1.School of Information Engineering, Jiangnan University, Wuxi 214122 2.School of Computer Science and Engineering, Changshu Institute of Technology, Changshu 215500
Abstract A clustering algorithm named Orthogonal Fuzzy k-Plane Clustering (OFKPC) is presented by introducing orthogonal restriction into Fuzzy k-Plane Clustering (FKPC). Similar to KPC and FKPC, OFKPC still uses k group hyperplanes as the prototypes of cluster centers. According to the idea of KPC and FKPC, the hyperplanes are built to distinguish samples in different classes. So the matrices constructed by the normal vectors of these hyperplanes can be used to reduce dimensionality. Experimental results on both artificial and UCI datasets show that OFKPC not only has better clustering results than FKPC but also has the ability of reducing dimensionality.
[1] Webb A R. Statistical Pattern Recognition. 2nd Edition. San Francisco, USA: John Wiley Sons, 2002 [2] Anderberg M R. Cluster Analysis for Applications. New York, USA: Academic Press,1973 [3] de Sá Marques J P. Pattern Recognition Concepts, Methods and Applications. New York, USA: Springer, 2001 [4] Huang Zhexue. A Fast Clustering Algorithm to Cluster Very Large Categorical Data Sets in Data Mining // Proc of the SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery. Tucson, USA, 1997: 146-151 [5] Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms. Norwell, USA: Kluwer Academic Publishers, 1981 [6] Lyer N S, Kandel A, Schneider M. Feature-Based Fuzzy Classification for Interpretation of Mammograms. Fuzzy Sets and Systems, 2000, 114(2): 271-280 [7] Yang M S, Hu Y J, Lin K C, et al. Segmentation Techniques for Tissue Differentiation in MRI of Ophthalmology Using Fuzzy Clustering Algorithm. Journal of Magnetic Resonance Imaging, 2002, 20(2):173-179 [8] Bradley P S, Mangasarian O L. k-Plane Clustering. Journal of Global Optimization, 2000, 16(1): 23-32 [9] Wang Ying, Chen Songcan, Zhang Daoqiang, et al. Fuzzy k-Plane Clustering Algorithm. Pattern Recognition and Artificial Intelligence, 2007, 20(5): 704-710 (in Chinese) (王 颖,陈松灿,张道强,等.模糊k平面聚类算法.模式识别与人工智能, 2007, 20(5): 704-710) [10] Duchene J, Leclercq S. An Optimal Transformation for Discriminant and Principal Component Analysis. IEEE Trans on Pattern Analysis and Machine Intelligence, 1988, 10 (6) : 978-983 [11] Okada T, Tomita S. An Optimal Orthonormal System for Discriminant Analysis. Pattern Recognition,1985, 18(2):139-144 [12] Zhu Lin, Wang Shitong, Pan Yonghui, et al. Improved Fuzzy Partitions for k-Plane Clustering Algorithm and Its Robustness Research. Journal of Electronics and Information Technology, 2008, 30(8): 1923-1927 (in Chinese) (朱 林,王士同,潘永惠,等.k平面聚类算法的模糊改进及其鲁棒性研究.电子与信息学报, 2008, 30(8): 1923-1927) [13] Tao Xiaoyan, Ji Hongbing, Jing Zhihong. Orthogonal Neighborhood Preserving Embedding Algorithm for Face Recognition. Journal of Xidian University, 2008, 35(3): 439-443 (in Chinese) (陶晓燕,姬红兵,景志宏.一种用于人脸识别的正交邻域保护嵌入算法.西安电子科技大学学报, 2008, 35(3): 439-443) [14] Rand W M. Objective Criteria for the Evaluation of Clustering Methods. Journal of the American Statistical Association, 1971, 66(336): 846-850 [15] Steinbach M, Karypis G, Kumar V. A Comparison of Document Clustering Techniques // Proc of the KDD Workshop on Text Mining. Boston, USA, 2000: 109-111 [16] Sammouda R, Sammouda M. Improving the Performance of Hopfield Neural Network to Segment Pathological Liver Color Images. Computer Assisted Radiology and Surgery, 2003, 1256: 232-239 [17] Fukunaga K, Hostetler L. The Estimation of the Gradient of a Density Function, with Applications in Pattern Recognition. Information Theory, 1975, 21(1): 32-40 [18] Cover T W, Hart P E. Nearest Neighbor Pattern Classification. IEEE Trans on Information Theory, 1967, 13(6): 21-27
2011, Vol. 24 
