A generalized hybrid unsupervised learning algorithm, termed as rough-fuzzy-possibilistic c-means, is proposed in this work. It comprises a judicious integration of the principles of rough sets and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of overlapping partitions. It incorporates both probabilistic and possibilistic memberships simultaneously to avoid the problems of noise sensitivity of fuzzy c-means and the coincident clusters of possibilistic c-means. The concept of crisp lower bound and fuzzy boundary of a class, introduced in rough-fuzzy-possibilistic c-means, enables efficient selection of cluster prototypes. The algorithm is generalized in the sense that all the existing variants of c-means algorithms can be derived from the proposed algorithm as a special case. Several quantitative indices are introduced based on rough sets for evaluating the performance of the proposed c-means algorithm. The effectiveness of the algorithm, along with a comparison with other algorithms, has been demonstrated both qualitatively and quantitatively on a set of real life data sets.

Source Code:

1. Executable code for rough-fuzzy-possibilistic c-means algorithm

Publication:

1. P. Maji and S. K. Pal, Rough Set Based Generalized Fuzzy C-Means Algorithm and Quantitative Indices, IEEE Transactions on System, Man and Cybernetics, Part B, Cybernetics, 37(6), pp. 1529--1540, December 2007.

2. P. Maji and S. K. Pal, RFCM: A Hybrid Clustering Algorithm Using Rough and Fuzzy Sets, Fundamenta Informaticae, 80(4), pp. 475--496, November 2007.

3. P. Maji and S. K. Pal, Maximum Class Separability for Rough-Fuzzy C-Means Based Brain MR Image Segmentation, LNCS Transactions on Rough Sets, IX(LNCS 5390), pp. 114--134, December 2008.