I am recently study clustering quality metrics like Normalized Mutual Information and Fowlkes-Mallows scores.
Both of the scoring metrics seem to focus on a summary of the entire clustering quality. I am wondering whether there is a standard way or variant of the metrics above to measure the quality of a certain cluster or a certain class? The basic idea is that even if the overall looks good but some certain cluster is problematic, the metrics will still give warnings.
PS: I am not looking for any intrinsic methods. More precise, let's assume what I have is, for each data point x_i belong to dataset X, there is a ground truth class mapping x_i -> y_i, and a clustering x_i -> z_i, where y_i, z_i indicates the membership and don't necessarily have the same cardinality. Besides, I would like to further assume there is no distance measure d(x_i, x_j) defined.
One can evaluate clusters using extrinsic and intrinsic measures. Some methods of extrinsic measures are Mutual information and Adjusted rand Index, and intrinsic methods are the Silhouette coefficient, Calinski, etc. Refer to link.
https://towardsdatascience.com/clustering-evaluation-strategies-98a4006fcfc
Have a look at :: Article Clustering quality metrics for subspace clustering
https://medium.com/@ODSC/assessment-metrics-for-clustering-algorithms-4a902e00d92d
See also
https://stats.stackexchange.com/questions/6252/clustering-quality-measure
https://uhlibraries.pressbooks.pub/buildingskillsfordatascience/chapter/cluster-validity/
You can use the MATLAB 'silhouette' command to print the metric value for each individual point
https://in.mathworks.com/help/stats/silhouette.html
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