Continuous Kendall Shape Variational Autoencoders.

We present an approach for unsupervised learning of geometrically meaningful representations via equivariant variational autoencoders (VAEs) with hyperspherical latent representations. The equivariant encoder/decoder ensures that these latents are geometrically meaningful and grounded in the input space. Mapping these geometry- grounded latents to hyperspheres allows us to interpret them as points in a Kendall shape space. This paper extends the recent Kendall-shape VAE paradigm by Vadgama et al. by providing a general definition of Kendall shapes in terms of group representations to allow for more flexible modeling of KS-VAEs. We show that learning with generalized Kendall shapes, instead of landmark-based shapes, improves representation capacity.