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

Table of Links

Abstract and 1. Introduction

2. Preliminaries

3. 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

4. Experiments

5. Conclusion and References

A. Notations

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:

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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).

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

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