Generalised Mutual Information: a Framework for Discriminative Clustering
This work addresses a foundational issue in unsupervised deep clustering for machine learning researchers, offering a novel framework to enhance discriminative clustering methods.
The paper tackles the problem of mutual information (MI) being an unsatisfying objective for deep clustering by introducing Generalised Mutual Information (GEMINI), a set of metrics that improve clustering performance without requiring regularizations and enable automatic selection of the number of clusters.
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.