Speed improvement of multivariate algorithms by the method of postponed basis matrix multiplication: Part I. Principal component analysis

https://doi.org/10.1016/0169-7439(94)00013-1Get rights and content

Abstract

Compression is one way of making analysis of large data matrices faster. Compression is here defined as the case when a large matrix X is replaced by a smaller coefficient matrix C. The coefficients are obtained by least squares fitting to some compression basis. When performing, e.g., principal component analysis (PCA) of C, the results are comparable but not equal to the results from analyzing X. In this paper we suggest a solution to this problem by rewriting the PCA algorithm in terms of C and the compression basis matrices. This has been accomplished by applying a method where speed improvement is achieved by postponing basis matrix calculations in key steps of the PCA algorithm. The method suggested can also be applied to other (but not all kinds of) multivariate algorithms.

References (10)

  • S. Wold et al.

    Principal component analysis

    Chemometrics and Intelligent Laboratory Systems

    (1987)
    S. Wold et al.

    Principal component analysis

    Chemometrics and Intelligent Laboratory Systems

    (1987)
  • S. Pissanetsky
    (1984)
  • B.K. Alsberg

    Representation of spectra by continuous functions

    Journal of Chemometrics

    (1993)
  • B.K. Alsberg et al.

    Compression of nth-order data arrays by B-splines. Part 1. Theory

    Journal of Chemometrics

    (1993)
  • G. Farin
There are more references available in the full text version of this article.

Cited by (0)

View full text