  Supervised classification can be effective for prediction but sometimes weak
on interpretability or explainability (XAI). Clustering, on the other hand,
tends to isolate categories or profiles that can be meaningful but there is no
guarantee that they are useful for labels prediction. Predictive clustering
seeks to obtain the best of the two worlds. Starting from labeled data, it
looks for clusters that are as pure as possible with regards to the class
labels. One technique consists in tweaking a clustering algorithm so that data
points sharing the same label tend to aggregate together. With distance-based
algorithms, such as k-means, a solution is to modify the distance used by the
algorithm so that it incorporates information about the labels of the data
points. In this paper, we propose another method which relies on a change of
representation guided by class densities and then carries out clustering in
this new representation space. We present two new algorithms using this
technique and show on a variety of data sets that they are competitive for
prediction performance with pure supervised classifiers while offering
interpretability of the clusters discovered.
