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 publicationComputer Analysis of Images and Patterns - 14th International Conference, CAIP 2011, Proceedings
Pages278-285
Number of pages8
EditionPART 1
DOIs
Publication statusPublished - 2011 Sep 20
Event14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011 - Seville, Spain
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)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011
CountrySpain
CitySeville
Period11/8/2911/8/31

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Fujiki, J., Akaho, S., Hino, H., & Murata, N. (2011). Robust hyperplane fitting based on k-th power deviation and α-quantile. In Computer Analysis of Images and Patterns - 14th International Conference, CAIP 2011, Proceedings (PART 1 ed., 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