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• Finite training sets lead to classifier error rates above the Bayes error rate. • The training set size required in a practical setting is a relevant information. • Most approaches are purely experimental or consider just two classes. • A theoretical expression for the relative excess over the Bayes error rate is provided. In this paper, a theoretical learning curve is derived for the multi-class Bayes classifier. This curve fits general multivariate parametric models of the class-conditional probability density. The derivation uses a proxy approach based on analyzing the convergence of a statistic which is proportional to the posterior probability of the true class. By doing so, the curve depends only on the training set size and on the dimension of the feature vector; it does not depend on the model parameters. Essentially, the learning curve provides an estimate of the reduction in the excess of the probability of error that can be obtained by increasing the training set size. This makes it attractive in order to deal with the practical problems of defining appropriate training set sizes. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new procedure for learning mixtures of independent component analyzers. The procedure includes non-parametric estimation of the source densities, supervised–unsupervised learning of the model parameters, incorporation of any independent component analysis (ICA) algorithm into the learning of the ICA mixtures, and estimation of residual dependencies after training for correction of the posterior probability of every class to the testing observation vector. We demonstrate the performance of the procedure in the classification of ICA mixtures of two, three, and four classes of synthetic data, and in the classification of defective materials, consisting of 3D finite element models and lab specimens, in non-destructive testing using the impact-echo technique. The application of the proposed posterior probability correction demonstrates an improvement in the classification accuracy. Semi-supervised learning shows that unlabeled data can degrade the performance of the classifier when they do not fit the generative model. Comparative results of the proposed method and standard ICA algorithms for blind source separation in one and multiple ICA data mixtures show the suitability of the non-parametric ICA mixture-based method for data modeling. [Copyright &y& Elsevier]

• A new method for oversampling very scarce training sets. • Based on Generative Adversarial Networks and Markov Random Field models. • Much better performance than SMOTE on simulated and real data experiment. In this work, we propose a new method for oversampling the training set of a classifier, in a scenario of extreme scarcity of training data. It is based on two concepts: Generative Adversarial Networks (GAN) and vector Markov Random Field (vMRF). Thus, the generative block of GAN uses the vMRF model to synthesize surrogates by the Graph Fourier Transform. Then, the discriminative block implements a linear discriminant on features measuring clique similarities between the synthesized and the original instances. Both blocks iterate until the linear discriminant cannot discriminate the synthetic from the original instances. We have assessed the new method, called Generative Adversarial Network Synthesis for Oversampling (GANSO), with both simulated and real data in experiments where the classifier is to be trained with just 3 or 5 instances. The applications consisted of classification of stages of neuropsychological tests using electroencephalographic (EEG) and functional magnetic resonance imaging (fMRI) data and classification of sleep stages using electrocardiographic (ECG) data. We have verified that GANSO can effectively improve the classifier performance, while the benchmark method SMOTE is not appropriate to deal with such a small size of the training set. [ABSTRACT FROM AUTHOR]