Function approximation using generalized adalines

This paper proposes neural organization of generalized adalines (gadalines) for data driven function approximation. By generalizing the threshold function of adalines, we achieve the K-state transfer function of gadalines which responds a unitary vector of K binary values to the projection of a predictor on a receptive field. A generative component that uses the K-state activation of a gadaline to trigger K posterior independent normal variables is employed to emulate stochastic predictor-oriented target generation. The fitness of a generative component to a set of paired data mathematically translates to a mixed integer and linear programming. Since consisting of continuous and discrete variables, the mathematical framework is resolved by a hybrid of the mean field annealing and gradient descent methods. Following the leave-one-out learning strategy, the obtained learning method is extended for optimizing multiple generative components. The learning result leads to parameters of a deterministic gadaline network for function approximation. Numerical simulations further test the proposed learning method with paired data oriented from a variety of target functions. The result shows that the proposed learning method outperforms the MLP and RBF learning methods for data driven function approximation.