### 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 language | English |
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Title of host publication | Computer Analysis of Images and Patterns - 14th International Conference, CAIP 2011, Proceedings |

Pages | 278-285 |

Number of pages | 8 |

Edition | PART 1 |

DOIs | |

Publication status | Published - 2011 Sep 20 |

Event | 14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011 - Seville, Spain Duration: 2011 Aug 29 → 2011 Aug 31 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 6854 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011 |
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Country | Spain |

City | Seville |

Period | 11/8/29 → 11/8/31 |

### 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

*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