How Are Silhouette Scores Calculated?

Silhouette scores are used to determine the quality of a given clustering result. They quantify the amount of separation between clusters and provide a measure of how well samples have been assigned to their respective clusters. A higher Silhouette score indicates that the clustering result is better and that the samples have been assigned more accurately to their respective clusters.

Silhouette scores are calculated by taking into account both the intra-cluster distance and inter-cluster distance. The intra-cluster distance is defined as the average distance between a sample and all other samples within its own cluster, while the inter-cluster distance is defined as the average distance between a sample and all other samples in different clusters. The Silhouette score is then computed as the difference between these two distances, divided by the maximum of both distances.

The calculation of Silhouette scores can be further broken down into two steps. First, for each sample, we calculate its average intra-cluster distance (a) and its average inter-cluster distance (b). Then, for each sample, we compute its Silhouette score as: s = (b – a) / max(a, b)

The Silhouette score of a particular clustering result is determined by taking the mean of all individual Silhouette scores. In other words, it is calculated by taking the mean of all individual s values.

In conclusion, Silhouette scores are used to assess the quality of a given clustering result. They are calculated by taking into account both intra-cluster and inter-cluster distances and computing an individual score for each sample before finally taking the mean to determine an overall score for the whole clustering result.