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

Javier Melenchón; Elisa Martínez

doi:10.1007/978-3-540-72849-8_55

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 Book › Conference contribution › peer-review

5 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 language	English
Title of host publication	Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings
Subtitle of host publication	Lecture Notes in Computer Science
Place of Publication	Girona, Spain
Publisher	Springer
Pages	436-443
Number of pages	8
ISBN (Print)	9783540728481
DOIs	https://doi.org/10.1007/978-3-540-72849-8_55
Publication status	Published - 6 Jun 2007
Externally published	Yes
Event	3rd Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA 2007 - Girona, Spain Duration: 6 Jun 2007 → 8 Jun 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 2
Volume	4478 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA 2007
Country/Territory	Spain
City	Girona
Period	6/06/07 → 8/06/07

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

https://link.springer.com/chapter/10.1007/978-3-540-72849-8_55

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 (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). 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. 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).

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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",

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doi = "10.1007/978-3-540-72849-8_55",

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booktitle = "Pattern Recognition and Image Analysis - Third Iberian Conference, IbPRIA 2007, Proceedings",

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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. 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. 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 Book › Conference contribution › peer-review

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

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

M3 - Conference contribution

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SN - 9783540728481

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

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

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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. 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). doi: 10.1007/978-3-540-72849-8_55

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

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