Estimating the quality of clustering with silhouette scores

If the data is naturally organized into a number of distinct clusters, then it is easy to visually examine it and draw some inferences. But this is rarely the case in the real world. The data in the real world is huge and messy. So we need a way to quantify the quality of the clustering.

Silhouette refers to a method used to check the consistency of clusters in our data. It gives an estimate of how well each data point fits with its cluster. The silhouette score is a metric that measures how similar a data point is to its own cluster, as compared to other clusters. The silhouette score works with any similarity metric.

For each data point, the silhouette score is computed using the following formula:

silhouette score = (p - q) / max(p, q)

Here, p is the mean distance to the points in the nearest cluster that the data point is not a part of, and q is the mean intra-cluster distance to all the points in its own cluster.

The value of...