Visualizing Riemannian data with Rie-SNE

• URL: http://arxiv.org/abs/2203.09253v1
• Date: Thu, 17 Mar 2022 11:21:44 GMT
• Title: Visualizing Riemannian data with Rie-SNE
• Authors: Andri Bergsson, S{\o}ren Hauberg
• Abstract summary: We extend the classic neighbor embedding algorithm to data on general Riemannian manifold. We replace standard assumptions with Riemannian diffusion counterparts and propose an efficient approximation. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

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