Keywords
algorithm
fuzzy cluster
minimization
variance accounted for
partición bimodal
algoritmo
clase difusa
minimizar
varianza explicada
How to Cite
Abstract
It is presented a new fuzzy partitioning criterion for two-mode data and an algorithm is formulated for its optmization. We study the convergence properties of the method. The method was tested on real data. It is deduced that better results can be obtained with this new method than with other methods.
References
Baier, D.; Gaul, W.; Schader, M. (1997) “Two-mode overlapping clustering with applications to simultaneous benefit segmentation and market structuring”, in: R. Klar & O. Opitz (Eds.), Classification and Knowledge Organization. Springer, Heidelberg, 557–566.
Bezdek, J.C. (1980) “A convergence theorem for the fuzzy ISODATA clustering algorithms”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2(1): 1–8.
Bezdek, J.C. (1981) Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York and London.
Bezdek, J.C.; Hathaway, R.J.; Sabin, M.J.; Tucker, W.T. (1987) “Convergence theory for fuzzy c-means: counterexamples and repairs”, IEEE Transactions on Systems, Man and Cybernetics, 17(5): 873–877.
Bock, H.H. (1979) “Fuzzy clustering procedures”, in: R. Tomassone (Ed.) Analyse des Données et Informatique, INRIA, Paris: 205–218.
Castillo, W. (1999) Métodos de Particionamiento Bimodal y Trimodal. Tesis de Maestría, Universidad de Costa Rica.
Eckes, T.; Orlik, P. (1993) “An error variance approach to two-mode hierarchical clustering”, Journal of Classification 10, 51-74.
Gaul, W.; Schader, M. (1996) “A new algorithm for two-mode clustering”, in: H.H. Bock & W. Polasek (Eds.) Data Analysis and Information Systems. Springer, Heidelberg, 15–23.
Groenen, P.J.F.; Jajuga, K. (2001) “Fuzzy clustering with squared Minkowski distances”, Fuzzy Sets and Systems 120(2): 227–237.
Groenen, P.J.F.; Rosmalen, J. van; Trejos, J.; Castillo, W. (2009) “Optimization strategies for two-mode partitioning”, aceptado en Journal of Classification.
Mirkin, B.G.; Arabie, P.; Hubert, L.J. (1995) “Additive two-mode clustering: the error-variance approach revisited”, Journal of Classification 12(2): 243–263.
Roberts, A.W.; Varberg, D.E. (1973) Convex Functions. Academic Press, New York.
Trejos, J.; Castillo, W. (2000) “Simulated annealing optimization for two-mode partitioning”, in: W. Gaul & R. Decker (Eds.) Classification and Information at the Turn of the Millenium. Springer-Verlag, Berlin: 133–142.