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The art of centering without centering for robust principal component analysis

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Abstract

Many robust variants of Principal Component Analysis remove outliers from the data and compute the principal components of the remaining data. The robust centered variant requires knowledge of the center of the non-outliers. Unfortunately, the center of non-outliers is unknown until after the outliers are determined, and using an inaccurate center may lead to the detection of wrong outliers. We demonstrate this problem in several known robust PCA algorithms. We describe a method that implicitly centers the non-outliers, implemented by appending a constant value (bias) to each data point. This bias method can be used with “black box” robust PCA algorithms by augmenting their input with minimal change to the algorithm itself.

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Notes

  1. There is a sign ambiguity in calculating eigenvectors, since whenever v is an eigenvector with \(\lambda\) eigenvalue then so is \({-}v\). All eigenvectors in Fig. 2 were normalized so that their coordinate sum is positive.

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Authors and Affiliations

  1. Massachusetts General Hospital, Harvard Medical School, Boston, MA, 02115, USA

    Guihong Wan

  2. Departments of Biostatistics and Epidemiology, Harvard T. H. Chan School of Public Health, Boston, MA, 02115, USA

    Guihong Wan

  3. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Baokun He & Haim Schweitzer

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  1. Guihong Wan
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  2. Baokun He
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Correspondence to Guihong Wan.

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Guihong Wan and Baokun He have contributed equally to this work.

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Wan, G., He, B. & Schweitzer, H. The art of centering without centering for robust principal component analysis. Data Min Knowl Disc 38, 699–724 (2024). https://doi.org/10.1007/s10618-023-00976-y

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