Robust hyperplane fitting based on k-th power deviation and α-quantile

Jun Fujiki, Shotaro Akaho, Hideitsu Hino, Noboru Murata

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    1 Citation (Scopus)

    Abstract

    In this paper, two methods for one-dimensional reduction of data by hyperplane fitting are proposed. One is least α-percentile of squares, which is an extension of least median of squares estimation and minimizes the α-percentile of squared Euclidean distance. The other is least k-th power deviation, which is an extension of least squares estimation and minimizes the k-th power deviation of squared Euclidean distance. Especially, for least k-th power deviation of 0 < k ≤ 1, it is proved that a useful property, called optimal sampling property, holds in one-dimensional reduction of data by hyperplane fitting. The optimal sampling property is that the global optimum for affine hyperplane fitting passes through N data points when an -dimensional hyperplane is fitted to the N-dimensional data. The performance of the proposed methods is evaluated by line fitting to artificial data and a real image.

    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Pages278-285
    Number of pages8
    Volume6854 LNCS
    EditionPART 1
    DOIs
    Publication statusPublished - 2011
    Event14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011 - Seville
    Duration: 2011 Aug 292011 Aug 31

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    NumberPART 1
    Volume6854 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011
    CitySeville
    Period11/8/2911/8/31

    Fingerprint

    Quantile
    Hyperplane
    Deviation
    Sampling
    Dimensional Reduction
    Percentile
    Euclidean Distance
    Least Median of Squares
    Minimise
    Least Squares Estimation
    Global Optimum
    Line

    Keywords

    • hyperplane fitting
    • least α-percentile of squares
    • least k-th power deviations
    • optimal sampling property
    • random sampling

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Fujiki, J., Akaho, S., Hino, H., & Murata, N. (2011). Robust hyperplane fitting based on k-th power deviation and α-quantile. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 1 ed., Vol. 6854 LNCS, pp. 278-285). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6854 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-23672-3_34

    Robust hyperplane fitting based on k-th power deviation and α-quantile. / Fujiki, Jun; Akaho, Shotaro; Hino, Hideitsu; Murata, Noboru.

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6854 LNCS PART 1. ed. 2011. p. 278-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6854 LNCS, No. PART 1).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Fujiki, J, Akaho, S, Hino, H & Murata, N 2011, Robust hyperplane fitting based on k-th power deviation and α-quantile. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 edn, vol. 6854 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6854 LNCS, pp. 278-285, 14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011, Seville, 11/8/29. https://doi.org/10.1007/978-3-642-23672-3_34
    Fujiki J, Akaho S, Hino H, Murata N. Robust hyperplane fitting based on k-th power deviation and α-quantile. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 ed. Vol. 6854 LNCS. 2011. p. 278-285. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-642-23672-3_34
    Fujiki, Jun ; Akaho, Shotaro ; Hino, Hideitsu ; Murata, Noboru. / Robust hyperplane fitting based on k-th power deviation and α-quantile. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6854 LNCS PART 1. ed. 2011. pp. 278-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).
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