Robust hypersurface fitting based on random sampling approximations

Authors:
Jun Fujiki;Shotaro Akaho;Hideitsu Hino;Noboru Murata
Affiliations:
Fukuoka University, Japan;National Institute of Advanced Industrial Science and Technology, Japan;Waseda University, Japan;Waseda University, Japan
Venue:
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Year:
2012

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Abstract

This paper considers N−1-dimensional hypersurface fitting based on L2 distance in N-dimensional input space. The problem is usually reduced to hyperplane fitting in higher dimension. However, because feature mapping is generally a nonlinear mapping, it does not preserve the order of lengthes, and this derives an unacceptable fitting result. To avoid it, JNLPCA is introduced. JNLPCA defines the L2 distance in the feature space as a weighted L2 distance to reflect the metric in the input space. In the fitting, random sampling approximation of least k-th power deviation, and least α-percentile of squares are introduced to make estimation robust. The proposed hypersurface fitting method is evaluated by quadratic curve fitting and quadratic curve segments extraction from artificial data and a real image.