Gaussian Collaborative Fuzzy C-Means Clustering

For most FCM-based fuzzy clustering algorithms, several problems, such as noise, non-spherical clusters, and size-imbalanced clusters, are difficult to solve. Different fuzzy clustering algorithms are developed to deal with these problems from different perspectives. However, no comprehensive viewpoint to generalize these problems has been put forward. In this paper, we reveal the inherent deficiency of FCM and propose a new fuzzy clustering method called Gaussian Collaborative Fuzzy C-means (GCFCM) to solve these problems. In GCFCM, Gaussian mixture model (GMM) and collaborative technology are adopted to enhance the ability of recognizing the intrinsic structure of clusters. Experimental results confirm that GCFCM is effective in dealing with noise, non-spherical clusters, size-imbalanced clusters, and those also show excellent performance in dealing with real-world data sets.

[1]  Jitendra Malik,et al.  Normalized Cuts and Image Segmentation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Pritpal Singh,et al.  A Type-2 Fuzzy Clustering and Quantum Optimization Approach for Crops Image Segmentation , 2021, International Journal of Fuzzy Systems.

[3]  Paul S. Bradley,et al.  k-Plane Clustering , 2000, J. Glob. Optim..

[4]  Witold Pedrycz,et al.  Advances in Fuzzy Clustering and its Applications , 2007 .

[5]  Witold Pedrycz,et al.  Rough–Fuzzy Collaborative Clustering , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Anil K. Jain Data clustering: 50 years beyond K-means , 2008, Pattern Recognit. Lett..

[7]  Zexuan Ji,et al.  Interval-valued possibilistic fuzzy C-means clustering algorithm , 2014, Fuzzy Sets Syst..

[8]  Zhaohong Deng,et al.  Transfer Prototype-Based Fuzzy Clustering , 2014, IEEE Transactions on Fuzzy Systems.

[9]  C. L. Philip Chen,et al.  Fuzzy Clustering in Cascaded Feature Space , 2019, International Journal of Fuzzy Systems.

[10]  Frank Chung-Hoon Rhee,et al.  An interval type-2 fuzzy pcm algorithm for pattern recognition , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[11]  Jerry M. Mendel,et al.  Computing derivatives in interval type-2 fuzzy logic systems , 2004, IEEE Transactions on Fuzzy Systems.

[12]  Lida Xu,et al.  A local-density based spatial clustering algorithm with noise , 2007, Inf. Syst..

[13]  Rui-Ping Li,et al.  A maximum-entropy approach to fuzzy clustering , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

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

[15]  Dzung L. Pham,et al.  Spatial Models for Fuzzy Clustering , 2001, Comput. Vis. Image Underst..

[16]  Pengjiang Qian,et al.  Fast Graph-Based Relaxed Clustering for Large Data Sets Using Minimal Enclosing Ball , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Hava T. Siegelmann,et al.  Support Vector Clustering , 2002, J. Mach. Learn. Res..

[18]  Zijiang Yang,et al.  A Fuzzy Subspace Algorithm for Clustering High Dimensional Data , 2006, ADMA.

[19]  Soon-H. Kwon Cluster validity index for fuzzy clustering , 1998 .

[20]  Yuan Zhang,et al.  Fuzzy clustering with the entropy of attribute weights , 2016, Neurocomputing.

[21]  Chenghu Zhou,et al.  DECODE: a new method for discovering clusters of different densities in spatial data , 2009, Data Mining and Knowledge Discovery.

[22]  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.

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

[24]  Jianhong Wu,et al.  Projective ART for clustering data sets in high dimensional spaces , 2002, Neural Networks.

[25]  Jin Liu,et al.  A spatially constrained fuzzy hyper-prototype clustering algorithm , 2012, Pattern Recognit..

[26]  Mohammad Hossein Fazel Zarandi,et al.  Relative entropy fuzzy c-means clustering , 2014, Inf. Sci..

[27]  Michael K. Ng,et al.  Automated variable weighting in k-means type clustering , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

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

[30]  J. Bezdek,et al.  FCM: The fuzzy c-means clustering algorithm , 1984 .

[31]  Witold Pedrycz,et al.  Collaborative clustering with the use of Fuzzy C-Means and its quantification , 2008, Fuzzy Sets Syst..

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

[33]  Sadaaki Miyamoto,et al.  Fuzzy clustering by quadratic regularization , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[34]  Inderjit S. Dhillon,et al.  Kernel k-means: spectral clustering and normalized cuts , 2004, KDD.

[35]  J. Mendel Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[36]  Hans-Peter Kriegel,et al.  Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications , 1998, Data Mining and Knowledge Discovery.

[37]  Mohammad Hossein Fazel Zarandi,et al.  Relative entropy collaborative fuzzy clustering method , 2015, Pattern Recognit..

[38]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[39]  James M. Keller,et al.  A possibilistic fuzzy c-means clustering algorithm , 2005, IEEE Transactions on Fuzzy Systems.

[40]  Douglas A. Reynolds,et al.  Gaussian Mixture Models , 2018, Encyclopedia of Biometrics.

[41]  J. Mendel,et al.  A fundamental decomposition of type-2 fuzzy sets , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[42]  Douglas A. Reynolds Gaussian Mixture Models , 2009, Encyclopedia of Biometrics.

[43]  Ron Shamir,et al.  A clustering algorithm based on graph connectivity , 2000, Inf. Process. Lett..

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

[45]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[46]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

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

[48]  Lin-Yu Tseng,et al.  A genetic approach to the automatic clustering problem , 2001, Pattern Recognit..

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

[50]  Dexin Wang,et al.  A Novel Fuzzy c-Means Clustering Algorithm Using Adaptive Norm , 2019, International Journal of Fuzzy Systems.

[51]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[52]  Daniel A. Keim,et al.  An Efficient Approach to Clustering in Large Multimedia Databases with Noise , 1998, KDD.

[53]  Teuvo Kohonen,et al.  The self-organizing map , 1990 .

[54]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[55]  Witold Pedrycz,et al.  Collaborative fuzzy clustering , 2002, Pattern Recognit. Lett..

[56]  L. Zadeh Is there a need for fuzzy logic , 2008, NAFIPS 2008.