Supporting vectors vs. principal components-Reference-Cited by-同舟云学术

Supporting vectors vs. principal components

Published:2023 Issue:1 Volume:8 Page:1937-1958
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Márquez Almudena P.¹,García-Pacheco Francisco Javier¹,Mengibar-Rodríguez Míriam²,Sánchez-Alzola Alberto³

Affiliation:

1. Department of Mathematics, College of Engineering, University of Cadiz, 11519 Puerto Real, Spain

2. Department of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain

3. Department of Statistics and Operation Research, University of Cadiz, 11519 Puerto Real, Spain

Abstract

<abstract><p>Let $ T:X\to Y $ be a bounded linear operator between Banach spaces $ X, Y $. A vector $ x_0\in {\mathsf{S}}_X $ in the unit sphere $ {\mathsf{S}}_X $ of $ X $ is called a supporting vector of $ T $ provided that $ \|T(x_0)\| = \sup\{\|T(x)\|:\|x\| = 1\} = \|T\| $. Since matrices induce linear operators between finite-dimensional Hilbert spaces, we can consider their supporting vectors. In this manuscript, we unveil the relationship between the principal components of a matrix and its supporting vectors. Applications of our results to real-life problems are provided.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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