Clustering Mixtures of Discrete Distributions: A Note on Mitra's Algorithm

TL;DR

This paper refines the analysis of Mitra's spectral clustering algorithm for discrete mixture models, especially in bipartite stochastic block models, providing improved separation conditions for better classification accuracy.

Contribution

It offers a more precise theoretical analysis of Mitra's algorithm, tailored to bipartite stochastic block models, with improved separation conditions compared to prior work.

Findings

Enhanced separation conditions for discrete mixture models

Refined analysis tailored to bipartite stochastic block models

Improved theoretical guarantees for clustering accuracy

Abstract

In this note, we provide a refined analysis of Mitra's algorithm \cite{mitra2008clustering} for classifying general discrete mixture distribution models. Built upon spectral clustering \cite{mcsherry2001spectral}, this algorithm offers compelling conditions for probability distributions. We enhance this analysis by tailoring the model to bipartite stochastic block models, resulting in more refined conditions. Compared to those derived in \cite{mitra2008clustering}, our improved separation conditions are obtained.