Canonical Representations and Computation in SPD Matrices

Written by hyperbole | Published 2024/12/04
Tech Story Tags: deep-neural-networks | riemannian-manifolds | spd-manifolds | graph-convolutional-networks | spdnet | manifold-neural-networks | logistic-regression | euclidean-neural-networks

TLDR

The computation of canonical representations for SPD matrices involves transforming orthonormal matrices and using Singular Value Decomposition (SVD) to calculate subspaces and bases. This process helps derive the SPD matrix in its canonical form, enabling better manipulation and understanding in geometric applications.via the TL;DR App

Table of Links

Abstract and 1. Introduction

Preliminaries
Proposed Approach

3.1 Notation

3.2 Nueral Networks on SPD Manifolds

3.3 MLR in Structure Spaces

3.4 Neural Networks on Grassmann Manifolds
Experiments
Conclusion and References

B. MLR in Structure Spaces

C. Formulation of MLR from the Perspective of Distances to Hyperplanes

D. Human Action Recognition

E. Node Classification

F. Limitations of our work

G. Some Related Definitions

H. Computation of Canonical Representation

I. Proof of Proposition 3.2

J. Proof of Proposition 3.4

K. Proof of Proposition 3.5

L. Proof of Proposition 3.6

M. Proof of Proposition 3.11

N. Proof of Proposition 3.12

H COMPUTATION OF CANONICAL REPRESENTATIONS

Authors:

(1) Xuan Son Nguyen, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (xuan-son.nguyen@ensea.fr);

(2) Shuo Yang, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (son.nguyen@ensea.fr);

(3) Aymeric Histace, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France (aymeric.histace@ensea.fr).

This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license.

Written by hyperbole | Amplifying words and ideas to separate the ordinary from the extraordinary, making the mundane majestic.

Published by HackerNoon on 2024/12/04