Skip to main content

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

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 465))

Abstract

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.

This is a preview of subscription content, log in via an institution.

References

  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 Company

    Google Scholar 

  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. 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. Cyganek, B.: Object Detection and Recognition in Digital Images: Theory and Practice. Wiley (2013)

    Google Scholar 

  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. 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)

    Article  Google Scholar 

  7. Demmel J.W.: Applied Numerical Linear Algebra. Siam (1997)

    Google Scholar 

  8. Grandvalet, Y.: Bagging equalizes influence. Mach. Learn. 55, 251–270 (2004)

    Article  MATH  Google Scholar 

  9. Hull, J.: A database for handwritten text recognition research. IEEE Trans. Pattern Anal. Mach. Intell. 16(5), 550–554 (1994)

    Article  Google Scholar 

  10. Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 455–500 (2008)

    Google Scholar 

  11. Krawczyk, B.: One-class classifier ensemble pruning and weighting with firefly algorithm. Neurocomputing 150, 490–500 (2015)

    Article  Google Scholar 

  12. de Lathauwer, L.: Signal Processing Based on Multilinear Algebra. Ph.D. dissertation, Katholieke Universiteit Leuven (1997)

    Google Scholar 

  13. de Lathauwer, L., de Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  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. Marot J., Fossati C., Bourennane S.: About advances in tensor data denoising methods. EURASIP J. Adv. Sig. Process. (2008)

    Google Scholar 

  16. Savas, B., Eldén, L.: Handwritten digit classification using higher order singular value decomposition. Pattern Recogn. 40, 993–1003 (2007)

    Article  MATH  Google Scholar 

  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. www-stat.stanford.edu/~tibs/ElemStatLearn/

Download references

Acknowledgement

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 (http://engine.pwr.wroc.pl/). All computer experiments were carried out using computer equipment sponsored by ENGINE project.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bogusław Cyganek .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Cyganek, B., Woźniak, M. (2016). On Robust Computation of Tensor Classifiers Based on the Higher-Order Singular Value Decomposition. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds) Software Engineering Perspectives and Application in Intelligent Systems. ICTIS CSOC 2017 2016. Advances in Intelligent Systems and Computing, vol 465. Springer, Cham. https://doi.org/10.1007/978-3-319-33622-0_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-33622-0_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33620-6

  • Online ISBN: 978-3-319-33622-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics