Ensemble of Rough RBF Neural Networks for Pattern Recognition
XIAO Di1, HU Shou-Song2
1.College of Automation, Nanjing University of Technology, Nanjing 2100092. College of Automation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016
Abstract:A method of defining attribute importance is presented. In this method, the distance between samples can be measured to determine the training set clustering. The combination of two radial basis-function (RBF) neural networks for pattern recognition is proposed. The two RBF neural networks have different radial centers and they come from lower approximation and upper approximation of the clustering sets respectively. The designed rough approximation sets can solve the problem on uncertain clustering. Then, the two networks are combined under the experience risk minimum criterion. Thus, the different belief weights for outputs of neurons and the last neural networks output are determined. Finally, the simulation results of pattern recognition on UCI database show the proposed method is valid and effective.
[1] Kagan T, Joydeep G. Robust Combining of Disparate Classifiers through Order Statistics. Pattern Analysis and Application, 2002, 5(2): 189-200 [2] Granitto P M, Verdes P F, Ceccatto H A. Neural Network Ensembles: Evaluation of Aggregation Algorithms. Artificial Intelligence, 2005, 163(2): 139-162 [3] Lee D S, Srihari S N. A Theory of Classifier Combination: The Neural Network Approach // Proc of the 3rd International Conference on Document Analysis and Recognition. Montreal, Canada, 1995, Ⅰ: 42-45 [4] Krasnopolsky V M. Reducing Uncertainties in Neural Network Jacobians and Improving Accuracy of Neural Network Emulations with NN Ensemble Approaches. Neural Networks, 2007, 20(4): 454-461 [5] Ueda N. Optimal Linear Combination of Neural Networks for Improving Classification Performance. IEEE Trans on Pattern Analysis and Machine Intelligence, 2000, 22(2): 207-215 [6] Hashem S. Optimal Linear Combinations of Neural Networks. Neural Networks, 1997, 10(4): 599-614 [7] Alexandridis A, Sarimveis H, Bafas G. A New Algorithm for Online Structure and Parameter Adaptation of RBF Networks. Neural Networks, 2003, 16(7): 1003-1017 [8] de Castro L N, Zuben F J V. Automatic Determination of Radial Basis Functions: An Immunity-Based Approach. International Journal of Neural Systems, 2001, 11(6): 523-535 [9] Liu Qing. Rough Set and Rough Reasoning. Beijing, China: Science Press, 2001 (in Chinese) (刘 清.Rough集与Rough推理.北京:科学出版社, 2001) [10] Bandyopadhyay S, Saha S. GAPS: A Clustering Method Using a New Point Symmetry-Based Distance Measure. Pattern Recognition, 2007, 40(12): 3430-3451 [11] Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356 [12] Bian Zhaoqi, Zhang Xuegong. Pattern Recognition. 2nd Edition. Beijing, China: Tshinghua University Press, 2000 (in Chinese) (边肇祺,张学工.模式识别.第2版.北京:清华大学出版社, 2000) [13] Haddadnia J, Faez K, Ahmadi M. A Fuzzy Hybrid Learning Algorithm for Radial Basis Function Neural Network with Application in Human Face Recognition. Pattern Recognition, 2003, 36(5): 1187-1202 [14] Xiao Di, Hu Shousong. Real Rough Set Theory and Attribute Reduction. Acta Automatica Sinica, 2007, 33(3): 253-258 (in Chinese) (肖 迪,胡寿松.实域粗糙集理论及属性约简.自动化学报, 2007, 33(3): 253-258)