CEC Theses and Dissertations

Title

Contributions to Supervised Learning of Real-Valued Functions Using Neural Networks

Date of Award

1998

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Graduate School of Computer and Information Sciences

Advisor

W. Shane Bruce

Committee Member

S. Rollins Guild

Committee Member

Junping Sun

Abstract

This dissertation presents a new strategy for the automatic design of neural networks. The learning environment addressed is supervised learning from examples. Specifically, Radial Basis Functions (RBF) networks learning real-valued functions of real vectors as in non-linear regression applications are considered. The strategy is based upon the application of strong theoretical relationships between RBF networks and methods from approximation theory, robust statistics, and computational learning theory.

The complexity of the network design is examined in detail from the formal definition of the learning problem to the establishment of the corresponding optimization problem. A novel strategy for the systematic and automatic design of RBF networks is developed based upon the coordinated evaluation of memorization and generalization of an incremental architecture.

The architecture grows according to the monotonous increase of its generalization. Its corresponding learning method stands out due to its fast convergence and robustness. It represents one of the few learning methods whose computational complexity is precisely stated. It can be used in any non-linear regression tasks which are common in different disciplines of the natural and engineering sciences.

Four learning methods are implemented for evaluation. The most complex is the one for the novel self-generating network architecture. Another learning method constitutes a strong contribution to the area of robust learning allowing the automatic detection of data outliers and the removal of their negative influence in the network approximation. It represents the first robust learning method for RBF networks available in the literature and is integrated into the overall strategy introduced in this work. Diverse functions are used to simulate training and test data. Data generated for evaluation is: noise-free, noisy, and with outliers as well as one- and multidimensional.

The data with outliers allows the verification of the robustness of the introduced method. In addition, an evaluation example from the area of sensory data processing is chosen. This example consists in localizing a generic object based on range information in the framework of a grasping strategy. The relation to other works and a perspective for further research concludes this work.

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