Logistic regression by means of evolutionary radial basis function neural networks.

This paper proposes a hybrid multilogistic methodology, named logistic regression using initial and radial basis function (RBF) covariates. The process for obtaining the coefficients is carried out in three steps. First, an evolutionary programming (EP) algorithm is applied, in order to produce an RBF neural network (RBFNN) with a reduced number of RBF transformations and the simplest structure possible. Then, the initial attribute space (or, as commonly known as in logistic regression literature, the covariate space) is transformed by adding the nonlinear transformations of the input variables given by the RBFs of the best individual in the final generation. Finally, a maximum likelihood optimization method determines the coefficients associated with a multilogistic regression model built in this augmented covariate space. In this final step, two different multilogistic regression algorithms are applied: one considers all initial and RBF covariates (multilogistic initial-RBF regression) and the other one incrementally constructs the model and applies cross validation, resulting in an automatic covariate selection [simplelogistic initial-RBF regression (SLIRBF)]. Both methods include a regularization parameter, which has been also optimized. The methodology proposed is tested using 18 benchmark classification problems from well-known machine learning problems and two real agronomical problems. The results are compared with the corresponding multilogistic regression methods applied to the initial covariate space, to the RBFNNs obtained by the EP algorithm, and to other probabilistic classifiers, including different RBFNN design methods [e.g., relaxed variable kernel density estimation, support vector machines, a sparse classifier (sparse multinomial logistic regression)] and a procedure similar to SLIRBF but using product unit basis functions. The SLIRBF models are found to be competitive when compared with the corresponding multilogistic regression methods and the RBFEP method. A measure of statistical significance is used, which indicates that SLIRBF reaches the state of the art.

Hybridization of evolutionary algorithms and local search by means of a clustering method.

This paper presents a hybrid evolutionary algorithm (EA) to solve nonlinear-regression problems. Although EAs have proven their ability to explore large search spaces, they are comparatively inefficient in fine tuning the solution. This drawback is usually avoided by means of local optimization algorithms that are applied to the individuals of the population. The algorithms that use local optimization procedures are usually called hybrid algorithms. On the other hand, it is well known that the clustering process enables the creation of groups (clusters) with mutually close points that hopefully correspond to relevant regions of attraction. Local-search procedures can then be started once in every such region. This paper proposes the combination of an EA, a clustering process, and a local-search procedure to the evolutionary design of product-units neural networks. In the methodology presented, only a few individuals are subject to local optimization. Moreover, the local optimization algorithm is only applied at specific stages of the evolutionary process. Our results show a favorable performance when the regression method proposed is compared to other standard methods.