Given a set of points labeled with k labels, we introduce the heat map sorting problem as reordering and merging the points and dimensions while preserving the clusters (labels). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. We prove the problem is NP-hard and we give a fixed-parameter algorithm with a constant number of rounds in the massively parallel computation model, where each machine has a sublinear memory and the total memory of the machines is linear. We give an approximation algorithm for a NP-hard special case of the problem. We empirically compare our algorithm with k-means and density-based clustering (DBSCAN) using a dimensionality reduction via locality-sensitive hashing on several directed and undirected graphs of email and computer networks.
@article{arxiv.2309.07486,
title = {Massively-Parallel Heat Map Sorting and Applications To Explainable Clustering},
author = {Sepideh Aghamolaei and Mohammad Ghodsi},
journal= {arXiv preprint arXiv:2309.07486},
year = {2023}
}