Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

Gaussian Artmap: A Neural Network for Fast Incremental Learning of Noisy Multidimensional Maps

A new neural network architecture for incremental supervised learning of analalog multidimensional maps is introduced. The architecture, called Gaussian ARTMAP, is a synthesis of a Gaussian classifier and an Adaptive Resonance Theory (ART) neural network, achieved by defining the ART choice function as the discriminant function of a Gaussian classifer with separable distributions, and the ART match function as the same, but with the a priori probabilities of the distributions discounted. While Gaussian ARTMAP retains the attractive parallel computing and fast learning properties of fuzzy ARTMAP, it learns a more efficient internal representation of a mapping while being more resistant to noise than fuzzy ARTMAP on a number of benchmark databases. Several simulations are presented which demonstrate that Gaussian ARTMAP consistently obtains a better trade-off of classification rate to number of categories than fuzzy ARTMAP. Results on a vowel classiflcation problem are also presented which demonstrate that Gaussian ARTMAP outperforms many other classifiers.National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-92-J-4015, 40014-91-J-4100