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We introduce Constr-DRKM, a deep kernel method for the unsupervised learningof disentangled data representations. We propose augmenting the original deeprestricted kernel machine formulation for kernel PCA by orthogonalityconstraints on the latent variables to promote disentanglement and to make itpossible to carry out optimization without first defining a stabilizedobjective. After illustrating an end-to-end training procedure based on aquadratic penalty optimization algorithm with warm start, we quantitativelyevaluate the proposed method's effectiveness in disentangled feature learning.We demonstrate on four benchmark datasets that this approach performs similarlyoverall to $\beta$-VAE on a number of disentanglement metrics when few trainingpoints are available, while being less sensitive to randomness andhyperparameter selection than $\beta$-VAE. We also present a deterministicinitialization of Constr-DRKM's training algorithm that significantly improvesthe reproducibility of the results. Finally, we empirically evaluate anddiscuss the role of the number of layers in the proposed methodology, examiningthe influence of each principal component in every layer and showing thatcomponents in lower layers act as local feature detectors capturing the broadtrends of the data distribution, while components in deeper layers use therepresentation learned by previous layers and more accurately reproducehigher-level features.

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