Principal components: A descent algorithm

Rebeca Salas-Boni; Esteban G. Tabak

doi:10.1016/j.jcp.2014.02.033

Principal components: A descent algorithm

Rebeca Salas-Boni, Esteban G. Tabak

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A descent procedure is proposed for the search of low-dimensional subspaces of a high-dimensional space that satisfy an optimality criterion. Specifically, the procedure is applied to finding the subspace spanned by the first m singular components of an n-dimensional dataset. The procedure minimizes the associated cost function through a series of orthogonal transformations, each represented economically as the exponential of a skew-symmetric matrix drawn from a low-dimensional space.

Original language	English (US)
Pages (from-to)	162-175
Number of pages	14
Journal	Journal of Computational Physics
Volume	267
DOIs	https://doi.org/10.1016/j.jcp.2014.02.033
State	Published - Jun 15 2014

Keywords

Principal component analysis

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.jcp.2014.02.033

Cite this

@article{f93fe5adbe854287b1b0fa38ac65599c,

title = "Principal components: A descent algorithm",

abstract = "A descent procedure is proposed for the search of low-dimensional subspaces of a high-dimensional space that satisfy an optimality criterion. Specifically, the procedure is applied to finding the subspace spanned by the first m singular components of an n-dimensional dataset. The procedure minimizes the associated cost function through a series of orthogonal transformations, each represented economically as the exponential of a skew-symmetric matrix drawn from a low-dimensional space.",

keywords = "Principal component analysis",

author = "Rebeca Salas-Boni and Tabak, {Esteban G.}",

note = "Funding Information: The work of Rebeca Salas-Boni is partially supported by the CONACYT and NYU's GSAS MacCracken Fellowship , and the work of E.G. Tabak is partially supported by the Division of Mathematical Sciences of the National Science Foundation . Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

year = "2014",

month = jun,

day = "15",

doi = "10.1016/j.jcp.2014.02.033",

language = "English (US)",

volume = "267",

pages = "162--175",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Principal components

T2 - A descent algorithm

AU - Salas-Boni, Rebeca

AU - Tabak, Esteban G.

N1 - Funding Information: The work of Rebeca Salas-Boni is partially supported by the CONACYT and NYU's GSAS MacCracken Fellowship , and the work of E.G. Tabak is partially supported by the Division of Mathematical Sciences of the National Science Foundation . Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2014/6/15

Y1 - 2014/6/15

N2 - A descent procedure is proposed for the search of low-dimensional subspaces of a high-dimensional space that satisfy an optimality criterion. Specifically, the procedure is applied to finding the subspace spanned by the first m singular components of an n-dimensional dataset. The procedure minimizes the associated cost function through a series of orthogonal transformations, each represented economically as the exponential of a skew-symmetric matrix drawn from a low-dimensional space.

AB - A descent procedure is proposed for the search of low-dimensional subspaces of a high-dimensional space that satisfy an optimality criterion. Specifically, the procedure is applied to finding the subspace spanned by the first m singular components of an n-dimensional dataset. The procedure minimizes the associated cost function through a series of orthogonal transformations, each represented economically as the exponential of a skew-symmetric matrix drawn from a low-dimensional space.

KW - Principal component analysis

UR - http://www.scopus.com/inward/record.url?scp=84896516582&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896516582&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2014.02.033

DO - 10.1016/j.jcp.2014.02.033

M3 - Article

AN - SCOPUS:84896516582

SN - 0021-9991

VL - 267

SP - 162

EP - 175

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Principal components: A descent algorithm

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this