Semi-Supervised Clustering via Information-Theoretic Markov Chain Aggregation

TL;DR

This paper introduces Constrained Markov Clustering (CoMaC), a semi-supervised clustering method that leverages Markov chain aggregation and information theory, demonstrating competitive performance with existing state-of-the-art techniques.

Contribution

It extends an information-theoretic Markov aggregation framework to semi-supervised clustering, incorporating hard constraints and generalizing previous objectives.

Findings

CoMaC is competitive with state-of-the-art methods.

The approach effectively integrates semi-supervision into Markov chain clustering.

Generalizes previous unsupervised information-theoretic clustering objectives.

Abstract

We connect the problem of semi-supervised clustering to constrained Markov aggregation, i.e., the task of partitioning the state space of a Markov chain. We achieve this connection by considering every data point in the dataset as an element of the Markov chain's state space, by defining the transition probabilities between states via similarities between corresponding data points, and by incorporating semi-supervision information as hard constraints in a Hartigan-style algorithm. The introduced Constrained Markov Clustering (CoMaC) is an extension of a recent information-theoretic framework for (unsupervised) Markov aggregation to the semi-supervised case. Instantiating CoMaC for certain parameter settings further generalizes two previous information-theoretic objectives for unsupervised clustering. Our results indicate that CoMaC is competitive with the state-of-the-art.