Improving geodesic distance estimation based on locally linear assumption

  • Authors:

  • Deyu Meng;Yee Leung;Zongben Xu;Tung Fung;Qingfu Zhang

  • Affiliations:

  • Institute for Information and System Sciences, Xi'an Jiaotong University, Xi'an, Shaan'xi 710049, PR China;Department of Geography and Resource Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Institute for Information and System Sciences, Xi'an Jiaotong University, Xi'an, Shaan'xi 710049, PR China;Department of Geography and Resource Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Department of Computer Science, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2008

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Abstract

Geodesic distance estimation for data lying on a manifold is an important issue in many applications of nonlinear dimensionality reduction. In this paper, a method aiming at improving the precision of geodesic distance estimation is proposed. The method is constructed on the basic principle, locally linear assumption, underlying the manifold data. It presumes that the locally linear patch, expressed as a convex combination of neighbors of a vertex, approximately resides on the manifold, as well as the local neighborhood edge does. The proposed method essentially extends the search area from local edges, employed by existing methods, to local patches. This naturally leads to a more accurate geodesic distance estimation. An efficient algorithm for the method is constructed, and its computational complexity is also analyzed. Experiment results also show that the proposed method outperforms the existing methods in geodesic distance estimation.