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 \(N\!-\!1\)-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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Fujiki, J., Akaho, S., Hino, H., Murata, N. (2011). Robust Hyperplane Fitting Based on k-th Power Deviation and α-Quantile. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds) Computer Analysis of Images and Patterns. CAIP 2011. Lecture Notes in Computer Science, vol 6854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23672-3_34
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DOI: https://doi.org/10.1007/978-3-642-23672-3_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23671-6
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