Generalized Fuzzy C-Means Clustering Algorithm With Improved Fuzzy Partitions

The fuzziness index m has important influence on the clustering result of fuzzy clustering algorithms, and it should not be forced to fix at the usual value m = 2. In view of its distinctive features in applications and its limitation in having m = 2 only, a recent advance of fuzzy clustering called fuzzy c-means clustering with improved fuzzy partitions (IFP-FCM) is extended in this paper, and a generalized algorithm called GIFP-FCM for more effective clustering is proposed. By introducing a novel membership constraint function, a new objective function is constructed, and furthermore, GIFP-FCM clustering is derived. Meanwhile, from the viewpoints of L p norm distance measure and competitive learning, the robustness and convergence of the proposed algorithm are analyzed. Furthermore, the classical fuzzy c-means algorithm (FCM) and IFP-FCM can be taken as two special cases of the proposed algorithm. Several experimental results including its application to noisy image texture segmentation are presented to demonstrate its average advantage over FCM and IFP-FCM in both clustering and robustness capabilities.

[1]  Jiong Yang,et al.  STING: A Statistical Information Grid Approach to Spatial Data Mining , 1997, VLDB.

[2]  Hans-Peter Kriegel,et al.  OPTICS: ordering points to identify the clustering structure , 1999, SIGMOD '99.

[3]  Wang Shitong,et al.  The Directional Similarity-Based Clustering Method DSCM , 2006 .

[4]  Joydeep Ghosh,et al.  Cluster Ensembles --- A Knowledge Reuse Framework for Combining Multiple Partitions , 2002, J. Mach. Learn. Res..

[5]  Frank Chung-Hoon Rhee,et al.  Uncertain Fuzzy Clustering: Interval Type-2 Fuzzy Approach to $C$-Means , 2007, IEEE Transactions on Fuzzy Systems.

[6]  Jiawei Han,et al.  CLARANS: A Method for Clustering Objects for Spatial Data Mining , 2002, IEEE Trans. Knowl. Data Eng..

[7]  Joydeep Ghosh,et al.  Cluster Ensembles A Knowledge Reuse Framework for Combining Partitionings , 2002, AAAI/IAAI.

[8]  Weixin Xie,et al.  Suppressed fuzzy c-means clustering algorithm , 2003, Pattern Recognit. Lett..

[9]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[10]  Tian Zhang,et al.  BIRCH: A New Data Clustering Algorithm and Its Applications , 1997, Data Mining and Knowledge Discovery.

[11]  Dimitrios Gunopulos,et al.  Automatic subspace clustering of high dimensional data for data mining applications , 1998, SIGMOD '98.

[12]  Jian Yu,et al.  Alpha-Cut Implemented Fuzzy Clustering Algorithms and Switching Regressions , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Korris Fu-Lai Chung,et al.  Fuzzy competitive learning , 1994, Neural Networks.

[14]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[15]  W. T. Tucker,et al.  Convergence theory for fuzzy c-means: Counterexamples and repairs , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Jiong Yang,et al.  An Approach to Active Spatial Data Mining Based on Statistical Information , 2000, IEEE Trans. Knowl. Data Eng..

[17]  Korris Fu-Lai Chung,et al.  Possibility Theoretic Clustering and its Preliminary Application to Large Image Segmentation , 2007, Soft Comput..

[18]  Erkki Oja,et al.  Rival penalized competitive learning for clustering analysis, RBF net, and curve detection , 1993, IEEE Trans. Neural Networks.

[19]  Vipin Kumar,et al.  Chameleon: Hierarchical Clustering Using Dynamic Modeling , 1999, Computer.

[20]  Joni-Kristian Kämäräinen,et al.  Simple Gabor feature space for invariant object recognition , 2004, Pattern Recognit. Lett..

[21]  Aidong Zhang,et al.  WaveCluster: A Multi-Resolution Clustering Approach for Very Large Spatial Databases , 1998, VLDB.

[22]  Frank Klawonn,et al.  Improved fuzzy partitions for fuzzy regression models , 2003, Int. J. Approx. Reason..

[23]  Zhi-Qiang Liu,et al.  Self-splitting competitive learning: a new on-line clustering paradigm , 2002, IEEE Trans. Neural Networks.

[24]  Hong Yan,et al.  Cluster analysis of gene expression data based on self-splitting and merging competitive learning , 2004, IEEE Transactions on Information Technology in Biomedicine.

[25]  Xinbo Gao,et al.  Advances in theory and applications of fuzzy clustering , 2000 .

[26]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[27]  Takenobu Tokunaga,et al.  Hierarchical Bayesian Clustering for Automatic Text Classification , 1995, IJCAI.

[28]  Shitong Wang,et al.  Attribute weighted mercer kernel based fuzzy clustering algorithm for general non-spherical datasets , 2006, Soft Comput..

[29]  Vipin Kumar,et al.  Introduction to Data Mining, (First Edition) , 2005 .

[30]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[31]  Wei Li-mei.  Rival Checked Fuzzy C-Means Algorithm , 2000 .

[32]  Frank Hoeppner,et al.  Fuzzy shell clustering algorithms in image processing: fuzzy C-rectangular and 2-rectangular shells , 1997, IEEE Trans. Fuzzy Syst..

[33]  Frank Klawonn,et al.  A contribution to convergence theory of fuzzy c-means and derivatives , 2003, IEEE Trans. Fuzzy Syst..

[34]  Zhaohong Deng,et al.  Robust maximum entropy clustering algorithm with its labeling for outliers , 2006, Soft Comput..

[35]  Carlos Ordonez,et al.  FREM: fast and robust EM clustering for large data sets , 2002, CIKM '02.

[36]  Jiawei Han,et al.  Efficient and Effective Clustering Methods for Spatial Data Mining , 1994, VLDB.

[37]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.