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Principal loading analysis

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  • Bauer, Jan O.
  • Drabant, Bernhard

Abstract

This paper proposes a tool for dimension reduction where the dimension of the original space is reduced: the principal loading analysis. Principal loading analysis is a tool to reduce dimensions by discarding variables. The intuition is that variables are dropped which distort the covariance matrix only by a little. Our method is introduced and an algorithm for conducting principal loading analysis is provided. Further, we give bounds for the noise arising in the sample case.

Suggested Citation

  • Bauer, Jan O. & Drabant, Bernhard, 2021. "Principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000324
    DOI: 10.1016/j.jmva.2021.104754
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    References listed on IDEAS

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    1. Kollo, T. & Neudecker, H., 1993. "Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 283-300, November.
    2. Peres-Neto, Pedro R. & Jackson, Donald A. & Somers, Keith M., 2005. "How many principal components? stopping rules for determining the number of non-trivial axes revisited," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 974-997, June.
    3. I. T. Jolliffe, 1972. "Discarding Variables in a Principal Component Analysis. I: Artificial Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 160-173, June.
    4. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    5. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    6. E. R. Mansfield & J. T. Webster & R. F. Gunst, 1977. "An Analytic Variable Selection Technique for Principal Component Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 34-40, March.
    7. I. T. Jolliffe, 1973. "Discarding Variables in a Principal Component Analysis. Ii: Real Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(1), pages 21-31, March.
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    Cited by:

    1. J. O. Bauer & B. Drabant, 2021. "Regression based thresholds in principal loading analysis," Papers 2103.06691, arXiv.org, revised Mar 2022.
    2. Bauer, Jan O. & Drabant, Bernhard, 2023. "Regression based thresholds in principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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