Partial common principal component subspaces

    Authors

    J. R. Schott

    Comments

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    Abbreviated Journal Title

    Biometrika

    Keywords

    dimensionality reduction; principal components analysis; REGRESSION; TESTS; Biology; Mathematical & Computational Biology; Statistics & Probability

    Abstract

    We consider the principal components analysis of g groups of m variables for those situations in which, for each group, the first k principal components account for most of the total variability of observations in that group. If the set of these gk principal component vectors spans a space of dimension r, where r is less than m, then it will be possible simultaneously to reduce the dimensionality, for all groups, from m to r while retaining most of the within-group variability. Methods are already available for determining if r = k, in which case the g groups have a common principal component subspace. In this paper, we develop a general procedure for determining if r = s for arbitrary s. This can then be used repeatedly to determine r when r > k.

    Journal Title

    Biometrika

    Volume

    86

    Issue/Number

    4

    Publication Date

    1-1-1999

    Document Type

    Article

    Language

    English

    First Page

    899

    Last Page

    908

    WOS Identifier

    WOS:000084833000012

    ISSN

    0006-3444

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