Unsupervised learning of disentangled representations in deep restricted kernel machines with orthogonality constraints

TL;DR

This paper presents Constr-DRKM, an unsupervised deep kernel method with orthogonality constraints that effectively learns disentangled data representations, showing competitive performance and improved reproducibility over existing models like $eta$-VAE.

Contribution

The paper introduces a novel deep kernel approach with orthogonality constraints for disentangled representation learning, enhancing stability and reproducibility.

Findings

Performs comparably to $eta$-VAE on disentanglement metrics with limited data.

Less sensitive to randomness and hyperparameters than $eta$-VAE.

Lower layers detect broad data trends, higher layers refine features.

Abstract

We introduce Constr-DRKM, a deep kernel method for the unsupervised learning of disentangled data representations. We propose augmenting the original deep restricted kernel machine formulation for kernel PCA by orthogonality constraints on the latent variables to promote disentanglement and to make it possible to carry out optimization without first defining a stabilized objective. After illustrating an end-to-end training procedure based on a quadratic penalty optimization algorithm with warm start, we quantitatively evaluate the proposed method's effectiveness in disentangled feature learning. We demonstrate on four benchmark datasets that this approach performs similarly overall to $\beta$-VAE on a number of disentanglement metrics when few training points are available, while being less sensitive to randomness and hyperparameter selection than $\beta$-VAE. We also present a deterministic initialization of Constr-DRKM's training algorithm that significantly improves the reproducibility of the results. Finally, we empirically evaluate and discuss the role of the number of layers in the proposed methodology, examining the influence of each principal component in every layer and showing that components in lower layers act as local feature detectors capturing the broad trends of the data distribution, while components in deeper layers use the representation learned by previous layers and more accurately reproduce higher-level features.