The silhouette coefficient

The silhouette coefficient finds the similarity of an item in a cluster to its own cluster items and other nearest clusters. It is also used to find the number of clusters, as we have seen elsewhere in this chapter. A high silhouette coefficient means better clustering results. This can be calculated as follows:

a_i is the average distance of the i^th data point to other points within the cluster.

b_i is the average distance of the i^th data point to other cluster points.

So, we can say that S(i) would be between [-1, 1]. So, for S(i) to be near to 1, a_i must be very small compared to b_i, that is, a_i << b_i.