Non-iterative heteroscedastic linear dimension reduction for two-class data; from Fisher to Chernoff

M Loog, RPW Duin

    Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

    16 Citations (Scopus)

    Abstract

    Linear discriminant analysis (LDA) is a traditional solution to the linear dimension reduction (LDR) problem, which is based on the maximization of the between-class scatter over the within-class scatter. This solution is incapable of dealing with heteroscedastic data in a proper way, because of the implicit assumption that the covariance matrices for all the classes are equal. Hence, discriminatory information in the difference between the covariance matrices is not used and, as a consequence, we can only reduce the data to a single dimension in the two-class case. We propose a fast non-iterative eigenvector-based LDR technique for heteroscedastic two-class data, which generalizes, and improves upon LDA by dealing with the aforementioned problem. For this purpose, we use the concept of directed distance matrices, which generalizes the between-class covariance matrix such that it captures the differences in (co)variances.
    Original languageUndefined/Unknown
    Title of host publicationStructural, Syntactic, and Statistical Pattern Recognition, Proceedings
    EditorsT Caelli, A Amin, RPW Duin, M Kamel, D de Ridder
    Place of PublicationBerlin
    PublisherSpringer
    Pages488-496
    Number of pages9
    ISBN (Print)3-540-44011-9
    Publication statusPublished - 2002
    EventJoint IAPR International Workshops SSPR'02 and SPR'02 (Windsor, Canada) - Berlin
    Duration: 6 Aug 20029 Aug 2002

    Publication series

    Name
    PublisherSpringer Verlag
    NameLecture Notes in Computer Science
    Volume2396
    ISSN (Print)0302-9743

    Conference

    ConferenceJoint IAPR International Workshops SSPR'02 and SPR'02 (Windsor, Canada)
    Period6/08/029/08/02

    Keywords

    • conference contrib. refereed
    • ZX CWTS JFIS < 1.00

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