K-Means Clustering — SegmentIQ

⚙️ How K-Means Works

Initialise

Place K centroids randomly (k-means++ places them smart — far apart) to seed the algorithm.

Assign

Each customer is assigned to the nearest centroid using Euclidean distance.

Update

Recompute each centroid as the mean of all customers in that cluster.

Repeat

Steps 2–3 are repeated until centroids stop moving (convergence) or max_iter is reached.

Evaluate

The final WCSS and Silhouette Score confirm cluster quality.

💻 Final Model Code

          Python
            from sklearn.cluster import KMeans

            import joblib

            # Instantiate with k-means++ initialisation

            km = KMeans(

                n_clusters   = 5,        # Optimal K from Elbow

                init         = 'k-means++',   # Smart seeding

                n_init       = 10,       # Run 10 times, pick best

                random_state = 42,       # Reproducibility

               max_iter     = 300,      # Safety limit

           )

           km.fit(X_scaled)           # Train on scaled data

           df['Cluster'] = km.labels_  # Add labels to df

           joblib.dump(km, 'kmeans_model.pkl')  # Save model

📍 Cluster Centroids (Scaled Space)

Cluster	Income (z)	Spending (z)
C0	-0.201	-0.026
C1	0.992	1.240
C2	-1.330	1.132
C3	1.055	-1.284
C4	-1.308	-1.137

📉 Silhouette Score Analysis

Silhouette Score vs Number of Clusters

Silhouette Score measures cluster separation and compactness on a scale from -1 to +1. Higher values indicate better-defined segments.

            s(i) = (b − a) / max(a, b)
          

a = intra-cluster distance · b = nearest-cluster distance

k	Silhouette Score	Quality
2	0.3213	Good
3	0.4666	Excellent
4	0.4939	Excellent
5	0.5547	Excellent
6	0.5399	Excellent
7	0.5281	Excellent
8	0.4552	Excellent
9	0.4571	Excellent
10	0.4432	Excellent

📊 Cluster Summary Statistics

Cluster	Customers	Share %	Avg Age	Avg Income (k$)	Avg Spending	Males	Females
Cluster 0	81	40.5%	42.7	55.3	49.5	33	48
Cluster 1	39	19.5%	32.7	86.5	82.1	18	21
Cluster 2	22	11.0%	25.3	25.7	79.4	9	13
Cluster 3	35	17.5%	41.1	88.2	17.1	19	16
Cluster 4	23	11.5%	45.2	26.3	20.9	9	14

⚙️ K-Means Clustering