Information Theoretical Kernels for Generative Embeddings Based on Hidden Markov Models

  • André F. T. Martins
  • Manuele Bicego
  • Vittorio Murino
  • Pedro M. Q. Aguiar
  • Mário A. T. Figueiredo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6218)

Abstract

Many approaches to learning classifiers for structured objects (e.g., shapes) use generative models in a Bayesian framework. However, state-of-the-art classifiers for vectorial data (e.g., support vector machines) are learned discriminatively. A generative embedding is a mapping from the object space into a fixed dimensional feature space, induced by a generative model which is usually learned from data. The fixed dimensionality of these feature spaces permits the use of state of the art discriminative machines based on vectorial representations, thus bringing together the best of the discriminative and generative paradigms.

Using a generative embedding involves two steps: (i) defining and learning the generative model used to build the embedding; (ii) discriminatively learning a (maybe kernel) classifier on the adopted feature space. The literature on generative embeddings is essentially focused on step (i), usually adopting some standard off-the-shelf tool (e.g., an SVM with a linear or RBF kernel) for step (ii). In this paper, we follow a different route, by combining several Hidden Markov Models-based generative embeddings (including the classical Fisher score) with the recently proposed non-extensive information theoretic kernels. We test this methodology on a 2D shape recognition task, showing that the proposed method is competitive with the state-of-art.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andreu, G., Crespo, A., Valiente, J.: Selecting the toroidal self-organizing feature maps (TSOFM) best organized to object recognition. In: Proc. of IEEE ICNN 1997, vol. 2, pp. 1341–1346 (1997)Google Scholar
  2. 2.
    Bahl, L., Brown, P., de Souza, P., Mercer, R.: Maximum mutual information estimation of hidden Markov model parameters for speech recognition. In: IEEE International Conference on Acoustics, Speech and Signal Processing, Tokyo, Japan, vol. I, pp. 49–52 (2000)Google Scholar
  3. 3.
    Bicego, M., Cristani, M., Murino, V., Pekalska, E., Duin, R.: Clustering-based construction of hidden Markov models for generative kernels. In: Cremers, D., Boykov, Y., Blake, A., Schmidt, F.R. (eds.) Energy Minimization Methods in Computer Vision and Pattern Recognition. LNCS, vol. 5681, pp. 466–479. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Bicego, M., Murino, V., Figueiredo, M.: Similarity-based classification of sequences using hidden Markov models. Pattern Recognition 37(12), 2281–2291 (2004)CrossRefGoogle Scholar
  5. 5.
    Bicego, M., Pekalska, E., Tax, D., Duin, R.: Component-based discriminative classification for hidden Markov models. Pattern Recognition 42(11), 2637–2648 (2009)MATHCrossRefGoogle Scholar
  6. 6.
    Bicego, M., Trudda, A.: 2D shape classification using multifractional Brownian motion. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 906–916. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Bosch, A., Zisserman, A., Munoz, X.: Scene classification via PLSA. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3954, pp. 517–530. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Carli, A., Bicego, M., Baldo, S., Murino, V.: Non-linear generative embeddings for kernels on latent variable models. In: Proc. ICCV 2009 Workshop on Subspace Methods (2009)Google Scholar
  9. 9.
    Chen, L., Man, H., Nefian, A.: Face recognition based on multi-class mapping of Fisher scores. Pattern Recognition, 799–811 (2005)Google Scholar
  10. 10.
    Cuturi, M., Fukumizu, K., Vert, J.P.: Semigroup kernels on measures. Journal of Machine Learning Research 6, 1169–1198 (2005)MATHMathSciNetGoogle Scholar
  11. 11.
    Gales, M.: Discriminative models for speech recognition. In: Information Theory and Applications Workshop (2007)Google Scholar
  12. 12.
    Hein, M., Bousquet, O.: Hilbertian metrics and positive definite kernels on probability measures. In: Ghahramani, Z., Cowell, R. (eds.) Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics, AISTATS (2005)Google Scholar
  13. 13.
    Jaakkola, T., Haussler, D.: Exploiting generative models in discriminative classifiers. In: Advances in Neural Information Processing Systems – NIPS, pp. 487–493 (1999)Google Scholar
  14. 14.
    Jebara, T., Kondor, R., Howard, A.: Probability product kernels. Journal of Machine Learning Research 5, 819–844 (2004)MathSciNetGoogle Scholar
  15. 15.
    Kaiser, Z., Horvat, B., Kacic, Z.: A novel loss function for the overall risk criterion based discriminative training of HMM models. In: International Conference on Spoken Language Processing, Beijing, China, vol. 2, pp. 887–890 (2000)Google Scholar
  16. 16.
    Lafferty, J., McCallum, A., Pereira, F.: Conditional random fields: probabilistic models for segmenting and labelling sequence data. In: International Conference on Machine Learning, pp. 591–598 (2001)Google Scholar
  17. 17.
    Martins, A., Smith, N., Xing, E., Aguiar, P., Figueiredo, M.: Nonextensive information theoretic kernels on measures. Journal of Machine Learning Research 10, 935–975 (2009)MathSciNetGoogle Scholar
  18. 18.
    Mollineda, R., Vidal, E., Casacuberta, F.: Cyclic sequence alignments: Approximate versus optimal techniques. Int. Journal of Pattern Recognition and Artificial Intelligence 16(3), 291–299 (2002)CrossRefGoogle Scholar
  19. 19.
    Neuhaus, M., Bunke, H.: Edit distance-based kernel functions for structural pattern classification. Pattern Recognition 39, 1852–1863 (2006)MATHCrossRefGoogle Scholar
  20. 20.
    Ng, A., Jordan, M.: On discriminative vs generative classifiers: A comparison of logistic regression and naive Bayes. In: Advances in Neural Information Processing Systems (2002)Google Scholar
  21. 21.
    Perina, A., Cristani, M., Castellani, U., Murino, V.: A new generative feature set based on entropy distance for discriminative classification. In: Proc. Int. Conf. on Image Analysis and Processing, pp. 199–208 (2009)Google Scholar
  22. 22.
    Perina, A., Cristani, M., Castellani, U., Murino, V., Jojic, N.: A hybrid generative/discriminative classification framework based on free-energy terms. In: Proc. Int. Conf. on Computer Vision (2009)Google Scholar
  23. 23.
    Rabiner, L.: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. of IEEE 77(2), 257–286 (1989)CrossRefGoogle Scholar
  24. 24.
    Rubinstein, Y., Hastie, T.: Discriminative vs informative learning. In: Knowledge Discovery and Data Mining, pp. 49–53 (1997)Google Scholar
  25. 25.
    Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)Google Scholar
  26. 26.
    Smith, N., Gales, M.: Speech recognition using SVMs. In: Advances in Neural Information Processing Systems, pp. 1197–1204 (2002)Google Scholar
  27. 27.
    Tsuda, K., Kin, T., Asai, K.: Marginalised kernels for biological sequences. Bioinformatics 18, 268–275 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • André F. T. Martins
    • 3
  • Manuele Bicego
    • 1
    • 2
  • Vittorio Murino
    • 1
    • 2
  • Pedro M. Q. Aguiar
    • 4
  • Mário A. T. Figueiredo
    • 3
  1. 1.Computer Science DepartmentUniversity of VeronaVeronaItaly
  2. 2.Istituto Italiano di Tecnologia (IIT)GenovaItaly
  3. 3.Instituto de Telecomunicações, Instituto Superior TécnicoLisboaPortugal
  4. 4.Instituto de Sistemas e Robótica, Instituto Superior TécnicoLisboaPortugal

Personalised recommendations