Advertisement

Robust Learning from Ortho-Diffusion Decompositions

  • Sravan Gudivada
  • Adrian G. BorsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9256)

Abstract

This paper describes a new classification method based on modeling data by embedding diffusions into orthonormal decompositions of graph-based data representations. The training data is represented by an adjacency matrix calculated using either the correlation or the covariance of the training set. The application of the modified Gram-Schmidt orthonormal decomposition alternating with diffusion and data reduction stages, is applied recursively at each scale level. The diffusion process is strengthening the representation pattern of representative features. Meanwhile, noise is removed together with non-essential detail during the data reduction stage. The proposed methodology is shown to be robust when applied to face recognition considering low image resolution and corruption by various types of noise.

Keywords

Ortho-diffusion decompositions Gram-schmidt algorithm Robust face recognition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Belhumeur, P., Hespanha, J., Kriegman, D.: Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. IEEE Trans. on Pattern Analysis and Machine Intelligence 19(7), 711–720 (1997)CrossRefGoogle Scholar
  2. 2.
    Cai, D., He, X., Han, J., Zhang, H.J.: Orthogonal laplacianfaces for face recognition. IEEE Trans. on Image Processing 15(11), 3608–3614 (2006)CrossRefGoogle Scholar
  3. 3.
    Coifman, R.R., Lafon, S.: Diffusion maps. Applied Comput. Harmon. Anal. 21(1), 5–30 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Draper, B., Baek, K., Bartlett, M., Beveridge, R.: Recognizing faces with PCA and ICA. Computer Vision and Image Understanding 91(1–2), 115–137 (2003)CrossRefGoogle Scholar
  5. 5.
    Essafi, S., Langs, G., Paragios, N.: Hierarchical 3d diffusion wavelet shape priors. In: Proc. of IEEE Int. Conf. on Computer Vision, pp. 1717–1724 (2009)Google Scholar
  6. 6.
    Gudivada, S., Bors, A.G.: Face recognition using ortho-diffusion bases. In: Proc. 20th European Signal Processing Conference, pp. 1578–1582 (2012)Google Scholar
  7. 7.
    Gudivada, S., Bors, A.G.: Ortho-diffusion decompositions of graph-based representation of images. Pattern Recognition (2015)Google Scholar
  8. 8.
    He, X., Yan, S., Hu, Y., Niyogi, P., Zhang, H.J.: Face recognition using laplacianfaces. IEEE Trans. on Pattern Analysis and Machine Intelligence 27(3), 328–340 (2005)CrossRefGoogle Scholar
  9. 9.
    Lu, J., Dorsey, J., Rushmeier, H.: Dominant texture and diffusion distance manifolds. Proc. Eurographics Computer Graphics Forum 28(2), 667–676 (2009)CrossRefGoogle Scholar
  10. 10.
    Luxburg, U.: A tutorial on spectral clustering. J. of Statistics and Computing 17(4), 395–416 (2007)CrossRefGoogle Scholar
  11. 11.
    Magioni, M., Mahadevan, S.: Fast direct policy evaluation using multiscale analysis of markov diffusion processes. In: Proc. of the 23rd International Conference on Machine Learning, pp. 601–608 (2005)Google Scholar
  12. 12.
    Singer, A., Coifman, R.R.: Non-linear independent component analysis with diffusion maps. Applied and Computational Harmonic Analysis 25(1), 226–239 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Trefethen, L.N., Bau, D.: Numerical Linear Algebra. SIAM (1997)Google Scholar
  14. 14.
    Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cognitive Neuroscience 3(1), 71–86 (1991)CrossRefGoogle Scholar
  15. 15.
    Wang, C., Mahadevan, S.: Multiscale dimensionality reduction based on diffusion wavelets. Tech. rep., Univ. of Massachusetts (2009)Google Scholar
  16. 16.
    Wartak, S., Bors, A.G.: Optical flow estimation using diffusion distances. In: Proc. Int. Conf on Pattern Recognition, pp. 189–192 (2010)Google Scholar
  17. 17.
    Wild, M.: Nonlinear approximation of spatiotemporal data using diffusion wavelets. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 886–894. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  18. 18.
    Yan, S., Yu, D., Yang, Q., Zhang, L., Tang, X., Zhang, H.: Multilinear discriminant analysis for face recognition. IEEE Trans on Image Processing 16(1), 212–220 (2007)CrossRefGoogle Scholar
  19. 19.
    Zhang, B.C., Shan, S.G., Chen, X., Gao, W.: Histogram of gabor phase patterns: A novel object representation approach for face recognition. IEEE Trans. on Image Processing 16(1), 504–516 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of YorkYorkUK

Personalised recommendations