Iteratively reweighted least squares algorithms for L1-Norm principal component analysis

Young Woong Park; Diego Klabjan

doi:10.1109/ICDM.2016.14

Iteratively reweighted least squares algorithms for L1-Norm principal component analysis

Young Woong Park, Diego Klabjan

Industrial Engineering and Management Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of the reconstructed data, we propose an exact reweighted and an approximate algorithm based on iteratively reweighted least squares. We provide convergence analyses, and compare their performance against benchmark algorithms in the literature. The computational experiment shows that the proposed algorithms consistently perform best.

Original language	English (US)
Title of host publication	Proceedings - 16th IEEE International Conference on Data Mining, ICDM 2016
Editors	Francesco Bonchi, Xindong Wu, Ricardo Baeza-Yates, Josep Domingo-Ferrer, Zhi-Hua Zhou
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	430-438
Number of pages	9
ISBN (Electronic)	9781509054725
DOIs	https://doi.org/10.1109/ICDM.2016.14
State	Published - Jan 31 2017
Event	16th IEEE International Conference on Data Mining, ICDM 2016 - Barcelona, Catalonia, Spain Duration: Dec 12 2016 → Dec 15 2016

Publication series

Name	Proceedings - IEEE International Conference on Data Mining, ICDM
ISSN (Print)	1550-4786

Other

Other	16th IEEE International Conference on Data Mining, ICDM 2016
Country	Spain
City	Barcelona, Catalonia
Period	12/12/16 → 12/15/16

ASJC Scopus subject areas

Engineering(all)

Access to Document

10.1109/ICDM.2016.14

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Park, Y. W., & Klabjan, D. (2017). Iteratively reweighted least squares algorithms for L1-Norm principal component analysis. In F. Bonchi, X. Wu, R. Baeza-Yates, J. Domingo-Ferrer, & Z-H. Zhou (Eds.), Proceedings - 16th IEEE International Conference on Data Mining, ICDM 2016 (pp. 430-438). [7837867] (Proceedings - IEEE International Conference on Data Mining, ICDM). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICDM.2016.14

Park, Young Woong ; Klabjan, Diego. / Iteratively reweighted least squares algorithms for L1-Norm principal component analysis. Proceedings - 16th IEEE International Conference on Data Mining, ICDM 2016. editor / Francesco Bonchi ; Xindong Wu ; Ricardo Baeza-Yates ; Josep Domingo-Ferrer ; Zhi-Hua Zhou. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 430-438 (Proceedings - IEEE International Conference on Data Mining, ICDM).

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abstract = "Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of the reconstructed data, we propose an exact reweighted and an approximate algorithm based on iteratively reweighted least squares. We provide convergence analyses, and compare their performance against benchmark algorithms in the literature. The computational experiment shows that the proposed algorithms consistently perform best.",

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Park, YW & Klabjan, D 2017, Iteratively reweighted least squares algorithms for L1-Norm principal component analysis. in F Bonchi, X Wu, R Baeza-Yates, J Domingo-Ferrer & Z-H Zhou (eds), Proceedings - 16th IEEE International Conference on Data Mining, ICDM 2016., 7837867, Proceedings - IEEE International Conference on Data Mining, ICDM, Institute of Electrical and Electronics Engineers Inc., pp. 430-438, 16th IEEE International Conference on Data Mining, ICDM 2016, Barcelona, Catalonia, Spain, 12/12/16. https://doi.org/10.1109/ICDM.2016.14

Iteratively reweighted least squares algorithms for L1-Norm principal component analysis. / Park, Young Woong; Klabjan, Diego.

Proceedings - 16th IEEE International Conference on Data Mining, ICDM 2016. ed. / Francesco Bonchi; Xindong Wu; Ricardo Baeza-Yates; Josep Domingo-Ferrer; Zhi-Hua Zhou. Institute of Electrical and Electronics Engineers Inc., 2017. p. 430-438 7837867 (Proceedings - IEEE International Conference on Data Mining, ICDM).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of the reconstructed data, we propose an exact reweighted and an approximate algorithm based on iteratively reweighted least squares. We provide convergence analyses, and compare their performance against benchmark algorithms in the literature. The computational experiment shows that the proposed algorithms consistently perform best.

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Park YW, Klabjan D. Iteratively reweighted least squares algorithms for L1-Norm principal component analysis. In Bonchi F, Wu X, Baeza-Yates R, Domingo-Ferrer J, Zhou Z-H, editors, Proceedings - 16th IEEE International Conference on Data Mining, ICDM 2016. Institute of Electrical and Electronics Engineers Inc. 2017. p. 430-438. 7837867. (Proceedings - IEEE International Conference on Data Mining, ICDM). https://doi.org/10.1109/ICDM.2016.14