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A Theoretical Analysis of the Peaking Phenomenon in Classification

Author

Listed:
  • Amin Zollanvari

    (Nazarbayev University)

  • Alex Pappachen James

    (Nazarbayev University)

  • Reza Sameni

    (Shiraz University)

Abstract

In this work, we analytically study the peaking phenomenon in the context of linear discriminant analysis in the multivariate Gaussian model under the assumption of a common known covariance matrix. The focus is finite-sample setting where the sample size and observation dimension are comparable. Therefore, in order to study the phenomenon in such a setting, we use an asymptotic technique whereby the number of sample points is kept comparable in magnitude to the dimensionality of observations. The analysis provides a more thorough picture of the phenomenon. In particular, the analysis shows that as long as the Relative Cumulative Efficacy of an additional Feature set (RCEF) is greater (less) than the size of this set, the expected error of the classifier constructed using these additional features will be less (greater) than the expected error of the classifier constructed without them. Our result highlights underlying factors of the peaking phenomenon relative to the classifier used in this study and, at the same time, calls into question the classical wisdom around the peaking phenomenon.

Suggested Citation

  • Amin Zollanvari & Alex Pappachen James & Reza Sameni, 2020. "A Theoretical Analysis of the Peaking Phenomenon in Classification," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 421-434, July.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:2:d:10.1007_s00357-019-09327-3
    DOI: 10.1007/s00357-019-09327-3
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    References listed on IDEAS

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    1. Raudys, Sarunas & Young, Dean M., 2004. "Results in statistical discriminant analysis: a review of the former Soviet Union literature," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 1-35, April.
    2. Bradley Efron, 2005. "Bayesians, Frequentists, and Scientists," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1-5, March.
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    Cited by:

    1. Gaeithry Manoharam & Mohd Shareduwan Mohd Kasihmuddin & Siti Noor Farwina Mohamad Anwar Antony & Nurul Atiqah Romli & Nur ‘Afifah Rusdi & Suad Abdeen & Mohd. Asyraf Mansor, 2023. "Log-Linear-Based Logic Mining with Multi-Discrete Hopfield Neural Network," Mathematics, MDPI, vol. 11(9), pages 1-30, April.

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