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Construction Algorithm of Principal Curves in the Sense of Limit

  • Lianwei Zhao
  • Yanchang Zhao
  • Siwei Luo
  • Chao Shao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3809)

Abstract

Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.

Keywords

Random Vector Open Covering Principal Curve Reconstruction Error Construction Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Lianwei Zhao
    • 1
  • Yanchang Zhao
    • 2
  • Siwei Luo
    • 1
  • Chao Shao
    • 1
  1. 1.School of Computer and Information TechnologyBeijing Jiaotong UniversityBeijingChina
  2. 2.Faculty of Information TechnologyUniversity of TechnologySydneyAustralia

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