Generalised Mutual Information: a Framework for Discriminative Clustering

TL;DR

This paper introduces Generalised Mutual Information (GEMINI), a new framework that improves clustering by addressing limitations of traditional MI, enabling automatic cluster number selection and reducing the need for regularisations.

Contribution

The paper proposes GEMINI, a generalized mutual information framework that is geometry-aware, eliminates the need for regularisations, and can automatically determine the number of clusters.

Findings

GEMINI addresses MI limitations in clustering.

Some GEMINIs do not require regularisations.

GEMINI can automatically select the number of clusters.

Abstract

In the last decade, recent successes in deep clustering majorly involved the Mutual Information (MI) as an unsupervised objective for training neural networks with increasing regularisations. While the quality of the regularisations have been largely discussed for improvements, little attention has been dedicated to the relevance of MI as a clustering objective. In this paper, we first highlight how the maximisation of MI does not lead to satisfying clusters. We identified the Kullback-Leibler divergence as the main reason of this behaviour. Hence, we generalise the mutual information by changing its core distance, introducing the Generalised Mutual Information (GEMINI): a set of metrics for unsupervised neural network training. Unlike MI, some GEMINIs do not require regularisations when training as they are geometry-aware thanks to distances or kernels in the data space. Finally, we highlight that GEMINIs can automatically select a relevant number of clusters, a property that has been little studied in deep discriminative clustering context where the number of clusters is a priori unknown.