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Dynamic Neighborhood Selection for Nonlinear Dimensionality Reduction

  • Yubin Zhan
  • Jianping Yin
  • Jun Long
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5861)

Abstract

Neighborhood construction is a necessary and important step in nonlinear dimensionality reduction algorithm. In this paper, we first summarize the two principles for neighborhood construction via analyzing existing nonlinear dimensionality reduction algorithms: 1) data points in the same neighborhood should approximately lie on a low dimensional linear subspace; and 2) each neighborhood should be as large as possible. Then a dynamic neighborhood selection algorithm based on this two principles is proposed in this paper. The proposed method exploits PCA technique to measure the linearity of a finite points set. Moreover, for isometric embedding, we present an improved method of constructing neighborhood graph, which can improve the accuracy of geodesic distance estimation. Experiments on both synthetic data sets and real data sets show that our method can construct neighborhood according to local curvature of data manifold and then improve the performance of most manifold algorithms, such as ISOMAP and LLE.

Keywords

neighborhood construction manifold learning local linearity geodesic distance 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yubin Zhan
    • 1
  • Jianping Yin
    • 1
  • Jun Long
    • 1
  1. 1.Computer SchoolNational University of Defense TechnologyChangshaChina

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