Kernel PCA and Nonlinear ASM

  • Liu Fan
  • Xu Tao
  • Sun Tong
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 138)


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.


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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