Abstract - Ungar Radial Basis Functions (RBFs) are a class of artificial neural networks for process control applications. Commonly, the k-Means clustering algorithm is applied to the predictor ( independent variables), after which a linear regression layer maps the hidden unit activations to the appropriate responses (dependent variables). The PIs plan to explore an RBF architecture which is suited to statistical analysis. The statistical model underlying the architecture is a mixture model in which the mixture coefficients are radial basis functions and the mixture components are constant or polynomial functions. Depending on the assumptions used to generate the model, different generalizations of radial and elliptical basis functions result. This allows the use of the expectation maximization (EM) technique for finding maximum likelihood estimators of the parameters. In addition, algorithms will be developed to partially invert the networks, estimate the local prediction error of the network, recognize novel data points, automatically select the number of basis functions, and incrementally update the network efficiently as data are collected. The techniques will be tested on real data from chemical plants, compared to other approximation methods with respect to speed and accuracy, and modified as needed to achieve fast, accurate, and robust performance. This is a coordinated project between two investigators, a mathematician and a chemical engineer, at two different institutions. Industrial data are to be provided by the DuPont Company.
