Key Notations and Algorithm for Computing Pseudo-Gyrodistances in Structure Spaces

Written by hyperbole | Published 2024/12/02
Tech Story Tags: deep-neural-networks | riemannian-manifolds | spd-manifolds | graph-convolutional-networks | spdnet | manifold-neural-networks | logistic-regression | euclidean-neural-networks

TLDR

The paper outlines essential notations and provides an algorithm for computing pseudo-gyrodistances, crucial for MLR computation in structure spaces used in neural networks on Riemannian manifolds. 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

A NOTATIONS

Tab. 3 presents the main notations used in our paper.

B MLR IN STRUCTURE SPACES

Algorithm 1 summarizes all steps for the computation of pseudo-gyrodistances in Theorem 3.11.

Details of some steps are given below:

Authors:

(1) Xuan Son Nguyen, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France ([email protected]);

(2) Shuo Yang, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France ([email protected]);

(3) Aymeric Histace, ETIS, UMR 8051, CY Cergy Paris University, ENSEA, CNRS, France ([email protected]).

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

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Published by HackerNoon on 2024/12/02