Ranked layers of binary classifiers are used for the linearization of learning sets composed of multivariate feature vectors. After transformation by ranked layer, each learning set can be separated by a hyperplane from the sum of other learning sets. Ranked layers can be designed, among others, from radial binary classifiers. This work elaborates on designing ranked layers from radial binary classifiers with movable centers.

The design of piecewise-linear classifiers from formal neurons is considered. The design classifiers are based on hierarchical, multilayer neural networks. The described procedure allows to find both the structure of network (the numbers of layers and neurons) and weights of single neurons. The main principle of the synthesis procedure is to preserve separability of learning sets during data compression by successive neural layers. Different procedures aiming at improving the network compression ability are also considered.

Window training, based on an extended form of stochastic approximation, offers a means of producing linear classifiers that minimize the probability of misclassification of statistically generated data. Associated with window training is a window criterion function. We show that minimizing the window criterion function yields a linear classifier that minimizes the probability of misclassification (i.e., the "error rate"). However window training may produce a local minimum that exceeds the global minimum error rate. We show that this defect does not occur in the error-correcting perceptron. The criterion minimized by that training procedure is "convex"; i.e., the perceptron criterion has only one local minimum. Consequently we recommend that window training be preceded by perceptron training, the perceptron training producing a decision surface which the window training process will move to a position that is likely to be globally optimum.>

Window training, based on an extended form of stochastic approximation, offers a means of producing linear classifiers that minimize the probability of misclassification of statistically generated data. However, window training may produce a local minimum that exceeds the global minimum error rate. To overcome this defect it is useful to precede window training by perceptron training. When a significantly large set of exemplars of the data is available at the beginning of the training process, the basic exchange algorithm offers a computationally convenient alternative to the window training algorithm to achieve a locally minimum error rate.

An extension of the hard and fuzzy c-means (HCM/FCM) clustering algorithms is described. Specifically, these models are extended to admit the case where the (dis)similarity measure on pairs of numerical vectors includes two members of the Minkowski or p-norm family, viz., the p=1 and p= infinity norms. In the absence of theoretically necessary conditions to guide a numerical solution of the nonlinear constrained optimization problem associated with this case, it is shown that a certain basis exchange algorithm can be used to find approximate critical points of the new objective functions. This method broadens the applications horizon of the FCM family by enabling users to match discontinuous multidimensional numerical data structures with similarity measures that have nonhyperelliptical topologies.>

The homogeneity coefficient Phi /sup *//sub k/, described is an L/sub 1/-type criterion that can be used in measuring the degree of linear dependence among some measurements. Properties of the criterion Phi /sup *//sub k/ are analyzed. A feature selection procedure based on the coefficient Phi /sup *//sub k/ is described. Maps based on both the perception-criterion function and the homogeneity coefficients are used in the interactive computer system of diagnosis support, Hepar. This system is presently implemented on IBM PC and is to be used in the Clinic Gastroenterology in Warsaw.>