Fix definition of clustering silhouette coefficient for 1-element clusters

Reported by Samuel Kubler via email:

In the code https://github.com/apache/spark/blob/master/mllib/src/main/scala/org/apache/spark/ml/evaluation/ClusteringEvaluator.scala, I think there is a little mistake in the class “Silhouette” when you calculate the Silhouette coefficient for a point. Indeed, according to the scientific paper of reference “Silhouettes: a graphical aid to the interpretation and validation of cluster analysis” Peter J. ROUSSEEUW 1986, for the points which are alone in a cluster it is not the currentClusterDissimilarity which is supposed to be equal to 0 like it is the case in your code (“val currentClusterDissimilarity = if (pointClusterNumOfPoints == 1)

” but the silhouette coefficient itself. Indeed, “When cluster A contains only a single object it is unclear how a should be defined, and the we simply set s equal to zero”.

The problem of defining the currentClusterDissimilarity to zero like you have done is that you can’t use the silhouette coefficient anymore as a criterion to determine the optimal value of the number of clusters in your clustering process because your algorithm will answer that the more clusters you have, the better will be your clustering algorithm. Indeed, in that case when the number of clustering classes increases, s converges toward 1. (so your algorithm seems to be more efficient) I have, beside, check this result of my own clustering example.