Efficiently Downdating, Composing and Splitting Singular Value Decompositions Preserving the Mean Information

Authors:
Javier Melenchón;Elisa Martínez
Affiliations:
Communications and Signal Theory Department, Enginyeria La Salle, Universitat Ramon Llull, Pg. Bonanova, 8, 08002 Barcelona, Spain;Communications and Signal Theory Department, Enginyeria La Salle, Universitat Ramon Llull, Pg. Bonanova, 8, 08002 Barcelona, Spain
Venue:
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part II
Year:
2007

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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.