Kernel PCA and Nonlinear ASM

Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 138)

Abstract

As a nonlinear Principal Component Analysis (PCA) method, Kernel PCA (KPCA) can effectively extract nonlinear feature. For the object image which includes more nonlinear features, traditional Active Shape Model (ASM) couldn’t obtain a good result of localization. Concerning this, an extending research on nonlinear-ASM is brought here, and an algorithm of object localization based on nonlinear-ASM is proposed. In the research of nonlinear-ASM, the problem of high dimensionality caused by nonlinear mapping has been solved effectively by the kernel theory. Besides, KPCA can not reconstruct the pre-image of the input space, thus prior model is hardly constructed by the method of the nonlinear-ASM. For solving this problem, the theory of multi-dimensional scaling is researched in the paper. The validity of the proposed method is demonstrated by the results of experiments.

Keywords

Kernel Principal Component Analysis Multi-dimensional Scaling Active Shape Model Nonlinear Object Localization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kim, K.I., Jung, K., Kim, H.J.: Face Recognition Using Kernel Principal Component Analysis. IEEE Signal Processing Letters 9(2), 40–42 (2002)CrossRefGoogle Scholar
  2. 2.
    Rosipal, R., Girolami, M., Trejo, L.J.: Kernel PCA for Feature Extraction and De-noising in Non-linear Regression.Technical Report No.4, Department of Computing and Information Systems, University of Paisley (2000)Google Scholar
  3. 3.
    Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, 2nd edn. Monograghs on Statistics and Applied Probability, vol. 88. Chapman & Hall/CRC (2001)Google Scholar
  4. 4.
    Kwok, J.T., Tsang, I.W.: The Pre-Image Problem in Kernel Methods. IEEE Transactions on Neural Networks 15(6), 1517–1525 (2004)CrossRefGoogle Scholar
  5. 5.
    Scholkopf, B., Smola, A., Muller, K.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10(5), 1299–1319 (1998)CrossRefGoogle Scholar
  6. 6.
    Vapnik, V.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995)MATHGoogle Scholar
  7. 7.
    Williams, C.K.I.: On a Connection between Kernel PCA and Metric Multidimensional Scaling. In: Leen, T.K., Dietterich, T.G., Tresp, V. (eds.) Advances in Neural Information Processing Systems, vol. 13, pp. 675–681. MIT Press, Cambridge (2001)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Information and Network CenterCAUCTianjinChina
  2. 2.Information Technology Research Base of CAACCollege of Computer Science and Technology of CAUCTianjinChina

Personalised recommendations