Visualizing Riemannian data with Rie-SNE

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01_mlvis20241123.pdf (10.87 MB)
Date
2024
Authors
Bergsson, Andri
Hauberg, Søren
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
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 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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@inproceedings{
10.2312:mlvis.20241123
,
booktitle = {
Machine Learning Methods in Visualisation for Big Data
},
editor = {
Archambault, Daniel
 and 
Nabney, Ian
 and 
Peltonen, Jaakko
},
title = {{
Visualizing Riemannian data with Rie-SNE
}},
author = {
Bergsson, Andri
 and 
Hauberg, Søren
},
year = {
2024
},
publisher = {
The Eurographics Association
},
ISBN = {
978-3-03868-256-1
},
DOI = {
10.2312/mlvis.20241123
}
}
Citation
URI
https://doi.org/10.2312/mlvis.20241123
 https://diglib.eg.org/handle/10.2312/mlvis20241123
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Machine Learning Methods in Visualisation for Big Data 2024