Advertisement

Efficient Multidimensional Pattern Recognition in Kernel Tensor Subspaces

  • Bogusław CyganekEmail author
  • Michał Woźniak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9714)

Abstract

In this paper we discuss algorithmically efficient methods of multidimensional patter recognition in kernel tensor subspaces. The kernel principal component analysis, which originally operates only on vector data, is joined with the tensor chordal kernel which opens a way of direct usage of the multidimensional signals, such as color video streams, seismic signals or hyperspectral images. We address the problem of efficient implementation of the eigendecomposition problem which is a core algorithm for both methods. For this the fixed point algorithm is employed. We show usefulness of this approach on the problem of visual pattern recognition and show speed-up ratio when using the proposed implementation.

Keywords

Kernel PCA Chordal kernel Tensor Subspace classification 

Notes

Acknowledgments

This work was supported by the Polish National Science Center under the grant No. NCN DEC-2014/15/B/ST6/00609.

This work was also supported by EC under FP7, Coordination and Support Action, Grant Agreement Number 316097, ENGINE – European Research Centre of Network Intelligence for Innovation Enhancement (http://engine.pwr.wroc.pl/). All computer experiments were carried out using computer equipment sponsored by ENGINE project.

References

  1. 1.
    Bingham, E., Hyvärinen, A.: A fast fixed-point algorithm for independent component analysis of complex valued signals. Int. J. Neural Syst. 10(1), 1483–1492 (2000). World Scientic Publishing CompanyCrossRefGoogle Scholar
  2. 2.
    Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20, 273–297 (1995)zbMATHGoogle Scholar
  3. 3.
    Cyganek, B.: Object Detection and Recognition in Digital Images: Theory and Practice. Wiley, London (2013)CrossRefzbMATHGoogle Scholar
  4. 4.
    Cyganek, B., Krawczyk, B., Woźniak, M.: Multidimensional data classification with chordal distance based kernel and support vector machines. Eng. Appl. Artif. Intell. 46(Part A), 10–22 (2015). ElsevierCrossRefGoogle Scholar
  5. 5.
    Georgia Tech Face Database (2013). http://www.anefian.com/research/face_reco.htm
  6. 6.
    Golub, G.H., van Loan, C.F.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore (2013)zbMATHGoogle Scholar
  7. 7.
    Hamm, J., Lee, D.: Grassmann discriminant analysis: a unifying view on subspace-based learning. In: Proceedings of the 25th International Conference on Machine Learning, pp. 376–383. ACMGoogle Scholar
  8. 8.
    Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Krawczyk, B., Schaefer, G.: A hybrid classifier committee for analysing asymmetry features in breast thermograms. Appl. Soft Comput. 20, 112–118 (2014)CrossRefGoogle Scholar
  10. 10.
    Krawczyk, B., Galar, M., Jelen, L., Herrera, F.: Evolutionary undersampling boosting for imbalanced classification of breast cancer malignancy. Appl. Soft Comput. 38, 714–726 (2016)CrossRefGoogle Scholar
  11. 11.
    Kung, S.Y.: Kernel Methods and Machine Learning. Cambridge University Press, Cambridge (2014)CrossRefzbMATHGoogle Scholar
  12. 12.
    De Lathauwer, L.: Signal processing based on multilinear algebra. Ph.D. dissertation, Katholieke Universiteit Leuven (1997)Google Scholar
  13. 13.
    Marot, J., Fossati, C., Bourennane, S.: About advances in tensor data denoising methods. EURASIP J. Adv. Signal Process. 1, 1–12 (2008)CrossRefzbMATHGoogle Scholar
  14. 14.
    Meyer, C.D.: Matrix Analysis and Applied Linear Algebra Book and Solutions Manual. SIAM, Philadelphia (2001)Google Scholar
  15. 15.
    Schölkopf, B., Smola, A., Müller, K.-R.: Nonlinear component analysis as a kernel eigenvalue problem. Technical report No. 44, Max-Planck-Institut, pp. 1–18 (1996)Google Scholar
  16. 16.
    Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2002)zbMATHGoogle Scholar
  17. 17.
    Signoretto, M., De Lathauwer, L., Suykens, J.A.K.: A kernel-based framework to tensorial data analysis. Neural Netw. 24, 861–874 (2011)CrossRefzbMATHGoogle Scholar
  18. 18.
    Turk, M.A., Pentland, A.P.: Face recognition using eigenfaces. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 586–590 (1991)Google Scholar
  19. 19.
    Vasilescu, M.A.O., Terzopoulos, D.: Multilinear analysis of image ensembles: tensorfaces. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part I. LNCS, vol. 2350, pp. 447–460. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Woźniak, M.: A hybrid decision tree training method using data streams. Knowl. Inf. Syst. 29(2), 335–347 (2011)CrossRefGoogle Scholar
  21. 21.
    Woźniak, M., Grana, M., Corchado, E.: A survey of multiple classifier systems as hybrid systems. Inf. Fusion 16(1), 3–17 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.AGH University of Science and TechnologyKrakówPoland
  2. 2.Wroclaw University of TechnologyWrocławPoland

Personalised recommendations