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High-dimensional outlier detection using random projections

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Listed:
  • P. Navarro-Esteban

    (Universidad de Cantabria)

  • J. A. Cuesta-Albertos

    (Universidad de Cantabria)

Abstract

There exist multiple methods to detect outliers in multivariate data in the literature, but most of them require to estimate the covariance matrix. The higher the dimension, the more complex the estimation of the matrix becoming impossible in high dimensions. In order to avoid estimating this matrix, we propose a novel random projection-based procedure to detect outliers in Gaussian multivariate data. It consists in projecting the data in several one-dimensional subspaces where an appropriate univariate outlier detection method, similar to Tukey’s method but with a threshold depending on the initial dimension and the sample size, is applied. The required number of projections is determined using sequential analysis. Simulated and real datasets illustrate the performance of the proposed method.

Suggested Citation

  • P. Navarro-Esteban & J. A. Cuesta-Albertos, 2021. "High-dimensional outlier detection using random projections," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 908-934, December.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:4:d:10.1007_s11749-020-00750-y
    DOI: 10.1007/s11749-020-00750-y
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    References listed on IDEAS

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