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I have a set of clusters which each cluster contains a list of short documents. I want to compute how coherent and cohesive each cluster is and filter out the incoherent and in-cohesive ones.

I am aware of intra-cluster distance and within-cluster dispersion, which are part of computing clustering evaluation metrics Silhouette Coefficient and Calinski-Harabaz Index, respectively. My question is, is there any other metrics or ways to compute such intra-cluster coherence or cohesion? Is there any standard ways for this that I am not aware of? Thanks.

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The Silhouette Coefficient is a good option. The Calinski-Harabaz Index has been shown to be unstable for evaluating noisy datsets, so I would recommend the Silhouette Coefficient over Calinski-Harabaz Index.

The Clustering Validation index based on Nearest Neighbors (CVNN) index has been demonstrated to work well for many different datasets containing high noise, arbitrarily shaped clusters, and skewed distributions.

A few other validation measures you can try using are the SD validity index, the S_Dbw validitiy index, and the Xie-Beni index.

The following is a good manuscript for interal clustering validation metrics manuscript.

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