Learning Riemannian geometry for mixed-effect models using deep generative networks.

Abstract : We take up on recent work on the Riemannian geometry of generative networks to propose a new approach for learning both a manifold structure and a Riemannian metric from data. It allows the derivation of statistical analysis on manifolds without the need for the user to design new Riemannian structure for each specific problem. In high-dimensional data, it can learn non diagonal metrics, whereas manual design is often limited to the diagonal case. We illustrate how the method allows the construction of a meaningful low-dimensional representation of data and exhibit the geometry of the space of brain images during Alzheimer's progression.
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https://hal.inria.fr/hal-01828949
Contributor : Maxime Louis <>
Submitted on : Wednesday, July 4, 2018 - 10:22:29 AM
Last modification on : Tuesday, May 28, 2019 - 1:54:03 PM
Long-term archiving on : Monday, October 1, 2018 - 8:49:37 AM

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  • HAL Id : hal-01828949, version 1

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Maxime Louis, Benjamin Charlier, Stanley Durrleman. Learning Riemannian geometry for mixed-effect models using deep generative networks.. 2018. ⟨hal-01828949⟩

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