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On the Diversity-Performance Relationship for Majority Voting in Classifier Ensembles

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Book cover Multiple Classifier Systems (MCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4472))

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Abstract

Combining multiple classifier systems (MCS’) has been shown to outperform single classifier system. It has been demonstrated that improvement for ensemble performance depends on either the diversity among or the performance of individual systems. A variety of diversity measures and ensemble methods have been proposed and studied. It remains a challenging problem to estimate the ensemble performance in terms of the performance of and the diversity among individual systems. In this paper, we establish upper and lower bounds for P m (performance of the ensemble using majority voting) in terms of P̄(average performance of individual systems) and D̄ (average entropy diversity measure among individual systems). These bounds are shown to be tight using the concept of a performance distribution pattern (PDP) for the input set. Moreover, we showed that when P̄ is big enough, the ensemble performance P m resulting from a maximum (information-theoretic) entropy PDP is an increasing function with respect to the diversity measure D̄. Five experiments using data sets from various applications domains are conducted to demonstrate the complexity, richness, and diverseness of the problem in estimating the ensemble performance.

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References

  1. Ho, T., Hull, J., Srihari, S.: Decision combination in multiple classifier systems. IEEE Transactions on Pattern Analysis and Machine Intelligence 16, 66–75 (1994)

    Article  Google Scholar 

  2. Ho, T.K.: Multiple classifier combination: Lessons and next steps. In: Bunke, H., Kandel, A. (eds.) Hybrid Methods in Pattern Recognition, pp. 171–198. World Scientific, Singapore (2002)

    Google Scholar 

  3. Kuncheva, L.I.: Combining Pattern Classifiers: Methods and Algorithms. John Wiley & Sons, Chichester (2004)

    MATH  Google Scholar 

  4. Sharkey, A. (ed.): Combining Artificial Neural Nets. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  5. Dietterich, T.G.: Ensemble methods in machine learning. In: Kittler, J., Roli, F. (eds.) MCS 2000. LNCS, vol. 1857, pp. 1–15. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Kuncheva, L.I., Whitaker, C.J.: Measures of diversity in classifier ensembles and their relationship with the ensemble accuracy. Machine Learning 51, 181–207 (2003)

    Article  MATH  Google Scholar 

  7. Kuncheva, L.: That elusive diversity in classifier ensembles. In: Perales, F.J., et al. (eds.) IbPRIA 2003. LNCS, vol. 2652, pp. 1126–1138. Springer, Heidelberg (2003)

    Google Scholar 

  8. Hansen, L., Salamon, P.: Neural network ensembles. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(10), 993–1001 (1990)

    Article  Google Scholar 

  9. Krogh, A., Vedelsby, J.: Neural network ensembles, cross validation, and active learning. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) Advances in Neural Information Processing Systems, vol. 7, pp. 231–238. MIT Press, Volume  (1995)

    Google Scholar 

  10. Tumer, K., Ghosh, J.: Linear and order statistics combiners for pattern classification. In: Sharkey, A. (ed.) Combining Artificial Neural Nets, pp. 127–162. Springer, Heidelberg (1999)

    Google Scholar 

  11. Fumera, G., Roli, F.: A theoretical and experimental analysis of linear combiners and multiple classifier systems. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(6), 942–956 (2005)

    Article  Google Scholar 

  12. Aksela, M., Laaksonen, J.: Using diversity of errors for selecting members of a committee classifier. Pattern Recognition 39, 608–623 (2006)

    Article  MATH  Google Scholar 

  13. Partridge, D., Krzanowski, W.: Refining multiple classifier system diversity. Technical report, Computer Science Department, University of Exeter, UK (2003)

    Google Scholar 

  14. Ruta, D.: Classifier Diversity in Combined Pattern Recognition Systems. PhD thesis, University of Paisley, Scotland, UK (2003)

    Google Scholar 

  15. Shipp, C., Kuncheva, L.: Relationships between combination methods and measures of diversity in combining classifiers. Information Fusion 3(2), 135–148 (2002)

