Multi-Facet Clustering Variational Autoencoders

TL;DR

This paper introduces MFCVAE, a hierarchical variational autoencoder that learns multiple, disentangled clusterings of high-dimensional data simultaneously in an unsupervised manner, with theoretical and empirical validation.

Contribution

The paper proposes a novel multi-facet clustering VAE with a hierarchical structure and analytical ELBO optimization, advancing unsupervised multi-clustering capabilities.

Findings

Successfully separates and clusters different data aspects

Demonstrates stable training with ladder architecture

Enables controlled sample generation

Abstract

Work in deep clustering focuses on finding a single partition of data. However, high-dimensional data, such as images, typically feature multiple interesting characteristics one could cluster over. For example, images of objects against a background could be clustered over the shape of the object and separately by the colour of the background. In this paper, we introduce Multi-Facet Clustering Variational Autoencoders (MFCVAE), a novel class of variational autoencoders with a hierarchy of latent variables, each with a Mixture-of-Gaussians prior, that learns multiple clusterings simultaneously, and is trained fully unsupervised and end-to-end. MFCVAE uses a progressively-trained ladder architecture which leads to highly stable performance. We provide novel theoretical results for optimising the ELBO analytically with respect to the categorical variational posterior distribution, correcting earlier influential theoretical work. On image benchmarks, we demonstrate that our approach separates out and clusters over different aspects of the data in a disentangled manner. We also show other advantages of our model: the compositionality of its latent space and that it provides controlled generation of samples.