Principal component analysis over continuous subspaces and intersection of half-spaces

Anat Levin, Amnon Shashua

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

17 Scopus citations

Abstract

Principal Component Analysis (PCA)is one of the most popular techniques for dimensionality reduction of multivariate data points with application areas covering many branches of science. However, conventional PCA handles the multivariate data in a discrete manner only, i.e., the covariance matrix represents only sample data points rather than higher-order data representations. In this paper we extend conventional PCA by proposing techniques for constructing the covariance matrix of uniformly sampled continuous regions in parameter space. These regions include polytops defined by convex combinations of sample data, and polyhedral regions defined by intersection of half spaces. The applications of these ideas in practice are simple and shown to be very effective in providing much superior generalization properties than conventional PCA for appearance-based recognition applications.

Original languageAmerican English
Title of host publicationComputer Vision - ECCV 2002 - 7th European Conference on Computer Vision, Proceedings
EditorsAnders Heyden, Gunnar Sparr, Mads Nielsen, Peter Johansen
PublisherSpringer Verlag
Pages635-650
Number of pages16
ISBN (Print)3540437460, 9783540437468
DOIs
StatePublished - 2002
Externally publishedYes
Event7th European Conference on Computer Vision, ECCV 2002 - Copenhagen, Denmark
Duration: 28 May 200231 May 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2352
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th European Conference on Computer Vision, ECCV 2002
Country/TerritoryDenmark
CityCopenhagen
Period28/05/0231/05/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

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