Embedding new data points for manifold learning via coordinate propagation

Authors:
Shiming Xiang;Feiping Nie;Yangqiu Song;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;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:
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Year:
2007

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Abstract

In recent years, a series of manifold learning algorithms have been proposed for nonlinear dimensionality reduction (NLDR). Most of them can run in a batch mode for a set of given data points, but lack a mechanism to deal with new data points. Here we propose an extension approach, i.e., embedding new data points into the previously-learned manifold. The core idea of our approach is to propagate the known co-ordinates to each of the new data points. We first formulate this task as a quadratic programming, and then develop an iterative algorithm for coordinate propagation. Smoothing splines are used to yield an initial coordinate for each new data point, according to their local geometrical relations. Experimental results illustrate the validity of our approach.