Elbow Method — SegmentIQ

❓ What is the Elbow Method?

K-Means requires us to specify K (the number of clusters) upfront. The Elbow Method helps us choose K systematically by plotting the Within-Cluster Sum of Squares (WCSS) for different K values.

WCSS measures how tightly packed each cluster is. As K increases, WCSS always decreases. But the rate of improvement slows — creating an "elbow" shape in the plot.

The elbow point — where the curve bends sharply — indicates the optimal K where adding more clusters yields diminishing returns.

Algorithm Steps:

1 For k = 1 to 10, fit KMeans

2 Record WCSS (model.inertia_)

3 Plot K vs WCSS

4 Find the elbow (inflection point)

5 Choose K at the elbow

💻 Code

          Python
            from sklearn.cluster import KMeans

            wcss = []  # List to store WCSS per k

            for k in range(1, 11):

                km = KMeans(

                    n_clusters   = k,

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

                    n_init       = 10,

                   random_state = 42,

               )

               km.fit(X_scaled)     # Fit on scaled data

               wcss.append(km.inertia_)  # inertia_ = WCSS

WCSS vs Number of Clusters

📊 WCSS Values Table

k	1	2	3	4	5	6	7	8	9	10
WCSS	400.0	269.7	157.7	108.9	65.6	55.1	44.9	37.2	32.4	30.0

Conclusion: At k=5, the WCSS curve bends significantly. Adding a 6th cluster provides only marginal improvement. Optimal K = 5

📈 Elbow Method