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

Young Woong Park, Diego Klabjan

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationProceedings - 16th IEEE International Conference on Data Mining, ICDM 2016
EditorsFrancesco Bonchi, Xindong Wu, Ricardo Baeza-Yates, Josep Domingo-Ferrer, Zhi-Hua Zhou
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages430-438
Number of pages9
ISBN (Electronic)9781509054725
DOIs
StatePublished - Jan 31 2017
Event16th IEEE International Conference on Data Mining, ICDM 2016 - Barcelona, Catalonia, Spain
Duration: Dec 12 2016Dec 15 2016

Publication series

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

Other

Other16th IEEE International Conference on Data Mining, ICDM 2016
CountrySpain
CityBarcelona, Catalonia
Period12/12/1612/15/16

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    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