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

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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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Dates and versions

hal-01828949 , version 1 (04-07-2018)

Identifiers

  • HAL Id : hal-01828949 , version 1

Cite

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