Enhanced fuzzy partitions vs data randomness in FCM

IFP-FIM and GIFP-FCM are two typical enhanced fuzzy clustering algorithms in which the rationale of fuzzy clustering and its robustness to noise and/or outliers are enhanced by making the maximal fuzzy membership of each data point belonging to a cluster become as big as possible and other fuzzy memberships of this point belonging to all other clusters become as small as possible. In this study, a new finding will be revealed that their enhanced fuzzy partitions can be equivalently achieved by factitiously disturbing the given dataset using a random noise and then applying the proposed noise-resistant fuzzy clustering algorithm NR-FCM to the dataset with factitiously added random noise. NR-FCM is designed as an intermediate step for us to observe this finding. The virtue of this finding exists in that it indeed helps us witness from an alternative perspective that fuzziness of fuzzy partitions in fuzzy clustering and data randomness can be collaborative and even mutually transformable rather than competitive. Our several experimental results verify the above claim.

[1]  Henri Prade,et al.  Fuzzy sets and probability: misunderstandings, bridges and gaps , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

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

[3]  Korris Fu-Lai Chung,et al.  Note on the equivalence relationship between Renyi-entropy based and Tsallis-entropy based image thresholding , 2005, Pattern Recognit. Lett..

[4]  Hui Xiong,et al.  A Generalization of Distance Functions for Fuzzy $c$ -Means Clustering With Centroids of Arithmetic Means , 2012, IEEE Transactions on Fuzzy Systems.

[5]  Sanjay Ranka,et al.  Gene expression Distance-based clustering of CGH data , 2006 .

[6]  Korris Fu-Lai Chung,et al.  Generalized Fuzzy C-Means Clustering Algorithm With Improved Fuzzy Partitions , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Zhaohong Deng,et al.  EEW-SC: Enhanced Entropy-Weighting Subspace Clustering for high dimensional gene expression data clustering analysis , 2011, Appl. Soft Comput..

[8]  Palma Blonda,et al.  A survey of fuzzy clustering algorithms for pattern recognition. I , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[9]  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.

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

[11]  Umi Kalthum Ngah,et al.  Adaptive fuzzy moving K-means clustering algorithm for image segmentation , 2009, IEEE Transactions on Consumer Electronics.

[12]  Francesco Masulli,et al.  Soft transition from probabilistic to possibilistic fuzzy clustering , 2006, IEEE Transactions on Fuzzy Systems.

[13]  Michael K. Ng,et al.  An Entropy Weighting k-Means Algorithm for Subspace Clustering of High-Dimensional Sparse Data , 2007, IEEE Transactions on Knowledge and Data Engineering.

[14]  James C. Bezdek,et al.  Optimal Fuzzy Partitions: A Heuristic for Estimating the Parameters in a Mixture of Normal Distributions , 1975, IEEE Transactions on Computers.

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

[16]  Rajesh N. Davé,et al.  Characterization and detection of noise in clustering , 1991, Pattern Recognit. Lett..

[17]  Usman Qamar,et al.  A dissimilarity measure based Fuzzy c-means (FCM) clustering algorithm , 2014, J. Intell. Fuzzy Syst..

[18]  Zhaohong Deng,et al.  Fuzzy partition based soft subspace clustering and its applications in high dimensional data , 2013, Inf. Sci..

[19]  Brian Everitt,et al.  Cluster analysis , 1974 .

[20]  Marimuthu Palaniswami,et al.  Fuzzy c-Means Algorithms for Very Large Data , 2012, IEEE Transactions on Fuzzy Systems.

[21]  Korris Fu-Lai Chung,et al.  Note on the relationship between probabilistic and fuzzy clustering , 2004, Soft Comput..

[22]  Zhaohong Deng,et al.  Knowledge-Leverage-Based TSK Fuzzy System Modeling , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Witold Pedrycz,et al.  Collaborative Fuzzy Clustering Algorithms: Some Refinements and Design Guidelines , 2012, IEEE Transactions on Fuzzy Systems.

[24]  Shi Zhong,et al.  A Comparative Study of Generative Models for Document Clustering , 2003 .

[25]  Yung-Yu Chuang,et al.  Multiple Kernel Fuzzy Clustering , 2012, IEEE Transactions on Fuzzy Systems.

[26]  Zhaohong Deng,et al.  Enhanced soft subspace clustering integrating within-cluster and between-cluster information , 2010, Pattern Recognit..

[27]  Jian Yu,et al.  Optimality test for generalized FCM and its application to parameter selection , 2005, IEEE Transactions on Fuzzy Systems.

[28]  Yu-Ping Wang,et al.  Segmentation of M-FISH Images for Improved Classification of Chromosomes With an Adaptive Fuzzy C-means Clustering Algorithm , 2012, IEEE Transactions on Fuzzy Systems.

[29]  Hadi Sadoghi Yazdi,et al.  Fuzzy clustering algorithm for fuzzy data based on α-cuts , 2013, J. Intell. Fuzzy Syst..

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

[31]  Guoqiang Chen,et al.  SVM Combined with FCM and PSO for Fuzzy Clustering , 2011, 2011 Seventh International Conference on Computational Intelligence and Security.

[32]  Jian Yu,et al.  Analysis of the weighting exponent in the FCM , 2004, IEEE Trans. Syst. Man Cybern. Part B.