Approximation and Classification in Medicine with IncNet Neural Networks1

Structure of incremental neural network (IncNet) is controlled by growing and pruning to match the complexity of training data. Extended Kalman Filter algorithm and its fast version is used as learning algorithm. Bi-central transfer functions, more flexible than other functions commonly used in artificial neural networks, are used. The latest improvement added is the ability to rotate the contours of constant values of transfer functions in multidimensional spaces with only N − 1 adaptive parameters. Results on approximation benchmarks and on the real world psychometric classification problem clearly shows superior generalization performance of presented network comparing with other classification models. INTRODUCTION Artificial Neural Networks (ANN) are used to many different kinds of problems such as classification, approximation, pattern recognition, signal processing, prediction, feature extraction, etc. Most of them are solved with ANN by learning of the mapping between the input and output space for given data sets S = {〈x1, y1〉, . . . , 〈xn, yn〉}, where 〈xi, yi〉 is input – output pair (xi ∈ R, yi ∈ R). The underlying mapping F(·) can be written as F(xi) = yi + η, i = 1, . . . , n (1) where η is a zero mean white noise with variance σns. Building a network that preserves information with complexity matched to training data, using an architecture which is able to grow, shrink, and using flexible transfer functions to estimate complex probability density distributions, is the goal of this paper. The best known local learning models are the radial basis function networks (RBF) (Powell, 1987; Poggio and Girosi, 1990; Bishop, 1991), adaptive kernel methods and local risk minimization (Girosi, 1998). The RBF networks were designed as a solution to an approximation problem in multi–dimensional spaces. The typical form of the RBF network can be written as