Fuzzy c-means clustering methods for symbolic interval data

This paper presents adaptive and non-adaptive fuzzy c-means clustering methods for partitioning symbolic interval data. The proposed methods furnish a fuzzy partition and prototype for each cluster by optimizing an adequacy criterion based on suitable squared Euclidean distances between vectors of intervals. Moreover, various cluster interpretation tools are introduced. Experiments with real and synthetic data sets show the usefulness of these fuzzy c-means clustering methods and the merit of the cluster interpretation tools.

[1]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[2]  Allan D. Gordon,et al.  An Iterative Relocation Algorithm for Classifying Symbolic Data , 2000 .

[3]  Yves Lechevallier,et al.  Adaptative Hausdorff Distances and Dynamic Clustering of Symbolic Interval Data , 2017 .

[4]  Marie Chavent,et al.  A monothetic clustering method , 1998, Pattern Recognit. Lett..

[5]  Edwin Diday,et al.  Symbolic clustering using a new dissimilarity measure , 1991, Pattern Recognit..

[6]  Hans-Hermann Bock,et al.  Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data , 2000 .

[7]  P. Nagabhushan,et al.  Multivalued type proximity measure and concept of mutual similarity value useful for clustering symbolic patterns , 2004, Pattern Recognit. Lett..

[8]  Martin Schader,et al.  Data Analysis: Scientific Modeling And Practical Application , 2000 .

[9]  Francisco de A. T. de Carvalho,et al.  Clustering of interval data based on city-block distances , 2004, Pattern Recognit. Lett..

[10]  L. Billard,et al.  From the Statistics of Data to the Statistics of Knowledge , 2003 .

[11]  G. W. Milligan,et al.  CLUSTERING VALIDATION: RESULTS AND IMPLICATIONS FOR APPLIED ANALYSES , 1996 .

[12]  K. Chidananda Gowda,et al.  Symbolic clustering using a new similarity measure , 1992, IEEE Trans. Syst. Man Cybern..

[13]  Manabu Ichino,et al.  Generalized Minkowski metrics for mixed feature-type data analysis , 1994, IEEE Trans. Syst. Man Cybern..

[14]  K. Chidananda Gowda,et al.  Divisive clustering of symbolic objects using the concepts of both similarity and dissimilarity , 1995, Pattern Recognit..

[15]  Hans-Hermann Bock CLUSTERING ALGORITHMS AND KOHONEN MAPS FOR SYMBOLIC DATA(Symbolic Data Analysis) , 2003 .

[16]  Miin-Shen Yang,et al.  Fuzzy clustering algorithms for mixed feature variables , 2004, Fuzzy Sets Syst..

[17]  D. S. Guru,et al.  Multivalued type dissimilarity measure and concept of mutual dissimilarity value for clustering symbolic patterns , 2005, Pattern Recognit..

[18]  Mohamed A. Ismail,et al.  Fuzzy clustering for symbolic data , 1998, IEEE Trans. Fuzzy Syst..

[19]  K. Chidananda Gowda,et al.  Agglomerative clustering of symbolic objects using the concepts of both similarity and dissimilarity , 1995, Pattern Recognit. Lett..

[20]  Edwin Diday,et al.  Symbolic Cluster Analysis , 1989 .

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

[22]  K. Chidananda Gowda,et al.  Clustering of symbolic objects using gravitational approach , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[23]  Hans-Hermann Bock,et al.  Classification, Clustering, and Data Analysis , 2002 .

[24]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[25]  Otto Optiz,et al.  Conceptual and Numerical Analysis of Data , 1989 .

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

[27]  G. De Soete,et al.  Clustering and Classification , 2019, Data-Driven Science and Engineering.

[28]  H. Ralambondrainy,et al.  A conceptual version of the K-means algorithm , 1995, Pattern Recognit. Lett..