The Limitations Of Elbow Curve And What You Should Replace It With

We commonly use the Elbow curve to determine the number of clusters (k) for KMeans.

However, the Elbow curve:

• has a subjective interpretation

• involves ambiguity in determining the Elbow point accurately

• only considers a within-cluster distance, and more.

Silhouette score is an alternative measure used to evaluate clustering quality.

It is computed as follows:

• For every data point (i), find:

  • a(i): average distance to every other data point within the cluster

  • b(i): average distance to every data point in the nearest cluster.

• Silhouette score for a specific data point (i) is:

• Silhouette score for the whole clustering is:

Some properties of the Silhouette score are:

• it ranges from [-1,1]

• a higher score indicates better clustering

• it can be used as an evaluation metric for clustering in the absence of ground truth labels

In contrast to the Elbow curve, the Silhouette score:

• provides a quantitative (and objective) measure

• involves no ambiguity

• considers BOTH within-cluster and between-cluster distance.

The visual below compares the Elbow curve and the Silhouette plot.

It’s clear that the Elbow curve is highly misleading and inaccurate.

In a dataset with 25 clusters:

• The Elbow curve depicts 4 as the number of optimal clusters.

• The Silhouette curve depicts 25 as the number of optimal clusters.

Get started with Silhouette score here: Sklearn Docs.

👉 Over to you: What are some other measures to evaluate clustering quality?

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