Unsupervised possibilistic clustering

In fuzzy clustering, the fuzzy c-means (FCM) clustering algorithm is the best known and used method. Since the FCM memberships do not always explain the degrees of belonging for the data well, Krishnapuram and Keller proposed a possibilistic approach to clustering to correct this weakness of FCM. However, the performance of Krishnapuram and Keller's approach depends heavily on the parameters. In this paper, we propose another possibilistic clustering algorithm (PCA) which is based on the FCM objective function, the partition coefficient (PC) and partition entropy (PE) validity indexes. The resulting membership becomes the exponential function, so that it is robust to noise and outliers. The parameters in PCA can be easily handled. Also, the PCA objective function can be considered as a potential function, or a mountain function, so that the prototypes of PCA can be correspondent to the peaks of the estimated function. To validate the clustering results obtained through a PCA, we generalized the validity indexes of FCM. This generalization makes each validity index workable in both fuzzy and possibilistic clustering models. By combining these generalized validity indexes, an unsupervised possibilistic clustering is proposed. Some numerical examples and real data implementation on the basis of the proposed PCA and generalized validity indexes show their effectiveness and accuracy.

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

[2]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[3]  Gerardo Beni,et al.  A Validity Measure for Fuzzy Clustering , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Miin-Shen Yang,et al.  Alternative c-means clustering algorithms , 2002, Pattern Recognit..

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

[6]  James M. Keller,et al.  The possibilistic C-means algorithm: insights and recommendations , 1996, IEEE Trans. Fuzzy Syst..

[7]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[8]  Y. Fukuyama,et al.  A new method of choosing the number of clusters for the fuzzy c-mean method , 1989 .

[9]  J. Bezdek Numerical taxonomy with fuzzy sets , 1974 .

[10]  J. Bezdek Cluster Validity with Fuzzy Sets , 1973 .

[11]  Mauro Barni,et al.  Comments on "A possibilistic approach to clustering" , 1996, IEEE Trans. Fuzzy Syst..

[12]  Miin-Shen Yang A survey of fuzzy clustering , 1993 .

[13]  Hichem Frigui,et al.  Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation. II , 1995, IEEE Trans. Fuzzy Syst..

[14]  R. Yager,et al.  Approximate Clustering Via the Mountain Method , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[15]  James M. Keller,et al.  Will the real iris data please stand up? , 1999, IEEE Trans. Fuzzy Syst..

[16]  V. J. Rayward-Smith,et al.  Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition , 1999 .

[17]  KrishnapuramR.,et al.  The possibilistic C-means algorithm , 1996 .

[18]  Thomas A. Runkler,et al.  Alternating cluster estimation: a new tool for clustering and function approximation , 1999, IEEE Trans. Fuzzy Syst..

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

[20]  Noureddine Zahid,et al.  A new cluster-validity for fuzzy clustering , 1999, Pattern Recognit..

[21]  Isak Gath,et al.  Unsupervised Optimal Fuzzy Clustering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

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

[23]  Thomas A. Runkler,et al.  Function approximation with polynomial membership functions and alternating cluster estimation , 1999, Fuzzy Sets Syst..

[24]  James C. Bezdek,et al.  On cluster validity for the fuzzy c-means model , 1995, IEEE Trans. Fuzzy Syst..