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X(n) of the observation x to be classified in the training data set. These are given as w x, x(i) = W x(i) − x dn (x) (5) for i = 1, . . , n, with W representing a kernel function. The Euclidean distance dn (x) = x(n) − x to the farthest neighbor x(n) denotes the kernel width. The obtained weights are locally adaptive in the sense that they depend on the Euclidean distances of x and the training observations x(i) . Various kernel functions can be used. For the simulation study we choose the kernel WJ (y) = exp(−Jy) that was found to be robust against varying data characteristics by Czogiel et al.

For classification we used the L2–SVM with radial– basis Kernel function and a Neural Network with one hidden layer, both with the one–against–rest and the all–pairs approach. In every binary decision a separate 3– fold cross–validation grid search was used to find optimal parameters. The results of the analyzes with 10–fold cross–validation for calibrating L2–SVM and ANN are presented in Tables 1–2, respectively. Table 1 shows that for L2–SVM no overall best calibration method is available. For the Iris data set all–pairs with mapping outperforms the other methods, while for B3 the Dirichlet calibration and the all–pairs method without any calibration are performing best.

2. One the 50 histological features: Concentric arrangement. The tumor cells build concentric formations with different diameters. 2 Algorithms We chose LVQ (Kohonen (1995)), SRNG (Villmann et al. (2002)) and SVM (Vapnik (1995)) to classify this high dimensional data set, because the generalization error (expectation value of misclassification) of these algorithms does not depend on the dimension of the feature space (Barlett and Mendelson (2002), Crammer et al. (2003), Hammer et al. (2005)). For the computations we used the original LVQ-PAK (Kohonen et al.