Silhuettiindeksi

Silhuettiindeksi, often translated as silhouette index, is a metric used in data clustering to evaluate the quality of clusters. It quantifies how similar an object is to its own cluster compared to other clusters. The index ranges from -1 to 1. A silhouette index close to 1 indicates that the object is well-matched to its own cluster and poorly matched to neighboring clusters. A value close to 0 suggests that the object is near the decision boundary between two clusters. A negative silhouette index implies that the object may have been assigned to the wrong cluster.

To calculate the silhouette index for a single data point 'a', two values are determined: 'a' is the mean distance between 'a' and all other data points in the same cluster. 'b' is the mean distance between 'a' and all data points in the nearest neighboring cluster. The silhouette coefficient for 'a' is then calculated as (b - a) / max(a, b). The overall silhouette index for a clustering is the average of the silhouette coefficients for all data points. This metric is particularly useful for determining the optimal number of clusters in a dataset, as the number of clusters that yields the highest average silhouette index is often considered the best fit. It provides a visual and numerical way to assess how separated and coherent the clusters are.