MultiLogistic Regression using Initial and Radial Basis Function covariates

This paper proposes a hybrid multilogistic model, named multilogistic regression using initial and radial basis function covariates (MLRIRBF). The process for obtaining the coefficients is carried out in several steps. First, an evolutionary programming (EP) algorithm is applied, aimed to produce a RBF neural network (RBFNN) with a reduced number of RBF transformations and the simplest structure possible. Then, the input space is transformed by adding the nonlinear transformations of the input variables given by the RBFs of the best individual in the last generation. Finally, a maximum likelihood optimization method determines the coefficients associated with a multilogistic regression model built on this transformed input space. In this final step, two different multilogistic regression algorithms are applied, one that considers all initial and RBF covariates (MLRIRBF) and another one that incrementally constructs the model and applies cross-validation, resulting in an automatic covariate selection (MLRIRBF*). The methodology proposed is tested using six benchmark classification problems from well-known machine learning problems. The results are compared with the corresponding multilogistic regression methodologies applied over the initial input space, to the RBFNNs obtained by the EP algorithm (RBFEP) and to other competitive machine learning techniques. The MLRIRBF* models are found to be better than the corresponding multilogistic regression methodologies and the RBFEP method for almost all datasets, and obtain the highest mean accuracy rank when compared to the rest of methods in all datasets.