What indicates the optimal choice of k clusters in silhouette analysis?

In silhouette analysis, the silhouette coefficient is a measure used to assess how well-separated the clusters in a dataset are. The value of the silhouette coefficient ranges from -1 to +1, where a higher value indicates better-defined clusters.

A silhouette coefficient close to 1 is indicative of a good clustering solution. It signifies that the points in a cluster are well-separated from points in neighboring clusters. This means that data points are closer to other points within their own cluster than to points in other clusters, which reflects a strong clustering quality.

If the silhouette coefficient is near 0, it suggests that the data points are on or very close to the decision boundary between two neighboring clusters, indicating ambiguity in cluster assignment. A value above 1 is not possible, as the maximum value of the silhouette coefficient is 1, which represents perfect clustering.

Therefore, the best indication of the optimal choice of k clusters, as reflected by the silhouette analysis, is a silhouette coefficient close to 1, aligning well with the correct response.