By Iske A , Levesley J (Eds)
ISBN-10: 1402055722
ISBN-13: 9781402055720
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Georgiopoulos: Ellipsoid ART and ARTMAP for incremental unsupervised and supervised learning. In: Proceedings of the IEEEINNS-ENNS International Joint Conference on Neural Networks (IJCNN’01), 2001, 1221–1226. 4. A. Baraldi and E. Alpaydin: Constructive feedforward ART clustering networks - Part I and II. IEEE Transactions on Neural Networks, 2002, 645–677. 5. A. Baraldi and P. Blonda: A survey of fuzzy clustering algorithms for pattern recognition - Part I and II. IEEE Transactions on Systems, Man, And Cybernetics - Part B: Cybernetics, 1999, 778–801.
N }. For each singularity component Ci , we construct a mapping ” Φi (P ) = (Px , Py , hi (P )), i = 1, . . , N, where in the definition of Φi we ignore the other components Cj , j = i, and re˜ gard Ci as a unique singularity component. The resulting mapping Φ : Ω → Ω, ˜ ⊂ R2+N , is defined as Ω ⊂ R2 , Ω Φ(P ) = {Px , Py , h1 (P ), . . , hN (P )} , and is one-to-one and continuous. After the construction of the mapping Φ, we compute the best (N + 2)variate polynomial approximation to f ◦ Φ−1 , in the L2 (Φ(Ω))-norm.
In contrast to hierarchical clustering, partitional clustering assigns a set of objects into a pre-specified K clusters without a hierarchical structure. The principally optimal partition is infeasible in practice, due to the expensive computation [28]. Therefore, heuristic algorithms have been developed in order to seek approximate solutions. One of the important factors in partitional clustering is the criterion function [40], and the sum of squared error function is one of the most widely used, which aims to minimize the cost function.
Algorithms For Approximation Proc, Chester 2005 by Iske A , Levesley J (Eds)
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