Fuzzy clustering model for asymmetry and self-similarity

This paper shows a method of classification for asymmetric similarity data and non-reflexive data. In a clustering problem in which the similarities of the objects are given by the relation like mobility data which shows relation of proximity from one object to another object, the ordinary fuzzy clustering models are not available. In this paper, these data are treated as asymmetric similarity data including non-reflexive elements which are defined by diagonal elements of the similarity matrix. We define asymmetric aggregation operators to classify objects based on asymmetric similarities. Using the asymmetric aggregation operators, clusters which represent the asymmetric structure between objects are obtained. Moreover, the estimated parameter is introduced to show the non-reflexive data. The validity of this model is shown both by investigating the features of the asymmetric aggregation operators and through numerical applications.

[1]  W. Torgerson.  Multidimensional scaling: I. Theory and method , 1952 .

[2]  Enrique H. Ruspini,et al.  A New Approach to Clustering , 1969, Inf. Control..

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

[4]  L. Hubert.  Min and max hierarchical clustering using asymmetric similarity measures , 1973 .

[5]  Roger N. Shepard,et al.  Additive clustering: Representation of similarities as combinations of discrete overlapping properties. , 1979 .

[6]  W. DeSarbo.  Gennclus: New models for general nonhierarchical clustering analysis , 1982 .

[7]  Robert E. Tarjan.  An Improved Algorithm for Hierarchical Clustering Using Strong Components , 1983, Inf. Process. Lett..

[8]  A. D. Gordon.  A Review of Hierarchical Classification , 1987 .

[9]  M. Mizumoto.  Pictorial representations of fuzzy connectives, part I: cases of t-norms, t-conorms and averaging operators , 1989 .

[10]  Rajesh N. Davé,et al.  Adaptive fuzzy c-shells clustering and detection of ellipses , 1992, IEEE Trans. Neural Networks.

[11]  James C. Bezdek,et al.  A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain , 1992, IEEE Trans. Neural Networks.

[12]  Yoshiharu Sato,et al.  An Additive Fuzzy Clustering Model , 1994 .

[13]  Yoshiharu Sato,et al.  EXTENDED FUZZY CLUSTERING MODELS FOR ASYMMETRIC SIMILARITY , 1995 .

[14]  Yoshiharu Sato,et al.  On A General Fuzzy Additive Clustering Model , 1995, Intell. Autom. Soft Comput..