Spline Embedding for Nonlinear Dimensionality Reduction

  • Shiming Xiang
  • Feiping Nie
  • Changshui Zhang
  • Chunxia Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4212)


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.


Reconstruction Error Locally Linear Embedding Interpolation Condition Compatible Mapping Global Embedding 
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 2006

Authors and Affiliations

  • Shiming Xiang
    • 1
  • Feiping Nie
    • 1
  • Changshui Zhang
    • 1
  • Chunxia Zhang
    • 2
  1. 1.State Key Laboratory of Intelligent Technology and Systems, Department of AutomationTsinghua UniversityBeijingChina
  2. 2.School of Computer Science, Software SchoolBeijing Institute of TechnologyBeijingChina

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