Abstract

There is a growing interest in leveraging differential geometry in the machine learning community. Yet, the adoption of the associated geometric computations has been inhibited by the lack of a reference implementation. Such an implementation should typically allow its users: (i) to get intuition on concepts from differential geometry through a hands-on approach, often not provided by traditional textbooks; and (ii) to run geometric machine learning algorithms seamlessly, without delving into the mathematical details. To address this gap, we present the open-source Python package geomstats and introduce hands-on tutorials for differential geometry and geometric machine learning algorithms-Geometric Learning-that rely on it. Code and documentation: github.com/geomstats/geomstats and geomstats.ai.

Highlights

  • Introduction to Geometric Learning inPython with GeomstatsNina Miolane‡∗, Nicolas Guigui§, Hadi Zaatiti, Christian Shewmake, Hatem Hajri, Daniel Brooks, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Yann Cabanes, ThomasGerald, Paul Chauchat, Bernhard Kainz, Claire Donnat, Susan Holmes, Xavier Pennec https://youtu.be/Ju-Wsd84uG0 !Abstract—There is a growing interest in leveraging differential geometry in the machine learning community

  • We demonstrate that any standard machine learning algorithm can be applied to data on manifolds while respecting their geometry

  • We find published results that show how useful geometry can be with data on the Symmetric Positive Definite (SPD) manifold (e.g [WAZF18], [NDV+14])

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Summary

Introduction to Geometric Learning in Python with Geomstats

Nina Miolane‡∗, Nicolas Guigui§, Hadi Zaatiti, Christian Shewmake, Hatem Hajri, Daniel Brooks, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Yann Cabanes, Thomas. The adoption of the associated geometric computations has been inhibited by the lack of a reference implementation Such an implementation should typically allow its users: (i) to get intuition on concepts from differential geometry through a hands-on approach, often not provided by traditional textbooks; and (ii) to run geometric machine learning algorithms seamlessly, without delving into the mathematical details. To address this gap, we present the open-source Python package geomstats and introduce hands-on tutorials for differential geometry and geometric machine learning algorithms - Geometric Learning - that rely on it.

Introduction
Presentation of Geomstats
Points Fréchet mean
Initial point End point Geodesic
Tutorial context and description
SPD matrices in the literature
Manifold of SPD matrices
This tutorial showed how to leverage geomstats to use standard
We emphasize that ToTangentSpace computes the mean
Hyperbolic spaces and machine learning applications
Size of the context for each node
Learning graph representations with hyperbolic spaces in geomstats
Conclusion
Positive Definite
INTRODUCTION

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