On Robust Computation of Tensor Classifiers Based on the Higher-Order Singular Value Decomposition

  • Bogusław CyganekEmail author
  • Michał Woźniak
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 465)


In this paper a method of faster training of the ensembles of the tensor classifiers based on the Higher-Order Singular Value Decomposition is presented. The method relies on the fixed-point method of eigenvector computation which is employed at the stage of subspace construction of the flattened versions of the input tensor patterns. As verified experimentally, the proposed method allows up to five times speed-up factor at no significant difference in accuracy.


Tensor classifiers Subspace classification Higher-Order singular value decomposition 



This work was supported by the Polish National Science Centre under the grant no. DEC-2014/15/B/ST6/00609. This work was supported by EC under FP7, Coordination and Support Action, Grant Agreement Number 316097, ENGINE—European Research Centre of Network Intelligence for Innovation Enhancement ( All computer experiments were carried out using computer equipment sponsored by ENGINE project.


  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) (2000). World Scientic Publishing CompanyGoogle Scholar
  2. 2.
    Cyganek, B.: Ensemble of Tensor Classifiers Based on the Higher-Order Singular Value Decomposition. HAIS 2012, Part II, LNCS, vol. 7209, pp. 578–589. Springer (2012)Google Scholar
  3. 3.
    Cyganek B.: Embedding of the Extended Euclidean Distance into Pattern Recognition with Higher-Order Singular Value Decomposition of Prototype Tensors. In: Cortesi, A., et al. (eds.) IFIP International Federation for Information Processing, Venice, Italy CISIM 2012, Lecture Notes in Computer Science LNCS, vol. 7564, pp. 180–190. Springer (2012)Google Scholar
  4. 4.
    Cyganek, B.: Object Detection and Recognition in Digital Images: Theory and Practice. Wiley (2013)Google Scholar
  5. 5.
    Cyganek B., Krawczyk B., Woźniak, M.: Multidimensional data classification with chordal distance based kernel and support vector machines. Engineering Applications of Artificial Intelligence, Part A, vol. 46, pp. 10–22. Elsevier (2015)Google Scholar
  6. 6.
    Cyganek, B., Woźniak, M.: An improved vehicle logo recognition using a classifier ensemble based on pattern tensor representation and decomposition. New Gener. Comput. Springer 33(4), 389–408 (2015)CrossRefGoogle Scholar
  7. 7.
    Demmel J.W.: Applied Numerical Linear Algebra. Siam (1997)Google Scholar
  8. 8.
    Grandvalet, Y.: Bagging equalizes influence. Mach. Learn. 55, 251–270 (2004)CrossRefGoogle Scholar
  9. 9.
    Hull, J.: A database for handwritten text recognition research. IEEE Trans. Pattern Anal. Mach. Intell. 16(5), 550–554 (1994)CrossRefGoogle Scholar
  10. 10.
    Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 455–500 (2008)Google Scholar
  11. 11.
    Krawczyk, B.: One-class classifier ensemble pruning and weighting with firefly algorithm. Neurocomputing 150, 490–500 (2015)CrossRefGoogle Scholar
  12. 12.
    de Lathauwer, L.: Signal Processing Based on Multilinear Algebra. Ph.D. dissertation, Katholieke Universiteit Leuven (1997)Google Scholar
  13. 13.
    de Lathauwer, L., de Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000)MathSciNetCrossRefGoogle Scholar
  14. 14.
    LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-Based learning applied to document recognition. In: Proceedings of IEEE on Speech & Image Processing, vol. 86, No. 11, pp. 2278–2324 (1998)Google Scholar
  15. 15.
    Marot J., Fossati C., Bourennane S.: About advances in tensor data denoising methods. EURASIP J. Adv. Sig. Process. (2008)Google Scholar
  16. 16.
    Savas, B., Eldén, L.: Handwritten digit classification using higher order singular value decomposition. Pattern Recogn. 40, 993–1003 (2007)CrossRefGoogle Scholar
  17. 17.
    Woźniak, M., Grana, M., Corchado, E.: A survey of multiple classifier systems as hybrid systems. Inf. Fusion 16(1), 3–17 (2014)Google Scholar
  18. 18.

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Authors and Affiliations

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

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