Generalised Mutual Information for Discriminative Clustering

Louis Ohl, Pierre-Alexandre Mattei, Charles Bouveyron, Warith HARCHAOUI, Mickaël Leclercq, Arnaud Droit, Frederic Precioso

Keywords: Unsupervised learning, Clustering, Deep learning, Information Theory

TL;DR: We replace the Kullback-Leibler divergence inside the mutual information by other distances like the Wasserstein metric and improve thus clustering performances of deep models.

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. Some of these metrics 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 clustering context where the number of clusters is a priori unknown.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2210.06300/code)