Variable Width Rough-Fuzzy c-Means

The richness of soft clustering algorithms in the scientific literature reflects from one side the complexity of the underlying problem and from the other the many attempts that have been made to preserve interpretability while modeling vagueness through different theories. In this paper a hybrid rough-fuzzy unsupervised learning algorithm called Variable Width Rough-Fuzzy c-Means (VWRFCM) is derived from a unifying view of the most popular crisp, fuzzy, rough and fuzzy-rough partitive clustering algorithms. VWRFCM provides a user-defined parameter that sets the width of the core regions of all clusters in a probabilistic sense, allowing the domain experts to have both an intuitive interpretation and a powerful control possibility on the maximum allowed degree of vagueness in the clustering solution. Tests on several real datasets show a good effectiveness together with a speed-up in efficiency of VWRFCM compared to its baseline competitors.

[1]  Salvatore Cuomo,et al.  A Novel Triangle-based Method for Scattered Data Interpolation , 2014 .

[2]  James M. Keller,et al.  A possibilistic fuzzy c-means clustering algorithm , 2005, IEEE Transactions on Fuzzy Systems.

[3]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

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

[5]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[6]  Alessio Ferone,et al.  Decoy clustering through graded possibilistic c-medoids , 2017, 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[7]  Salvatore Cuomo,et al.  Piecewise Hermite interpolation via barycentric coordinates , 2015 .

[8]  Jian Yu,et al.  Partitive clustering (K‐means family) , 2012, WIREs Data Mining Knowl. Discov..

[9]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[10]  Witold Pedrycz,et al.  Rough–Fuzzy Collaborative Clustering , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Francesco Masulli,et al.  Soft transition from probabilistic to possibilistic fuzzy clustering , 2006, IEEE Transactions on Fuzzy Systems.

[12]  Sankar K. Pal,et al.  Rough Set Based Generalized Fuzzy $C$ -Means Algorithm and Quantitative Indices , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Pawan Lingras,et al.  Interval Set Clustering of Web Users with Rough K-Means , 2004, Journal of Intelligent Information Systems.

[14]  A. Asuncion,et al.  UCI Machine Learning Repository, University of California, Irvine, School of Information and Computer Sciences , 2007 .

[15]  Michele Ceccarelli,et al.  A Fuzzy Extension of Some Classical Concordance Measures and an Efficient Algorithm for Their Computation , 2008, KES.

[16]  Alfredo Petrosino,et al.  Feature Selection Through Composition of Rough-Fuzzy Sets , 2016, WILF.

[17]  Sankar K. Pal,et al.  RFCM: A Hybrid Clustering Algorithm Using Rough and Fuzzy Sets , 2007, Fundam. Informaticae.

[18]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[19]  Salvatore Cuomo,et al.  A class of piecewise interpolating functions based on barycentric coordinates , 2014 .

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

[21]  Alfredo Petrosino,et al.  A Rough Fuzzy Perspective to Dimensionality Reduction , 2012, CHDD.