Advertisement

Improved Locally Linear Embedding Through New Distance Computing

  • Heyong Wang
  • Jie Zheng
  • Zhengan Yao
  • Lei Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)

Abstract

Locally linear embedding (LLE) is one of the methods intended for dimensionality reduction, which relates to the number K of nearest-neighbors points to be initially chosen. So, in this paper, we want that the parameter K has little influence on the dimension reduction, that is to say, the parameter K can be widely chosen while not influence the effect of dimension reduction. Therefore, we propose a method of improved LLE, which uses new distance computing for weight of K nearest-neighbors points in LLE. Thus, even when the number K is little, the improved LLE can get good results of dimension reduction, while the traditional LLE needs a larger number of K to get the same results. When the number K of the nearest neighbors gets larger, test in this paper has proved that the improved LLE can still get correct results.

Keywords

Dimension Reduction Texture Image Locally Linear Embedding Nonlinear Dimensionality Reduction Distance Computing 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jolliffe, I.T.: Principal Component Analysis, 2nd edn. Springer, Heidelberg (2002)MATHGoogle Scholar
  2. 2.
    Scholkopf, B., Smola, A.J., Muller, K.R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10(5), 1299–1319 (1998)CrossRefGoogle Scholar
  3. 3.
    Mika, S., Rtsch, G., Weston, J., Scholkopf, B., Muller, K.R.: Fisher Discriminant Analysis with Kernels. Neural Networks for Signal Processing IX, 41–48 (1999)Google Scholar
  4. 4.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications. Springer, Heidelberg (1997)MATHGoogle Scholar
  5. 5.
    Kohonen, T.: The Self-Organizing Map, 3rd edn. Springer, Heidelberg (2000)Google Scholar
  6. 6.
    Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290(5500), 2319–2323 (2000)CrossRefGoogle Scholar
  7. 7.
    Roweis, S.T., Saul, L.K.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290(5500), 2323–2326 (2000)CrossRefGoogle Scholar
  8. 8.
    Bian, Z.Q., Zhang, X.G.: Pattern Recognition, 2nd edn. Tsinghua University Press, Beijing (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Heyong Wang
    • 1
  • Jie Zheng
    • 2
  • Zhengan Yao
    • 2
  • Lei Li
    • 1
  1. 1.Software Research InstituteSun Yat-sen UniversityGuangzhouChina
  2. 2.College of Mathematics and Computational ScienceSun Yat-sen UniversityGuangzhouChina

Personalised recommendations