An equivalence between log-sum-exp approximation and entropy regularization in K-means clustering

Abstract

In this paper, we show an equivalence between log-sum-exp approximation and entropy regularization in K-means clustering, which is a well-known algorithm for partitional clustering. We derive an identical equation for updating centroids of clusters from the two formulations. Additionally, we derive an alternative equation suitable for another formulation of entropy regularization, maximum entropy method. We also show experimental results which support the theoretical results.