Adaptive Two-View Online Learning for Math Topic Classification

  • Tam T. Nguyen
  • Kuiyu Chang
  • Siu Cheung Hui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7523)


Text categorization has been a popular research topic for years and has become more or less a practical technology. However, there exists little research on math topic classification. Math documents contain both textual data and math expressions. The text and math can be considered as two related but different views of a math document. The goal of online math topic classification is to automatically categorize a math document containing both mathematical expressions and textual content into an appropriate topic without the need for periodically retraining the classifier. To achieve this, it is essential to have a two-view online classification algorithm, which deals with the textual data view and the math expression view at the same time. In this paper, we propose a novel adaptive two-view online math document classifier based on the Passive Aggressive (PA) algorithm. The proposed approach is evaluated on real world math questions and answers from the Math Overflow question answering system. Compared to the baseline PA algorithm, our method’s overall F-measure is improved by up to 3%. The improvement of our algorithm over the plain math expression view is almost 6%.


Product Review Math Topic Question Answering System Document Topic Online Learning Algorithm 
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.


  1. 1.
    Ausbrooks, R., Buswell, S., Dalmas, S., Devitt, S., Diaz, A., Hunter, R., Smith, B., Soiffer, N., Sutor, R., Watt, S.: Mathematical markup language (mathml) version 2.0 (2000)Google Scholar
  2. 2.
    Block, H.: The perceptron: A model for brain functioning. Rev. Modern Phys. 34, 123–135 (1962)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Buswell, S., Caprotti, O., Carlisle, D.P., Dewar, M.C., Gaetano, M., Kohlhase, M.: The Open Math standard version 2.0 (2004)Google Scholar
  4. 4.
    Cesa-Bianchi, N., Conconi, A., Gentile, C.: A second-order perceptron algorithm. Siam J. of Comm. 34 (2005)Google Scholar
  5. 5.
    Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20, 273–297 (1995)zbMATHGoogle Scholar
  6. 6.
    Cover, T., Hart, P.: Nearest Neighbor Pattern Classification 13, 373–389 (2002)Google Scholar
  7. 7.
    Cover, T.M., Thomas, J.A.: Elements of information theory. Wiley-Interscience, New York (1991)zbMATHCrossRefGoogle Scholar
  8. 8.
    Crammer, K., Dekel, O., Keshet, J., Shalev-Shwartz, S., Singer, Y.: Online passive-aggressive algorithms. Journal of Machine Learning Research, 551–585 (2006)Google Scholar
  9. 9.
    Crammer, K., Dredze, M., Kulesza, A.: Multi-class confidence weighted algorithms. In: Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing, Singapore, pp. 496–504. Association for Computational Linguistics,Google Scholar
  10. 10.
    Dredze, M., Crammer, K., Pereira, F.: Confidence-weighted linear classification. In: ICML 2008: Proceedings of the 25th International Conference on Machine Learning, pp. 264–271. ACM, New York (2008)CrossRefGoogle Scholar
  11. 11.
    Farquhar, J.D.R., Hardoon, D.R., Meng, H., Shawe-Taylor, J., Szedmák, S.: Two view learning: Svm-2k, theory and practice. In: Proceedings of NIPS 2005 (2005)Google Scholar
  12. 12.
    Jipsen, P.: Translating ascii math notation to mathml and graphics (2007)Google Scholar
  13. 13.
    Kohlhase, M., Sucan, I.: A Search Engine for Mathematical Formulae. In: Calmet, J., Ida, T., Wang, D. (eds.) AISC 2006. LNCS (LNAI), vol. 4120, pp. 241–253. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Kushmerick, N.: Learning to remove internet advertisements. In: Proceedings of the Third Annual Conference on Autonomous Agents, AGENTS 1999, pp. 175–181. ACM, New York (1999)CrossRefGoogle Scholar
  15. 15.
    Langley, P., Iba, W., Thompson, K.: An analysis of bayesian classifiers. In: AAAI 1992: Proceedings of the Tenth National Conference on Artificial Intelligence, pp. 223–228. AAAI Press (1992)Google Scholar
  16. 16.
    Lewis, D.D.: Naive (bayes) at Forty: The Independence Assumption in Information Retrieval. In: Nédellec, C., Rouveirol, C. (eds.) ECML 1998. LNCS, vol. 1398, pp. 4–15. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  17. 17.
    Li, G., Hoi, S.C.H., Chang, K.: Two-view transductive support vector machines. In: Proceedings of SDM 2010, pp. 235–244 (2010)Google Scholar
  18. 18.
    Manning, C.D., Raghavan, P., Schütze, H.: Introduction to Information Retrieval. Cambridge University Press (2008)Google Scholar
  19. 19.
    Nguyen, T.T., Chang, K., Hui, S.C.: Distribution-aware online classifiers. In: Walsh, T. (ed.) IJCAI, pp. 1427–1432. IJCAI/AAAI (2011)Google Scholar
  20. 20.
    Nguyen, T.T., Chang, K., Hui, S.C.: Two-View Online Learning. In: Tan, P.-N., Chawla, S., Ho, C.K., Bailey, J. (eds.) PAKDD 2012, Part I. LNCS, vol. 7301, pp. 74–85. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  21. 21.
    Novikoff, A.: On convergence proofs of perceptrons. In: Proceedings of the Symposium on the Mathematical Theory of Automata, vol. 7, pp. 615–622 (1962)Google Scholar
  22. 22.
    Quinlan, J.R., Rivest, R.L.: Inferring decision trees using the minimum description length principle. Inf. Comput. 80(3), 227–248 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    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, ICML 2005, pp. 824–831. ACM, New York (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tam T. Nguyen
    • 1
  • Kuiyu Chang
    • 1
  • Siu Cheung Hui
    • 1
  1. 1.Nanyang Technological UniversitySingapore

Personalised recommendations