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An important problem that hinders the use of supervised classification algorithms for brain imaging is that the number of variables per single subject far exceeds the number of training subjects available. Deriving multivariate measures of variable importance becomes a challenge in such scenarios. This paper proposes a new measure of variable importance termed sign-consistency bagging (SCB). The SCB captures variable importance by analyzing the sign consistency of the corresponding weights in an ensemble of linear support vector machine (SVM) classifiers. Further, the SCB variable importances are enhanced by means of transductive conformal analysis. This extra step is important when the data can be assumed to be heterogeneous. Finally, the proposal of these SCB variable importance measures is completed with the derivation of a parametric hypothesis test of variable importance. The new importance measures were compared with a t-test based univariate and an SVM-based multivariate variable importances using anatomical and functional magnetic resonance imaging data. The obtained results demonstrated that the new SCB based importance measures were superior to the compared methods in terms of reproducibility and classification accuracy.Electronic supplementary materialThe online version of this article (10.1007/s12021-019-9415-3) contains supplementary material, which is available to authorized users.

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The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian models allows the model to better adapt to the data nature (i.e. heterogeneity, sparsity), obtaining a more representative latent space.The objective of this article is to propose a general FA framework capable of modelling any problem. To do so, we start from the Bayesian Inter-Battery Factor Analysis (BIBFA) model, enhancing it with new functionalities to be able to work with heterogeneous data, include feature selection, and handle missing values as well as semisupervised problems.The performance of the proposed model, Sparse Semi-supervised Heterogeneous Interbattery Bayesian Analysis (SSHIBA) has been tested on 4 different scenarios to evaluate each one of its novelties, showing not only a great versatility and an interpretability gain, but also outperforming most of the state-of-the-art algorithms.