Local smoothing for manifold learning

Authors:
JinHyeong Park;Zhenyue Zhang;Hongyuan Zha;Rangachar Kasturi
Affiliations:
Dept. of Computer Science and Engineering, The Pennsylvania State University;Dept. of Mathematics, Zhejiang University, Hangzhou, P.R. China;Dept. of Computer Science and Engineering, The Pennsylvania State University;Dept. of Computer Science and Engineering, University of South Florida
Venue:
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Year:
2004

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Abstract

We propose methods for outlier handling and noise reduction using weighted local linear smoothing for a set of noisy points sampled from a nonlinear manifold. Weighted PCA is used as a building block for our methods and we suggest an iterative weight selection scheme for robust local linear fitting together with an outlier detection method based on minimal spanning trees to further improve robustness. We also develop an efficient and effective bias-reduction method to deal with the "trim the peak and fill the valley" phenomenon in local linear smoothing. Synthetic examples along with several image data sets are presented to show that manifold learning methods combined with weighted local linear smoothing give more accurate results.