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Classifier Design Method Based on Piecewise Linearization |
WANG Qi, WANG Zeng-Fu |
Department of Automation, University of Science and Technology of China, Hefei 230027 |
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Abstract The minimax risk criterion based decision is an important method for making decisions when priori probabilities are unknown. However, the performance of a minimax risk criterion based classifier is poor in most cases. To improve the performance of the designed classifier, a piecewise linearization based design method is presented. Firstly, the proposed method makes a rough estimation of the prior probability. Then, it decides the right interval where the estimated prior lies. Finally, the corresponding classifier is employed to make a decision. The theoretical deduction and experimental results show that the presented method is efficient and the performance of the corresponding classifier designed by the method approaches to Bayesian classifier.
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Received: 02 April 2007
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[1] Wald A. Statistical Decision Functions Which Minimize the Maximum Risk. The Annals of Mathematics, 1945, 46(2): 265-280 [2] Berger J O. Minimax Estimation of a Multivariate Normal Mean under Arbitrary Quadratic Loss. Journal of Multivariate Analysis, 1976, 6(2): 256-264 [3] Berger J O. Selecting a Minimax Estimator of a Multivariate Normal Mean. The Annals of Statistics. 1982, 10(1): 81-92 [4] Efron B, Morris C. Families of Minimax Estimators of the Mean of a Multivariate Normal Distribution. The Annals of Statistics, 1976, 4(1): 11-21 [5] Fukunaga K. Introduction to Statistical Pattern Recognition. Boston, USA: Academic Press, 1990 [6] Duda R O, Hart P E, Stork D G. Pattern Classification. 2nd Edition. London, UK: Wiley & Sons, 2001 [7] Neyman J, Pearson E S. On the Problem of the Most Efficient Tests of Statistical Hypotheses. Philosophical Transactions of the Royal Society of London, Series A: Containing Papers of a Mathematical or Physical Character, 1928, 231: 289-337 [8] Boser B E, Guyon I, Vapnik V. A Training Algorithm for Optimal Margin Classifiers // Proc of the 5th Annual Workshop on Computational Learning Theory. Pittsburgh, USA, 1992: 144-152 [9] Schlkopf B, Burges C J C, Vapnik V. Extracting Support Data for a Given Task // Proc of the 1st International Conference on Knowledge Discovery and Data Mining. Menlo Park, USA, 1995: 252-257 [10] Yao Y Y, Yao J T. Induction of Classification Rules by Granular Computing // Proc of the 3rd International Conference on Rough Sets and Current Trends in Computing. Malvern, USA, 2002: 331-338 [11] Parpinelli R S, Lopes H S, Freitas A A. Data Mining with an Ant Colony Optimization Algorithm. IEEE Trans on Evolutionary Computation, 2002, 6(4): 321-332 [12] Parpinelli R S, Lopes H S , Freitas A A. Mining Comprehensible Rules from Data with an Ant Colony Algorithm // Proc of the 16th Brazilian Symposium on Artificial Intelligence. Porto de Galinhas, Brazil, 2002: 259-269 [13] Liu B, Hsu W, Ma Y. Integrating Classification and Association Rule Mining // Proc of the 4th International Conference on Knowledge Discovery and Data Mining. New York, USA: 1998: 80-86 [14] Wang Ke, Zhou Senqiang, He Yu. Growing Decision Tree on Support-Less Association Rules // Proc of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. Boston, USA, 2000: 265-269 [15] Wang Hui , Dubitzky W, Düntsch I, et al. A Lattice Machine Approach to Automated Casebase Design: Marrying Lazy and Eager Learning // Proc of the 16th International Joint Conference on Artificial Intelligence. Stockholm, Sweden, 1999: 254-259 [16] Breiman L. Bagging Predictors. Machine Learning, 1996, 24(2): 123-140 [17] Zhuang Zhaowen, Guo Guirong, Ke Youan. Minimax Approach to Radar Target Identification in Frequency Domain. Journal of National University of Defense Technology, 1993, 15(3): 58-64 (in Chinese) (庄钊文,郭桂蓉,柯有安.雷达目标识别的频域极小极大法.国防科技大学学报, 1993, 15(3): 58-64) [18] Rocío A R, Alicia G C, Jesús C S. Minimax Classifiers Based on Neural Networks. Pattern Recognition, 2005, 38(1): 29-39 [19] Chen Y K, Chang H H, Chiu F R. Optimization Design of Control Charts Based on Minimax Decision Criterion and Fuzzy Process Shifts. Expert Systems with Applications, 2008, 35(1/2): 207-213 [20] Fahidy T Z. Some Applications of Decision Theory to Electrochemical Processes. Electrochimica Acta, 1999, 44(20): 3559-3564 [21] Fahidy T Z. A Sensitivity Analysis of Minimax Strategies in Decision Theory Applied to Electrochemical Processes. Electrochimica Acta, 2002, 47(28): 4441-4449 [22] Vos H J. Contributions of Minimax Theory to Instructional Decision Making in Intelligent Tutoring Systems. Computers in Human Behavior, 1999, 15(5): 531-548 [23] Machine Learning Repository [DB/OL]. [2008-02-03]. http://archive.ics.uci.edu/me/ |
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