Silhouette Score 2D: Finding the Right Number of Clusters

Clustering

Clusters K 4

Blob spread 0.90

Live Readouts

Avg silhouette

0.00

Inertia (WCSS)

0.0

Lloyd iteration

Best K (scan)

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How it works

K-means (Lloyd's algorithm) repeats two steps until the centroids stop moving: assign every point to its nearest centroid, then move each centroid to the mean of the points assigned to it. That process always finds some K clusters — but it never tells you whether K was the right choice.

The silhouette coefficient answers that question, per point:

a(i) = mean distance from i to other points
       in its own cluster        (cohesion)
b(i) = mean distance from i to the points
       of its nearest other cluster (separation)
s(i) = ( b(i) − a(i) ) / max( a(i), b(i) )

s(i) sits in [-1, 1]. Near +1 means the point is far tighter to its own cluster than to any rival — a good assignment. Near 0 means it sits on a boundary. Negative means it is actually closer to another cluster than its own — likely mis-clustered. Averaging s(i) over every point gives one score per K.

K slider — sets the number of clusters K-means is asked to find; try one too small and one too large and watch the halos.
Spread — widens or tightens the Gaussian blobs the dataset is drawn from, controlling how separable the true groups are.
New Dataset — redraws a fresh mixture of 3–6 hidden Gaussian blobs.
Run K-Means — animates Lloyd's algorithm converging for the current K; halo radius = |s(i)|, halo color green→red as s(i) falls from +1 to negative.
Scan K = 2…8 — runs K-means to convergence for every K and plots the average silhouette per K. Unlike inertia (which always keeps dropping as K rises — the flaw the "elbow method" struggles with), average silhouette peaks near the true number of groups, then falls again once you over-split real clusters.

Real-world relevance: this is exactly how data scientists pick K for customer segmentation, document clustering, or anomaly-cluster discovery when the "true" group count is unknown — scikit-learn's silhouette_score implements precisely this formula. Drag to pan the scatter plot, scroll or pinch to zoom.

drag = pan · scroll = zoom

iter 0

Dot = data point (color = assignment) Halo radius = |silhouette|, green = good fit Red halo = negative silhouette (misfit)