Spline embedding for nonlinear dimensionality reduction

Authors:
Shiming Xiang;Feiping Nie;Changshui Zhang;Chunxia Zhang
Affiliations:
State Key Laboratory of Intelligent Technology and Systems, Department of Automation, Tsinghua University, Beijing, China;State Key Laboratory of Intelligent Technology and Systems, Department of Automation, Tsinghua University, Beijing, China;State Key Laboratory of Intelligent Technology and Systems, Department of Automation, Tsinghua University, Beijing, China;School of Computer Science, Software School, Beijing Institute of Technology, Beijing, China
Venue:
ECML'06 Proceedings of the 17th European conference on Machine Learning
Year:
2006

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Abstract

This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Smoothing splines are used to map the locally-coordinatized data points into a single global coordinate system of lower dimensionality. In this work setting, we can achieve two goals. First, a global embedding is obtained by minimizing the low-dimensional coordinate reconstruction error. Second, the NLDR algorithm can be naturally extended to deal with out-of-sample data points. Experimental results illustrate the validity of our method.