Fuzzy Kohonen clustering networks for interval data

The Fuzzy Kohonen Clustering Network combines the idea of fuzzy membership values for learning rates. It is a kind of self-organizing fuzzy neural network that can show great superiority in processing the ambiguity and the uncertainty of data sets or images. Symbolic data analysis provides suitable tools for managing aggregated data described by intervals. This paper introduces Fuzzy Kohonen Clustering Networks for partitioning interval data. The first network is based on a fixed Euclidean distance for interval and the second one considers weighted distances that change at each iteration, but are different from one cluster to another. Experiments with real and synthetic interval data sets demonstrate the usefulness of these networks.

[1]  Helge J. Ritter,et al.  Neural computation and self-organizing maps - an introduction , 1992, Computation and neural systems series.

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

[3]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

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

[5]  Partitional clustering algorithms for symbolic interval data based on single adaptive distances , 2009 .

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

[7]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

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

[9]  Teuvo Kohonen,et al.  Self-organization and associative memory: 3rd edition , 1989 .

[10]  M. Cugmas,et al.  On comparing partitions , 2015 .

[11]  Edwin Diday,et al.  An introduction to symbolic data analysis and the SODAS software , 2003, Intell. Data Anal..

[12]  Monique Noirhomme-Fraiture,et al.  Symbolic Data Analysis and the SODAS Software , 2008 .

[13]  James M. Keller,et al.  Fuzzy Models and Algorithms for Pattern Recognition and Image Processing , 1999 .

[14]  Hans-Hermann Bock,et al.  Dynamic clustering for interval data based on L2 distance , 2006, Comput. Stat..

[15]  Francisco de A. T. de Carvalho,et al.  Fuzzy c-means clustering methods for symbolic interval data , 2007, Pattern Recognit. Lett..

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

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

[18]  Yves Lechevallier,et al.  Dynamic Clustering of Interval-Valued Data Based on Adaptive Quadratic Distances , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

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

[20]  Yves Lechevallier,et al.  Dynamical Clustering of Interval Data: Optimization of an Adequacy Criterion Based on Hausdorff Distance , 2002 .

[21]  Balazs Feil,et al.  Cluster Analysis for Data Mining and System Identification , 2007 .

[22]  Thomas Villmann,et al.  Generalized relevance learning vector quantization , 2002, Neural Networks.

[23]  James M. Keller,et al.  Incorporating Fuzzy Membership Functions into the Perceptron Algorithm , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  James C. Bezdek,et al.  Fuzzy Kohonen clustering networks , 1994, Pattern Recognit..

[25]  Thomas Villmann,et al.  Relevance Learning in Unsupervised Vector Quantization Based on Divergences , 2011, WSOM.

[26]  Jan W. Owsiński,et al.  Book reviews: ''Cluster analysis for data mining and system identification'' by János Abonyi and Balázs Feil , 2008 .

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

[28]  Francisco de A. T. de Carvalho,et al.  Fuzzy K-means clustering algorithms for interval-valued data based on adaptive quadratic distances , 2010, Fuzzy Sets Syst..

[29]  Hans-Hermann Bock.  6. Symbolic Data Analysis , 2003 .

[30]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

[31]  Vikas Kumar,et al.  FUZZY NEURAL NETWORKS , 2012 .

[32]  Barbara Hammer,et al.  Local matrix learning in clustering and applications for manifold visualization , 2010, Neural Networks.

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

[34]  Yves Lechevallier,et al.  Partitional clustering algorithms for symbolic interval data based on single adaptive distances , 2009, Pattern Recognit..

[35]  P. Sopp.  Cluster analysis. , 1996, Veterinary immunology and immunopathology.

[36]  Terrance L. Huntsberger,et al.  PARALLEL SELF-ORGANIZING FEATURE MAPS FOR UNSUPERVISED PATTERN RECOGNITION , 1990 .

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

[38]  A. Boudou,et al.  Mercury in the food web: accumulation and transfer mechanisms. , 1997, Metal ions in biological systems.

[39]  Hongxing Li,et al.  Fuzzy Neural Network Theory and Application , 2004, Series in Machine Perception and Artificial Intelligence.

[40]  M. V. Velzen,et al.  Self-organizing maps , 2007 .

[41]  Francisco de A. T. de Carvalho,et al.  Partitional fuzzy clustering methods based on adaptive quadratic distances , 2006, Fuzzy Sets Syst..

[42]  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.

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

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

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

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

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

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

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