I have a dataset with 535 samples, 63 dimensions and 7 clusters (labels). I am going to run some processes on my dataset and then track the impact of the process on the dataset. What approach would you suggest? for some reasons, dimensionality reduction techniques didn't go well, so I prefer approaches like having some metrics to evaluate the clusters before and after the process, metrics like Silhouette index, DB, etc. what other approaches would you follow?
I tried UMAP as the dimensionality reduction technique, but I don't know how reliable the results would be in my case. and one of my problems is that the Silhouette score is negative which shows bad clustering in high-dimensional space but UMAP gives me very distinct clusters... are there any metrics that show the overlapping clusters in high-dimensional space? and how can I track changes that occur to my clusters after the process?