TY - GEN
T1 - LMI formulation for multiobjective learning in radial basis function neural networks
AU - Moreira, Gladston J.P.
AU - Wanner, Elizabeth F.
AU - Guimarães, Frederico G.
AU - Duczmal, Luiz H.
AU - Takahashi, Ricardo H.C.
PY - 2010/10/14
Y1 - 2010/10/14
N2 - This work presents a Linear Matrix Inequality (LMI) formulation for training Radial Basis Function (RBF) neural networks, considering the context of multiobjective learning. The multiobjective learning approach treats the bias-variance dilemma in neural network modeling as a bi-objective optimization problem: the minimization of the empirical risk measured by the sum of squared error over the training data, and the minimization of the structure complexity measured by the norm of the weight vector. We transform the multiobjective problem into a constrained mono-objective one, using the ε-constraint method. This mono-objective problem can be efficiently solved using an LMI formulation. A procedure for choosing the width parameter of the radial basis functions is also presented. The results show that the proposed methodology provides generalization control and high quality solutions.
AB - This work presents a Linear Matrix Inequality (LMI) formulation for training Radial Basis Function (RBF) neural networks, considering the context of multiobjective learning. The multiobjective learning approach treats the bias-variance dilemma in neural network modeling as a bi-objective optimization problem: the minimization of the empirical risk measured by the sum of squared error over the training data, and the minimization of the structure complexity measured by the norm of the weight vector. We transform the multiobjective problem into a constrained mono-objective one, using the ε-constraint method. This mono-objective problem can be efficiently solved using an LMI formulation. A procedure for choosing the width parameter of the radial basis functions is also presented. The results show that the proposed methodology provides generalization control and high quality solutions.
UR - http://www.scopus.com/inward/record.url?scp=79959406312&partnerID=8YFLogxK
UR - https://ieeexplore.ieee.org/document/5596964
U2 - 10.1109/IJCNN.2010.5596964
DO - 10.1109/IJCNN.2010.5596964
M3 - Conference publication
AN - SCOPUS:79959406312
SN - 9781424469178
T3 - Proceedings of the International Joint Conference on Neural Networks
BT - 2010 IEEE World Congress on Computational Intelligence, WCCI 2010 - 2010 International Joint Conference on Neural Networks, IJCNN 2010
T2 - 2010 6th IEEE World Congress on Computational Intelligence, WCCI 2010 - 2010 International Joint Conference on Neural Networks, IJCNN 2010
Y2 - 18 July 2010 through 23 July 2010
ER -