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In this chapter we discuss algorithms for clustering and visualization of large and multivariate data. We describe an algorithm for exploratory data analysis which combines adaptive c-means clustering and multi-dimensional scaling (ACMDS). ACMDS is an algorithm for the online visualization of clustering processes and may be considered as an alternative approach to Kohonen's self organizing feature map (SOM). Whereas SOM is a heuristic neural network algorithm, ACMDS is derived from multivariate statistical algorithms. The implications of ACMMDS are illustrated through five different data sets.

Learning in radial basis function (RBF) networks is the topic of this chapter. Whereas multilayer perceptions (MLP) are typically trained with backpropagation algorithms, starting the training procedure with a random initalization of the MLP's parameterms, an RBF network may be trained in different wyas. We distinguish one-, two-, and three phase learning. A very common learning scheme for RBF networks is two phase learning. Here, the two layers of an RBF network are trained seperately. First the RBF layer is calculated, including the RBF centers and scaling parameters, and then the weights of the output layer are adapted. The RBF centers may be trained through unsupervised or supervised learning procedures utilizing clustering, vector quantization of classification tree algorithms. The output layer of the network is adatped by supervised learning. Numerical experiments of RBF classifiers trained by two phase learning are presented for the classifiication of 3D visual objects and the recognition of hand-written digits. It can be observed that the performance of RBF classifiers trained with two phase learning can be improved through a thrid back propagation-like learning phase of teh RBF network, adapting the whole set of parameters (RBF centers, scaling parameters, and output layer weights) simultaneously. This, we call three phase learning in RBF networks. A practical advantage of two and three phase learning in RBF networks is the possibility to use unlabeled training data for the first training phase. Support vecgtor (SV) learning in RBFnetworks is a special type of one phase learning, where only the output layer wieghts of the RBF network are calculated, and the RBF centers are restricted to be a subset of the training data. Numerical experiments with several classifier schemes including nearest neighbor classifiers, learning vecgtor quantization networks and RBF classifiers trained through two phase, three phase and support vector learning are given. The performance of the RBF classifiers trained through SV learning and three phase learning are superior to the results of two phase learning.

In this chapter we present a 3-D visual object recognition system for an autonomous mobile robot. This object recognition system performs the following three tasks: Object localization in the camera images, feature extraction, and classification of the extracted feature vectors with hierarchical radial basis function (RBF) networks.

Non-invasive risk assessment after myocardial infarction is a major but still unresolved goal in clinical cardiology. Various parameters such as ventricular late potentials, T-wave alternans, and repetitive ventricular extrasystoles have been shown to indicate an increased risk of sudden cardiac death. However, the practical use of these arrhythmic markers into clinical decision making remains difficult. In this chapter we will describe two approaches of risk stratification with RBF networks using high-fidelity ECG recordings. Based on these high-fidelity recordings different aspects of conduction defects are exemplarily investigated. The first utilizes established features derived from signal averaged QRS complexes (heartbeats) and the second investigation centers on capturing morphology changes within the QRS complex.

Kunstliche neuronale Netze haben in den letzten Jahren in vielen Bereichen praktische Anwendung gefunden. Insbesondere in der Mustererkennung bzw. Klassifikation, sowie der Approximation und Interpolation hat sich gezeigt, das sich kunstliche neuronale Netze in sehr naturliche Weise als Erganzung in die klassischen mathematischen und statistischen Verfahren einreihen. Aus theoretischer Sicht werden diese Zusammenhange im Aufsatz von F. Schwenker Kunstliche neuronale Netze: Ein Uberblick uber die theoretischen Grundlagen in diesem Buch beleuchtet.

Das Forschungsgebiet der kunstlichen neuronalen Netze hat sich in den letzten 10 Jahren rasch weiterentwickelt. In diesem Zusammenhang sind eine Vielzahl unterschiedlicher Netzwerkarchitekturen und Lernverfahren vorgeschlagen worden, die wiederum zu Anwendungen in den Bereichen Mustererkennung und Klassifikation, Vorhersage von Zeitreihen, Steuerung und Regelung, Optimierung, Assoziativspeicher, etc. gefuhrt haben. Auch die Forschung zur Theorie neuronaler Netze hat bereits wesentliche Fortschritte erzielen konnen. In den beiden ersten Kapiteln werden wir Neuronenmodelle in kontinuierlicher und diskreter Zeit, sowie allgemeine lokale Lernregeln fur neuronale Netze vorstellen. Insbesondere wird gezeigt, wie man Lernregeln aus Zielfunktionen herleiten kann. Schlieslich werden Lernregeln fur mehrschichtige neuronale Netze und radiale Basisfunktionsnetze hergeleitet und einige Resultate im Zusammenhang mit multivariater Approximationstheorie diskutiert.