Improved Representation Learning Through Tensorized Autoencoders

TL;DR

This paper introduces a tensorized autoencoder (TAE) that learns cluster-specific representations, improving clustering and denoising performance over standard autoencoders by capturing data's inherent cluster structures.

Contribution

The paper proposes a meta-algorithm to extend arbitrary autoencoders into tensorized versions that learn cluster-specific embeddings and assignments.

Findings

TAE can recover principal components of individual clusters in linear settings.

Tensorizing autoencoders improves clustering accuracy.

Tensorized autoencoders enhance denoising performance.

Abstract

The central question in representation learning is what constitutes a good or meaningful representation. In this work we argue that if we consider data with inherent cluster structures, where clusters can be characterized through different means and covariances, those data structures should be represented in the embedding as well. While Autoencoders (AE) are widely used in practice for unsupervised representation learning, they do not fulfil the above condition on the embedding as they obtain a single representation of the data. To overcome this we propose a meta-algorithm that can be used to extend an arbitrary AE architecture to a tensorized version (TAE) that allows for learning cluster-specific embeddings while simultaneously learning the cluster assignment. For the linear setting we prove that TAE can recover the principle components of the different clusters in contrast to principle component of the entire data recovered by a standard AE. We validated this on planted models and for general, non-linear and convolutional AEs we empirically illustrate that tensorizing the AE is beneficial in clustering and de-noising tasks.