I know that feature selection methods such as the Laplacian score or Fisher score are typically used for dimension reduction prior to clustering, but is there any reason why the same methods couldn't be used post-clustering?

So, for example, suppose I had 4 clusters (Cluster A - Cluster D), could I use the Laplacian score on say, Cluster D, to reduce the dimensions further and specify a label for this cluster?

Any help on the theoretical limitations of using unsupervised feature selection post-clustering, would be appreciated.



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