Efficiently downdating, composing and splitting singular value decompositions preserving the mean information

Javier Melenchón, Elisa Martínez

Research output: A Conference proceeding or a Chapter in BookConference contribution

4 Citations (Scopus)

Abstract

Three methods for the efficient downdating, composition and splitting of low rank singular value decompositions are proposed. They are formulated in a closed form, considering the mean information and providing exact results. Although these methods are presented in the context of computer vision, they can be used in any field forgetting information, combining different eigenspaces in one or ignoring particular dimensions of the column space of the data. Application examples on face subspace learning and latent semantic analysis are given and performance results are provided.

Original languageEnglish
Title of host publicationPattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings
Subtitle of host publicationLecture Notes in Computer Science
Place of PublicationGirona, Spain
PublisherSpringer
Pages436-443
Number of pages8
Volume4478
EditionPART 2
ISBN (Print)9783540728481
DOIs
Publication statusPublished - 6 Jun 2007
Externally publishedYes
Event3rd Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA 2007 - Girona, Spain
Duration: 6 Jun 20078 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume4478 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA 2007
CountrySpain
CityGirona
Period6/06/078/06/07

Fingerprint

Singular value decomposition
Computer vision
Semantics
Column space
Latent Semantic Analysis
Eigenspace
Exact Results
Chemical analysis
Computer Vision
Closed-form
Subspace
Face
Context
Learning

Cite this

Melenchón, J., & Martínez, E. (2007). Efficiently downdating, composing and splitting singular value decompositions preserving the mean information. In Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings: Lecture Notes in Computer Science (PART 2 ed., Vol. 4478, pp. 436-443). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4478 LNCS, No. PART 2). Girona, Spain: Springer. https://doi.org/10.1007/978-3-540-72849-8_55
Melenchón, Javier ; Martínez, Elisa. / Efficiently downdating, composing and splitting singular value decompositions preserving the mean information. Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings: Lecture Notes in Computer Science. Vol. 4478 PART 2. ed. Girona, Spain : Springer, 2007. pp. 436-443 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).
@inproceedings{d9ec1ab5ad1a466e8046e03462e7d711,
title = "Efficiently downdating, composing and splitting singular value decompositions preserving the mean information",
abstract = "Three methods for the efficient downdating, composition and splitting of low rank singular value decompositions are proposed. They are formulated in a closed form, considering the mean information and providing exact results. Although these methods are presented in the context of computer vision, they can be used in any field forgetting information, combining different eigenspaces in one or ignoring particular dimensions of the column space of the data. Application examples on face subspace learning and latent semantic analysis are given and performance results are provided.",
keywords = "Computer vision, Eigenvalues and eigenfunctions, Learning algorithms, Semantics, Singular value decomposition, Face subspace learning, Latent semantic analysis, Feature extraction",
author = "Javier Melench{\'o}n and Elisa Mart{\'i}nez",
year = "2007",
month = "6",
day = "6",
doi = "10.1007/978-3-540-72849-8_55",
language = "English",
isbn = "9783540728481",
volume = "4478",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer",
number = "PART 2",
pages = "436--443",
booktitle = "Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings",
address = "Netherlands",
edition = "PART 2",

}

Melenchón, J & Martínez, E 2007, Efficiently downdating, composing and splitting singular value decompositions preserving the mean information. in Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings: Lecture Notes in Computer Science. PART 2 edn, vol. 4478, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 4478 LNCS, Springer, Girona, Spain, pp. 436-443, 3rd Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA 2007, Girona, Spain, 6/06/07. https://doi.org/10.1007/978-3-540-72849-8_55

Efficiently downdating, composing and splitting singular value decompositions preserving the mean information. / Melenchón, Javier; Martínez, Elisa.

Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings: Lecture Notes in Computer Science. Vol. 4478 PART 2. ed. Girona, Spain : Springer, 2007. p. 436-443 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4478 LNCS, No. PART 2).

Research output: A Conference proceeding or a Chapter in BookConference contribution

TY - GEN

T1 - Efficiently downdating, composing and splitting singular value decompositions preserving the mean information

AU - Melenchón, Javier

AU - Martínez, Elisa

PY - 2007/6/6

Y1 - 2007/6/6

N2 - Three methods for the efficient downdating, composition and splitting of low rank singular value decompositions are proposed. They are formulated in a closed form, considering the mean information and providing exact results. Although these methods are presented in the context of computer vision, they can be used in any field forgetting information, combining different eigenspaces in one or ignoring particular dimensions of the column space of the data. Application examples on face subspace learning and latent semantic analysis are given and performance results are provided.

AB - Three methods for the efficient downdating, composition and splitting of low rank singular value decompositions are proposed. They are formulated in a closed form, considering the mean information and providing exact results. Although these methods are presented in the context of computer vision, they can be used in any field forgetting information, combining different eigenspaces in one or ignoring particular dimensions of the column space of the data. Application examples on face subspace learning and latent semantic analysis are given and performance results are provided.

KW - Computer vision

KW - Eigenvalues and eigenfunctions

KW - Learning algorithms

KW - Semantics

KW - Singular value decomposition

KW - Face subspace learning

KW - Latent semantic analysis

KW - Feature extraction

UR - http://www.scopus.com/inward/record.url?scp=38049132767&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-72849-8_55

DO - 10.1007/978-3-540-72849-8_55

M3 - Conference contribution

SN - 9783540728481

VL - 4478

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 436

EP - 443

BT - Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings

PB - Springer

CY - Girona, Spain

ER -

Melenchón J, Martínez E. Efficiently downdating, composing and splitting singular value decompositions preserving the mean information. In Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings: Lecture Notes in Computer Science. PART 2 ed. Vol. 4478. Girona, Spain: Springer. 2007. p. 436-443. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). https://doi.org/10.1007/978-3-540-72849-8_55