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Given a set of points labeled with $k$ labels, we introduce the heat mapsorting problem as reordering and merging the points and dimensions whilepreserving the clusters (labels). A cluster is preserved if it remainsconnected, i.e., if it is not split into several clusters and no two clustersare merged.  We prove the problem is NP-hard and we give a fixed-parameter algorithm witha constant number of rounds in the massively parallel computation model, whereeach machine has a sublinear memory and the total memory of the machines islinear. We give an approximation algorithm for a NP-hard special case of theproblem. We empirically compare our algorithm with k-means and density-basedclustering (DBSCAN) using a dimensionality reduction via locality-sensitivehashing on several directed and undirected graphs of email and computernetworks.

Massively-Parallel Heat Map Sorting and Applications To Explainable Clustering