    Article  Google Scholar 

  16. Narasimhamurthy, A.: Evaluation of diversity measures for binary classifier ensembles. In: Oza, N.C., et al. (eds.) MCS 2005. LNCS, vol. 3541, pp. 267–277. Springer, Heidelberg (2005)

    Google Scholar 

  17. Hsu, D.F., Chung, Y.S., Kristal, B.S.: Combinatorial fusion analysis: Methods and practices of combining multiple scoring systems. In: Hsu, H.H. (ed.) Advanced Data Mining Technologies in Bioinformatics, pp. 32–62. Idea Group, Hershey (2006)

    Google Scholar 

  18. Hsu, D.F., Taksa, I.: Comparing rank and score combination methods for data fusion in information retrieval. Information Retrieval 8(3), 449–480 (2005)

    Article  Google Scholar 

  19. Kuncheva, L.I., et al.: Limits on the majority vote accuracy in classifier fusion. Pattern Analysis and Applications 6, 22–31 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ruta, D., Gabrys, B.: A theoretical analysis of the majority voting errors for multiple classifier systems. Pattern Analysis and Applications 5, 333–350 (2002)

    Article  MathSciNet  Google Scholar 

  21. Kittler, J., et al.: On combining classifiers. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(3), 226–239 (1998)

    Article  Google Scholar 

  22. Kittler, J., Alkoot, F.: Sum versus vote fusion in multiple classifier systems. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(1), 110–115 (2003)

    Article  Google Scholar 

  23. Lam, L., Suen, C.Y.: Application of majority voting to pattern recognition: An analysis of its behaviour and performance. IEEE Transactions on Systems, Man, and Cybernetics 27(5), 533–568 (1997)

    Google Scholar 

  24. Zenobi, G., Cunningham, P.: Using diversity in preparing ensembles of classifiers based on different feature subsets to minimize generalization error. In: Flach, P.A., De Raedt, L. (eds.) ECML 2001. LNCS (LNAI), vol. 2167, pp. 576–587. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  25. Narasimhamurthy, A.: Theoretical bounds of majority voting performance for a binary classification problem. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(12), 1988–1995 (2005)

    Article  Google Scholar 

  26. Roli, F., Kittler, J.: Fusion of multiple classifiers. Information Fusion (Editorial) 3(4), 243 (2002)

    Article  Google Scholar 

  27. Kuncheva, L.I.: Diversity in multiple classifier systems. Information Fusion (Editorial) 6(1), 3–4 (2005)

    Article  MathSciNet  Google Scholar 

  28. Breiman, L.: Random forests. Machine Learning 45, 5–32 (2001)

    Article  MATH  Google Scholar 

  29. Matan, O.: On voting ensembles of classifiers. In: Proc. AAAI-96, Integrating Multiple Learned Models Workshop, pp. 84–88 (1996)

    Google Scholar 

  30. Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley & Sons, Chichester (1991)

    MATH  Google Scholar 

  31. Kuncheva, L.I.: Fuzzy Classifier Design. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  32. Breiman, L.: Arcing classifiers. The Annals of Statistics 26(3), 801–849 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  33. Kendall, M., Gibbons, J.D.: Rank Correlation Methods. Edward Arnold, London (1990)

    MATH  Google Scholar 

  34. Chung, Y.S., Hsu, D.F., Tang, C.Y.: On the diversity-performance relationship for plurality voting and disagreement diversity in classifier ensembles. Manuscript (2006)

    Google Scholar 

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Michal Haindl Josef Kittler Fabio Roli

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Chung, YS., Hsu, D.F., Tang, C.Y. (2007). On the Diversity-Performance Relationship for Majority Voting in Classifier Ensembles. In: Haindl, M., Kittler, J., Roli, F. (eds) Multiple Classifier Systems. MCS 2007. Lecture Notes in Computer Science, vol 4472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72523-7_41

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  • DOI: https://doi.org/10.1007/978-3-540-72523-7_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72481-0

  • Online ISBN: 978-3-540-72523-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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