Applications of Rough Set Based K-Means, Kohonen SOM, GA Clustering

Rough set theory provides an alternative way of representing sets whose exact boundary cannot be described due to incomplete information. Rough sets have been widely used for classification and can be equally beneficial in clustering. The clusters in practical data mining do not necessarily have crisp boundaries. An object may belong to more than one cluster. This paper describes modifications of clustering based on Genetic Algorithms, K-means algorithm, and Kohonen Self-Organizing Maps (SOM). These modifications make it possible to represent clusters as rough sets. Rough clusters are shown to be useful for representing groups of highway sections, Web users, and supermarket customers. The rough clusters are also compared with conventional and fuzzy clusters.

[1]  Hussein A. Abbass,et al.  Heuristics and optimization for knowledge discovery , 2002 .

[2]  Zdzislaw Pawlak,et al.  Rough classification , 1984, Int. J. Hum. Comput. Stud..

[3]  Pawan Lingras,et al.  Clustering Supermarket Customers Using Rough Set Based Kohonen Networks , 2003, ISMIS.

[4]  Maurice K. Wong,et al.  Algorithm AS136: A k-means clustering algorithm. , 1979 .

[5]  Pawan Lingras,et al.  Unsupervised Rough Set Classification Using GAs , 2001, Journal of Intelligent Information Systems.

[6]  Pawan Lingras,et al.  Rough set clustering for Web mining , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[7]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[8]  Yiyu Yao,et al.  Generalization of Rough Sets using Modal Logics , 1996, Intell. Autom. Soft Comput..

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

[10]  Nigel K. L. Pope,et al.  Cluster analysis of marketing data examining on-line shopping orientation: a comparison of k-means and rough clustering approaches , 2002 .

[11]  Satish Sharma,et al.  IMPROVED METHOD OF GROUPING PROVINCEWIDE PERMANENT TRAFFIC COUNTERS , 1981 .

[12]  Shusaku Tsumoto,et al.  Knowledge discovery in clinical databases and evaluation of discovered knowledge in outpatient clinic , 2000, Inf. Sci..

[13]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[14]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[15]  Andrzej Skowron,et al.  New Directions in Rough Sets, Data Mining, and Granular-Soft Computing , 1999, Lecture Notes in Computer Science.

[16]  Arkadiusz Wojna,et al.  Analogy-Based Reasoning in Classifier Construction , 2005, Trans. Rough Sets.

[17]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

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

[19]  Shusaku Tsumoto,et al.  Foundations of Intelligent Systems, 15th International Symposium, ISMIS 2005, Saratoga Springs, NY, USA, May 25-28, 2005, Proceedings , 2005, ISMIS.

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

[21]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[22]  Frederick E. Petry,et al.  Genetic Algorithms , 1992 .

[23]  Pawan Lingras,et al.  Interval set clustering of web users using modified Kohonen self-organizing maps based on the properties of rough sets , 2004, Web Intell. Agent Syst..

[24]  Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

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

[26]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[27]  Rui Yan,et al.  Fuzzy C-Means Clustering of Web Users for Educational Sites , 2003, Canadian Conference on AI.

[28]  Andrzej Skowron,et al.  Information Granules in Distributed Environment , 1999, RSFDGrC.