By Rudenskaya O.G.

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Consequently, computing resources may be wasted in that some initial centroids get stuck in regions of the input space with a scarcity of data points and may therefore never have the chance to move to new locations where they are needed. To overcome this limitation of the c-means algorithm, next a method is described to select initial centroids, which is based on discriminant analysis maximizing some measures of class separability (Otsu, 1979). It enables the algorithm to converge to an optimum or near optimum solutions (Maji and Pal, 2008).

Considering the convention 0 logβ 0 = 0, let us now discuss the L E properties of HR (A, B) and HR (A, B) along the lines of (Ebanks, 1983). L E P1. Nonnegativity: We have HR (A, B) ≥ 0 and HR (A, B) ≥ 0 with equality in both the cases if and only if A = 0 and B = 0. E P2. Continuity: As all first-order partial and total derivatives of HR (A, B) exists E for A, B ∈ [0, 1], HR (A, B) is a continuous function of A and B. On the other L hand, all first-order partial and total derivatives of HR (A, B) exists only for L A, B ∈ (0, 1].

This work was done when S. K. Pal was a Govt. C. Bose Fellow. Rough-Fuzzy Clustering Algorithm for Segmentation of Brain MR Images Bibliography Banerjee, Mohua, Sushmita Mitra, and Sankar K Pal. 1998. Rough Fuzzy MLP: Knowledge Encoding and Classification. IEEE Transactions on Neural Networks 9(6): 1203–1216. , V. Cappellini, and A. Mecocci. 1996. Comments on A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems 4(3):393–396. Bezdek, J. C. 1981. Pattern Recognition with Fuzzy Objective Function Algorithm.

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