I've seen posts discussing clustering on labelled datasets. Below is an approach I'm considering. IN short, I would be clustering "base data" vs. "XAI-calculated" data to see how the XAI-calculated data discriminates better. Do the steps below make sense? My specific questions are listed after the steps below, but in short:

The key question I have behind all this is, besides whether the overall flow below makes sense, is the very last question at the bottom.

This last question asks about what appropriate statistical test to use to test my hypothesis that XAI (Shapley values) discriminate data better than base data alone. The metrics I would use are summary metrics based on clustering. Would I still be able to perform a statistical test if the summary metrics are not observation-specific but instead aggregate metrics?

BACKGROUND OF PROCESS:

Note: raw dataset is labelled, i.e., includes a binary target outcome variable

My questions and problem related to the above are the following:

• When I apply PCA, my understanding is, it is on the raw data, not predicted output?
• I assume it is OK to apply (unsupervised) k-means cluster to a labelled dataset if I am clustering based on the top two features identified by Shapley values (XAI metric) vs. clustering base data using PCA values on the top two features?
• To test my hypothesis as to whether Shapley values are more effective at discriminating data than base data alone, I was going to perform a t-test (or non-parametric equivalent) on the clustering metrics based on Shapley values vs. clustering metrics using base data. The base data would be without any model or XAI applied ... Does this approach make sense? The clustering metrics would be summary-level, not for each observation.