Treinamento multiobjetivo de perceptron de múltiplas camadas comrepresentação esférica de pesos

Abstract

This work presents a novel representation of artificial neural networks(ANN) multiobjective learning in which the weights are described basedon the Euclidean norm, which is taken as a measure of model complexity. Weights are projected into a new space defined by a radius r and a vector of angles. This spherical representation further simplifies the multi-objective learning problem whose estimated Paretooptimalset is obtained in classical approaches by the e-constrained method, minimizing error with multiple constrained values of norm. The corresponding constrained optimization problem is transformed into unconstrained ones, what simplifies formulation and computationalefforts, besides allowing that any nonlinear optimization method could be used to train the ANN. Results indicate that the proposed spherical weights representation yields more accurate estimates of the Pareto set when compared to the classical multi-objective approach. Regarding the final solution taken from the Pareto set, our approach showed effectiveness, outperforming some state-of-the-art methods in several datasets based on Friedman's test.