from wholesale purchase data using unsupervised learning — without any ground-truth labels. Three clustering algorithms are benchmarked on the same preprocessed data, evaluated using three internal validity metrics, and compared across both original 6-D feature space and a 2-D PCA-reduced space.

Research question: Can annual spending patterns across six product categories reliably segment wholesale customers, and how do different algorithms compare on this task?

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Dataset

Source: UCI Wholesale Customers Dataset

Property	Value
Samples	440
Features used	6 (continuous spending variables)
Features excluded	Channel, Region (used for post-hoc validation only)
Missing values	None

Features: fresh, milk, grocery, frozen, detergents_paper, delicassen

All features exhibit heavy right skew (skewness 4–8) and coefficients of variation exceeding 1, necessitating log-transformation and standardisation before clustering.

The dataset is loaded directly from Google Drive in the notebook:

url = 'https://drive.google.com/uc?id=1yDhLUJoB-Z69OL2Ad7tvm_0Gt6Dh2a5o'
data = pd.read_csv(url)

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Repository Structure

.
├── Untitled10-Copy1.ipynb      # Main analysis notebook
├── cluster_plots.png           # PCA scatter plots for all three algorithms
├── selection_plots.png         # Silhouette curves + k-distance graph
├── clustering_report_5_page_draft.docx   # Draft report
├── Capstone_Group4_Final_Report.docx     # Final 5-page report (with figures)
└── README.md

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Pipeline

Raw CSV
   │
   ▼
Column normalisation (lowercase names)
   │
   ▼
Drop Channel & Region  →  Feature matrix X (440 × 6)
   │
   ▼
log1p transformation   (tame skewness 4–8)
   │
   ▼
StandardScaler         (zero mean, unit variance)
   │
   ├──────────────────────────────────────┐
   ▼                                      ▼
Cluster on X_scaled (6-D)         PCA(n_components=2)
   │                               71.3% variance retained
   ▼                                      │
Evaluate metrics                          ▼
                                  Cluster on X_pca (2-D)
                                          │
                                          ▼
                                  Evaluate metrics + plot

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Algorithms & Hyperparameter Tuning

K-Means

• Tuning range: k ∈ {2, …, 10}
• Settings: n_init=20, random_state=42
• Selection method: silhouette peak + elbow in inertia curve
• Optimal: k = 2

def tune_kmeans(X_scaled, k_range, random_state=42):
    # Returns DataFrame of silhouette, DBI, CH scores per k

Agglomerative Hierarchical Clustering

• Linkage: Ward (minimises within-cluster variance)
• Tuning range: n_clusters ∈ {2, …, 10}
• Selection method: silhouette score
• Optimal: n_clusters = 2

def tune_agglomerative(X_scaled, cluster_range, linkage="ward"):
    # Returns DataFrame of silhouette, DBI, CH scores per n_clusters

DBSCAN

• min_samples = 5 (standard rule-of-thumb for moderate-dimensional data)
• ε selected via 5-NN distance graph (knee of sorted distance curve ≈ 0.7)
• Optimal: eps = 0.7, min_samples = 5

def compute_k_distance(X_scaled, min_samples=5):
    # Plots sorted k-NN distances; returns distances array

def tune_dbscan(X_scaled, param_grid):
    # Returns DataFrame of cluster count, noise %, silhouette, DBI, CH per (eps, min_samples)

Evaluation Metrics

Metric	Better when	Notes
Silhouette Score	Higher ↑	Range −1 to 1; > 0.25 = weak, > 0.5 = strong
Davies-Bouldin Index (DBI)	Lower ↓	0 = perfect separation
Calinski-Harabasz Index (CH)	Higher ↑	Ratio of between- to within-cluster scatter

Note: For DBSCAN, all metrics are computed on non-noise points only (labels != -1). This inflates silhouette when noise ratio is high — always check noise % alongside the score.

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Results Summary

Original Feature Space (6-D)

Algorithm	k / ε	Silhouette	DBI	CH	Noise
K-Means	k=2	0.2903	1.3515	189.05	0.0%
Agglomerative	k=2	0.2585	1.6004	134.62	0.0%
DBSCAN †	ε=0.7	0.3640	1.2523	73.25	77.95%

PCA Space (2-D, 71.3% variance)

Algorithm	k / ε	Silhouette	DBI	CH	Noise
K-Means	k=2	0.4082 ★	0.9724 ★	320.89 ★	0.0%
Agglomerative	k=2	0.4043	0.9962	292.35	0.0%
DBSCAN	ε=0.7	0.3387	0.6324	16.10	6.59%

★ Best overall. † DBSCAN original-space silhouette computed on 22% of points — not directly comparable.

Recommended model: K-Means (k=2) on PCA-transformed data.

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Requirements

numpy
pandas
matplotlib
seaborn
scipy
scikit-learn

Install with:

pip install numpy pandas matplotlib seaborn scipy scikit-learn

The notebook was developed on Google Colab and loads data directly from Google Drive. No local data files are required.

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How to Run

1. Open Untitled10-Copy1.ipynb in Google Colab or Jupyter.
2. Run all cells top to bottom. The notebook is self-contained:
   • Data loads from the public Google Drive URL
   • All preprocessing, tuning, and evaluation runs sequentially
   • Cluster plots and selection plots are generated inline
3. To reproduce specific sections:

Section	What it does
Cells 1–2	Load data, EDA, normality tests, correlation heatmap
Cell 3	Full hyperparameter tuning for all three algorithms
Cell 4	Simplified comparative output table
Cell 5	PCA projection + cluster scatter plots

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Key Findings

• Two clusters is the optimal solution across all algorithms and both feature spaces — consistent with the known HoReCa (hospitality) vs. Retail channel split in the data.
• PCA improves clustering quality for all methods, not just visualisation. K-Means silhouette improves by 40.6% and DBI improves by 28% in PCA space.
• DBSCAN is unsuitable for primary segmentation on this dataset's original space (78% noise), but becomes practical after PCA reduction (6.6% noise). Its best use here is outlier/anomaly detection.
• Metric disagreement matters: DBSCAN's inflated silhouette (0.364) on original data is misleading — always pair silhouette with noise coverage when evaluating density-based methods.
• Preprocessing is critical: log1p + StandardScaler is not optional here; raw feature skewness of 4–8 makes Euclidean distances meaningless without it.