Silhouette Analysis: Determining the Optimal Number of Clusters in K-Means Clustering

Silhouette analysis is a method used to determine the optimal number of clusters in a dataset. It's a graphical representation showing how well each data point fits within its assigned cluster. The silhouette plot displays a measure of how similar an object is to its own cluster compared to other clusters.

The silhouette plot is a graph that depicts how tightly grouped the samples in the clusters are. It presents the silhouette coefficient for each data point, ranging from -1 to 1. A high silhouette coefficient indicates that the data point is well-matched to its own cluster and poorly matched to neighboring clusters. Conversely, a low silhouette coefficient suggests the data point might be assigned to the wrong cluster.

The silhouette plot consists of a vertical line for each data point, where the line's height represents the silhouette coefficient. The points are sorted by their cluster assignment, with clusters differentiated by color. The width of each cluster reflects the number of data points assigned to it.

The optimal number of clusters is the one that maximizes the average silhouette coefficient across all data points. A higher average silhouette coefficient signifies well-separated clusters with data points within each cluster being similar. The silhouette plot helps identify the optimal number of clusters by visualizing the distribution of the silhouette coefficients for each cluster.