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

Authors:
Jun Fujiki;Shotaro Akaho;Hideitsu Hino;Noboru Murata
Affiliations:
National Institute of Advanced Industrial Science and Technology;National Institute of Advanced Industrial Science and Technology;Waseda University;Waseda University
Venue:
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Year:
2011

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Abstract

In this paper, two methods for one-dimensional reduction of data by hyperplane fitting are proposed. One is least a-percentile of squares, which is an extension of least median of squares estimation and minimizes the a-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 N-1-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.