Semi-supervised learning for ordinal Kernel Discriminant Analysis.

Ordinal classification considers those classification problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or difficult to obtain in this type of problems because, in many cases, ordinal labels are given by a user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classification where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specifically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classification, which is combined with our developed classification strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classification in a battery of 30 datasets, showing (1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and (2) the advantage of computing distances in the feature space induced by the kernel function.

Evolutionary q-Gaussian radial basis function neural networks for multiclassification.

This paper proposes a radial basis function neural network (RBFNN), called the q-Gaussian RBFNN, that reproduces different radial basis functions (RBFs) by means of a real parameter q. The architecture, weights and node topology are learnt through a hybrid algorithm (HA). In order to test the overall performance, an experimental study with sixteen data sets taken from the UCI repository is presented. The q-Gaussian RBFNN was compared to RBFNNs with Gaussian, Cauchy and inverse multiquadratic RBFs in the hidden layer and to other probabilistic classifiers, including different RBFNN design methods, support vector machines (SVMs), a sparse classifier (sparse multinomial logistic regression, SMLR) and a non-sparse classifier (regularized multinomial logistic regression, RMLR). The results show that the q-Gaussian model can be considered very competitive with the other classification methods.

Multilogistic regression by means of evolutionary product-unit neural networks.

We propose a multilogistic regression model based on the combination of linear and product-unit models, where the product-unit nonlinear functions are constructed with the product of the inputs raised to arbitrary powers. The estimation of the coefficients of the model is carried out in two phases. First, the number of product-unit basis functions and the exponents' vector are determined by means of an evolutionary neural network algorithm. Afterwards, a standard maximum likelihood optimization method determines the rest of the coefficients in the new space given by the initial variables and the product-unit basis functions previously estimated. We compare the performance of our approach with the logistic regression built on the initial variables and several learning classification techniques. The statistical test carried out on twelve benchmark datasets shows that the proposed model is competitive in terms of the accuracy of the classifier.