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Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoders by Miolane, Nina; Holmes, Susan is a scholarly article available to read on EtoBox.

What is Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoders about?

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their functional Magnetic Resonance Imaging (fMRI) time series - an object thus constrained by construction to belong to the manifold of symmetric positive definite matrices. One of the challenges that naturally arises consists of finding a lower-dimensional subspace for representing such manifold-valued data. Traditional techniques, like principal component analysis, are ill-adapted to tackle non-Euclidean spaces and may fail to achieve a lower-dimensional representation of the data - thus potentially pointing to the absence of lower-dimensional representation of the data. However, these techniques are restricted in that: (i) they do not leverage the assumption that the connectomes belong on a pre-specified manifold, therefore discarding information; (ii) they can only fit a linear subspace to the data. In this paper, we are interested in variants to learn potentially highly curved submanifolds of manifold-valued data. Motivated by the brain connectomes

Author

Miolane, Nina; Holmes, Susan

Published

2019

Language

EN