TY - GEN

T1 - Robust hyperplane fitting based on k-th power deviation and α-quantile

AU - Fujiki, Jun

AU - Akaho, Shotaro

AU - Hino, Hideitsu

AU - Murata, Noboru

N1 - Publisher Copyright:
© 2011, Springer-Verlag Berlin Heidelberg.

PY - 2011

Y1 - 2011

N2 - 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 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.

AB - 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 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.

KW - Hyperplane fitting

KW - Least k-th power deviations

KW - Least α-percentile of squares

KW - Optimal sampling property

KW - Random sampling

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U2 - 10.1007/978-3-642-23672-3_34

DO - 10.1007/978-3-642-23672-3_34

M3 - Conference contribution

AN - SCOPUS:80052792975

SN - 9783642236716

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 278

EP - 285

BT - Computer Analysis of Images and Patterns - 14th International Conference, CAIP 2011, Proceedings

A2 - Real, Pedro

A2 - Diaz-Pernil, Daniel

A2 - Molina-Abril, Helena

A2 - Berciano, Ainhoa

A2 - Kropatsch, Walter

PB - Springer Verlag

T2 - 14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011

Y2 - 29 August 2011 through 31 August 2011

ER -