What is the optimal number of clusters based on the following results?

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To determine the optimal number of clusters from the silhouette plot, we examine how the silhouette coefficient changes as k (the number of clusters) increases.
Option 1: k = 3 vs k = 1. At k = 1 the silhouette coefficient is essentially zero, because there is no clustering structure when all data are merged into a single cluster. This makes k = 1 clearly unattractive.
Option 2: k = 2. The plot shows a moderate silhouette value at k = 2, but it is lower than at k = 3. This indicates that the clustering structure with two clusters is not as well separated as with three clusters.
Option 3: k = 3. Here the silhouette coefficient reaches its highest value among the shown options, indicating the best separation and cohesion of clusters in this range. The larger average silhouette score implies more well-defined clusters.
Option 4: k = 5. The silhouette value at k = 5 declines relative to k = 3 and is close to or slightly below the k = 4 value, suggesting less cohesive or well-separated clusters than at k = 3.
Overall, the highest average silhouette score occurs at k = 3, and since a higher silhouette value indicates better-defined clusters, 3 is the optimal choice among the given options.

COS10022 Lecture 3_Knowledge Check

What is the optimal number of clusters based on the following results?

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