  Disentanglement is a useful property in representation learning which
increases the interpretability of generative models such as Variational
autoencoders (VAE), Generative Adversarial Models, and their many variants.
Typically in such models, an increase in disentanglement performance is
traded-off with generation quality. In the context of latent space models, this
work presents a representation learning framework that explicitly promotes
disentanglement by encouraging orthogonal directions of variations. The
proposed objective is the sum of an autoencoder error term along with a
Principal Component Analysis reconstruction error in the feature space. This
has an interpretation of a Restricted Kernel Machine with the eigenvector
matrix-valued on the Stiefel manifold. Our analysis shows that such a
construction promotes disentanglement by matching the principal directions in
the latent space with the directions of orthogonal variation in data space. In
an alternating minimization scheme, we use Cayley ADAM algorithm - a stochastic
optimization method on the Stiefel manifold along with the ADAM optimizer. Our
theoretical discussion and various experiments show that the proposed model
improves over many VAE variants in terms of both generation quality and
disentangled representation learning.
