A Fuzzy C-Medoids Clustering Algorithm Based on Multiple Dissimilarity Matrices

This paper gives a relational fuzzy c-medoids clustering algorithm that is able to partition objects taking into account simultaneously several dissimilarity matrices. The aim is to obtain a collaborative role of the different dissimilarity matrices in order to obtain a final consensus partition. These matrices could have been obtained using different sets of variables and dissimilarity functions. This algorithm is designed to give a fuzzy partition and a prototype for each fuzzy cluster as well as to learn a relevance weight for each dissimilarity matrix by optimizing an objective function. These relevance weights change at each algorithm's iteration and are different from one cluster to another. Several examples illustrate the usefulness of the proposed algorithm.

[1]  Hichem Frigui,et al.  Clustering and aggregation of relational data with applications to image database categorization , 2007, Pattern Recognit..

[2]  Guillaume Cleuziou,et al.  CoFKM: A Centralized Method for Multiple-View Clustering , 2009, 2009 Ninth IEEE International Conference on Data Mining.

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

[4]  Marie Chavent,et al.  On Central Tendency and Dispersion Measures for Intervals and Hypercubes , 2008 .

[5]  L. Hubert,et al.  Comparing partitions , 1985 .

[6]  Yves Lechevallier,et al.  Relational partitioning fuzzy clustering algorithms based on multiple dissimilarity matrices , 2013, Fuzzy Sets Syst..

[7]  Rui Xu,et al.  Survey of clustering algorithms , 2005, IEEE Transactions on Neural Networks.

[8]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

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

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

[11]  Peter J. Rousseeuw,et al.  Finding Groups in Data: An Introduction to Cluster Analysis , 1990 .

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

[13]  James C. Bezdek,et al.  Nerf c-means: Non-Euclidean relational fuzzy clustering , 1994, Pattern Recognit..

[14]  Bruno Leclerc,et al.  Consensus en classification : une revue bibliographique , 1987 .

[15]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .