| | This Article | |
| |
| |
| | Share | |
| |
| |
| | Bibliographic References | |
| |
| |
| | Add to: | |
| |
 Digg
 Furl
 Spurl
 Blink
 Simpy
 Google
 Del.icio.us
 Y!MyWeb
| |
| | Search | |
| |
| |
| | |
Mixed Group Ranks: Preference and Confidence in Classifier Combination
August 2004 (vol. 26 no. 8)
pp. 973-981
Abstract—Classifier combination holds the potential of improving performance by combining the results of multiple classifers. For domains with very large numbers of classes, such as biometrics, we present an axiomatic framework of desirable mathematical properties for combination functions of rank-based classifiers. This framework represents a continuum of combination rules, including the Borda Count, Logistic Regression, and Highest Rank combination methods as extreme cases [CHECK END OF SENTENCE], [CHECK END OF SENTENCE], [CHECK END OF SENTENCE], [CHECK END OF SENTENCE]. Intuitively, this framework captures how the two complementary concepts of general preference for specific classifiers and the confidence it has in any specific result (as indicated by ranks) can be balanced while maintaining consistent rank interpretation. Mixed Group Ranks (MGR) is a new combination function that balances preference and confidence by generalizing these other functions. We demonstrate that MGR is an effective combination approach by performing multiple experiments on data sets with large numbers of classes and classifiers from the FERET face recognition study.
[1] 973 B. Achermann and H. Bunke, Combination of Classifiers on the Decision Level for Face Recognition technical report, Institut für Informatik und angewandte Mathematik, Universität Bern, Jan. 1996.[2] A. Agresti, An Introduction to Categorical Data Analysis. Wiley, 1996.[3] K. Arrow, Social Choice and Individual Values. Wiley, 1951.[4] J.A. Benediktsson, Consensus Theoretic Classification Methods IEEE Trans. Systems, Man, and Cybernetics, vol. 22, no. 4, pp. 688-704, 1992.[5] J.C. Borda, Memoire sur les Elections au Scrutin Histoire de l'Academie Royale des Sciences, 1781.[6] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Univ. Press, Mar. 2004.[7] T.G. Dietterich, Machine-Learning Research: Four Current Directions AI Magazine, vol. 18, no. 4, pp. 97-135, 1997.[8] C. Dwork, R. Kumar, M. Naor, and D. Sivakumar, Rank Aggregation Methods for the Web Proc. 10th Int'l World Wide Web Conf., pp. 613-622, 2001.[9] S. Gong and S.J. McKenna, Dynamic Vision: From Images to Face Recognition. Imperial College Press, Sept. 2000.[10] T.K. Ho, A Theory of Multiple Classifier Systems and Its Application to Visual Word Recognition PhD thesis, State Univ. of New York at Buffalo, May 1992.[11] T.K. Ho, J.J. Hull, and S.N. Srihari, Combination of Decisions by Multiple Classifiers Structured Document Image Analysis, H.S. Baird, H. Bunke, and K. Yamamoto eds., pp. 188-202, 1992.[12] J.J. Hull, T.K. Ho, and S.N. Srihari, "On multiple classifier systems for pattern recognition," Proc. Int'l Conf. Pattern Recognition, vol. 2, pp. 84-87, The Hague, Netherlands, 1992.[13] A.K. Jain, S. Prabhakar, and S. Chen, Combining Multiple Matchers for a High Security Fingerprint Verification System Pattern Recognition Letters, vol. 20, pp. 1371-1379, 1999.[14] J. Kittler and F. Roli, Multiple Classifier Systems, 2000.[15] G. Lebanon and J. Lafferty, Cranking: Combining Rankings Using Conditional Probability Models on Permutations Machine Learning: Proc. 19th Int'l Conf., 2002.[16] S.M. Lucas, Continuous n-Tuple Classifier and Its Application to Real-Time Face Recognition IEEE Proc. Visual Image and Signal Processing, vol. 145, no. 5, pp. 343-348, 1998.[17] C.L. Mallows, Non-Null Ranking Models Biometrika, vol. 44, pp. 114-130, 1957.[18] G.L. Marcialis and F. Roli, Fusion of PCA and LDA for Face Verification Proc. Post-ECCV Workshop Biometric Authentication (BIOMET 2002), M. Tistarelli, J. Bigun, and A.K. Jain, eds., pp. 30-37, 2002.[19] H. Moon and P.J. Phillips, Computational and Performance Aspects of PCA-Based Face-Recognition Algorithms Perception, vol. 30, pp. 303-321, 2001.[20] P. Penev and J. Atick, Local Feature Analysis: A General Statistical Theory for Object Representations Network: Computation in Neural Systems, pp. 477-500, Mar. 1996.[21] P.J. Phillips, Feret Evaluation, http://www.itl.nist.gov/iad/humanid/feret/ perfeval.html, 2001.[22] P.J. Phillips, H. Moon, and S.A. Rozvi, The FERET Evaluation Methodolody for Face Recognition Algorithms IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1090-1104, Oct. 2000.[23] F. Roli and G. Fumera, Analysis of Linear and Order Statistics Combiners for Fusion of Imbalanced Classifiers Proc. Third. Int'l Workshop Multiple Classifier Systems, 2002.[24] A.S. Tolba and A.N. Abu-Rezq, Combined Classifier for Invariant Face Recognition Pattern Analysis and Applications, vol. 3, no. 4, pp. 289-302, 2000.[25] K. Tumer and J. Ghosh, Robust Combining of Disparate Classifiers through Order Statistics Pattern Analysis and Applications, vol. 5, no. 2, pp. 189-200, 2002.[26] L. Wiskott, J.M. Fellous, N. Kruger, and C. von der Malsburg, Face Recognition by Elastic Bunch Graph Matching IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 775-779, July 1997.[27] L. Xu, A. Krzyzak, and C.Y. Suen, “Methods of Combining Multiple Classifiers and Their Applications to Handwriting Recognition,” IEEE Trans. Systems, Man, and Cybernetics, vol. 22, no. 3, pp. 418-435, 1992.[28] W. Zhao, R. Chellappa, A. Rosenfeld, and P.J. Phillips, Face Recognition: A Literature Survey Technical Report TR4167, Univ. of Maryland, Oct. 2000.[29] W. Zhao, A. Krishnaswamy, R. Chellappa, D. Swets, and J. Weng, Discriminant Analysis of Principal Components Face Recognition: From Theory to Applications, pp. 73-86, Berlin: Springer-Verlag, 1998.
Index Terms:
Classification, classifier combination, ensemble methods, sensor fusion, biometrics, face recognition, mixed group ranks, logistic regression, Borda count, highest rank, voting methods.
Citation:
Ofer Melnik, Yehuda Vardi, Cun-Hui Zhang, "Mixed Group Ranks: Preference and Confidence in Classifier Combination," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 8, pp. 973-981, Aug. 2004, doi:10.1109/TPAMI.2004.48
