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Manifold-Regularized Minimax Probability Machine

  • Kazuki Yoshiyama
  • Akito Sakurai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7081)

Abstract

In this paper we propose Manifold-Regularized Minimax Probability Machine, called MRMPM. We show that Minimax Probability Machine can properly be extended to semi-supervised version in the manifold regularization framework and that its kernelized version is obtained for non-linear case. Our experiments show that the proposed methods achieve results competitive to existing learning methods, such as Laplacian Support Vector Machine and Laplacian Regularized Least Square for publicly available datasets from UCI machine learning repository.

Keywords

Coordinate Descent Pairwise Constraint Unlabeled Sample Machine Learn Research Manifold Regularization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Argyriou, A., Micchelli, C.A., Pontil, M.: When is a representer theorem? vector versus matrix regularizers. Journal of Machine Learning Research 10, 2507–2529 (2009)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Belkin, M., Niyogi, P.: Towards a Theoretical Foundation for Laplacian-Based Manifold Methods. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 486–500. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Belkin, M., Niyogi, P., Sindhwani, V.: Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. Journal of Machine Learning Research 7, 2399–2434 (2006)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Belkin, M., Niyogi, P., Sindhwani, V.: On manifold regularization. In: International Conference on Artificial Intelligence and Statistics, AISTATS (2005)Google Scholar
  5. 5.
    Bertsimas, D., Popescu, I.: Optimal inequalities in probability theory: A convex optimization approach. SIAM Journal of Optimization 15(3), 780–804 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Bousquet, O., Chapelle, O., Hein, M.: Measure based regularization. In: Advances in Neual Information Processing Systems, vol. 16 (2004)Google Scholar
  7. 7.
    Chapell, O., Sindhwani, V., Keerthi, S.S.: Optimization techniques for semi-supervised support vector machine. Journal of Machine Learning Research 9, 203–233 (2008)zbMATHGoogle Scholar
  8. 8.
    Chapelle, O., Zien, A.: Semi-supervised classification by low density sepration. In: International Conference on Artificial Intelligence and Statistics, AISTATS (2005)Google Scholar
  9. 9.
    Davis, J.V., Kulis, B., Jain, P., Dhillon, S.I.S.: Information-theoretic metric learning. In: Proceedings of the 24th International Conference on Machine Learning (2007)Google Scholar
  10. 10.
    Bertsekas, D.P.: Nonlinear programming. Athena Scientific, Belmont (1999)Google Scholar
  11. 11.
    Goldberg, A.B., Zhu, X., Wright, S.: Dissimilarity in graph-based semi-supervised classification. In: Eleventh International Conference on Artificial Intelligence and Statistics, AISTATS (2007)Google Scholar
  12. 12.
    Jain, P., Kulis, B., Dhillon, I.: Inductive regularized learning of kernel functions. In: Advances in Neual Information Processing Systems (2010)Google Scholar
  13. 13.
    Kulis, B., Sustik, M., Dhillon, I.: Learning low-rank kernel matrices. In: Proceedings, the 23rd International Conference on Machine Learning (2006)Google Scholar
  14. 14.
    Lanckriet, G.R.G., Ghaoui, L.E., Bhattacharyya, C., Jordan, M.I.: A robust minimax approach to classification. Journal of Machine Learning Research 3, 555–582 (2002)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Li, Z., Liu, J., Tang, X.: Pairwise constraint propagation by semidefinite programming for semi-supervised classification. In: Proceedings of the International Conference on Machine Learning (2008)Google Scholar
  16. 16.
    Sindhwani, V., Niyogi, P., Belkin, M.: Beyond the point cloud: from transductive to semi-supervised learning. In: Proceedings of the 22nd International Conference on Machine Learning (2005)Google Scholar
  17. 17.
    Tong, W., Jin, R.: Semi-supervised learning by mixed label propagation. In: Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence, AAAI (2007)Google Scholar
  18. 18.
    Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using gaussian fields and harmonic functions. In: Proceedings of the International Conference on Machine Learning (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kazuki Yoshiyama
    • 1
  • Akito Sakurai
    • 1
  1. 1.School of Science for Open and Environmental SystemKeio UniversityKohoku-kuJapan

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