Abstract
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.
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Vadgama, S., Tomczak, J.M., Bekkers, E. (2023). Continuous Kendall Shape Variational Autoencoders. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_8
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DOI: https://doi.org/10.1007/978-3-031-38271-0_8
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