Non-parametric latent modeling and network clustering

TL;DR

This paper introduces a non-parametric latent modeling approach for bivariate data that uses an EM algorithm to generate soft clusterings, offering new methods for network clustering and HMM co-clustering.

Contribution

It presents a novel non-parametric EM-based method for latent and co-latent modeling, including network clustering and HMM co-clustering, with systematic revisiting of existing results and new variants.

Findings

Clustering algorithm for weighted networks from square contingency tables.

A co-clustering algorithm for HMM models different from Baum-Welch.

Three case studies demonstrating the effectiveness of the methods.

Abstract

The paper exposes a non-parametric approach to latent and co-latent modeling of bivariate data, based upon alternating minimization of the Kullback-Leibler divergence (EM algorithm) for complete log-linear models. For categorical data, the iterative algorithm generates a soft clustering of both rows and columns of the contingency table. Well-known results are systematically revisited, and some variants are presumably original. In particular, the consideration of square contingency tables induces a clustering algorithm for weighted networks, differing from spectral clustering or modularity maximization techniques. Also, we present a co-clustering algorithm applicable to HMM models of general kind, distinct from the Baum-Welch algorithm. Three case studies illustrate the theory.