Generalization

Abstract: A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of the classification functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjusted automatically to match the complexity of the problem. The solution is expressed as a linear combination of supporting patterns. These are the subset of training patterns that are closest to the decision boundary. Bounds on the generalization performance based on the leave-one-out method and the VC-dimension are given. Experimental results on optical character recognition problems demonstrate the good generalization obtained when compared with other learning algorithms.

Abstract: A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

Abstract: Abstract This book provides the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts of pattern recognition, the book describes techniques for modelling probability density functions, and discusses the properties and relative merits of the multi-layer perceptron and radial basis function network models. It also motivates the use of various forms of error functions, and reviews the principal algorithms for error function minimization. As well as providing a detailed discussion of learning and generalization in neural networks, the book also covers the important topics of data processing, feature extraction, and prior knowledge. The book concludes with an extensive treatment of Bayesian techniques and their applications to neural networks.

Abstract: A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a certain sense. As a demonstration of the effectiveness of this approach, results from numerical real-space renormalization-group calculations for Heisenberg chains are presented.