Silhouette Analysis: Finding the Optimal Number of Clusters for K-Means

A silhouette plot is a graphical representation of the silhouette coefficient for each data point in a dataset. The silhouette coefficient measures how similar a data point is to its own cluster compared to other clusters. The coefficient ranges from -1 to 1, where a value of 1 indicates that the data point is well-matched to its own cluster, and a value of -1 indicates that the data point is better matched to another cluster. The silhouette plot displays a vertical line for each data point, with the height of the line indicating the silhouette coefficient. The plot can be used to visually identify the optimal number of clusters for a k-means clustering algorithm by looking for the number of clusters with the highest average silhouette coefficient across all data points.