Random Subspace Method in Classification and Mapping of fMRI Data Patterns

Abstract

The functional magnetic resonance imaging (fMRI) technique is widely used in studying human brain functions. It measures brain activities both spatially and temporally. The past decade has witnessed a growing interest in the fMRI community in constructing accurate predictive models. Though achieving high prediction accuracy is crucial in building strong diagnostic models (e.g. for brain functional disorders), information mapping or model interpretability is critical in advancing a fundamental understanding of brain functions. Recently, two notable multivariate methods, recursive feature elimination using support vector machine (RFESVM) and logistic regression with an elastic net penalty (LREN), have been applied to meet the challenge of simultaneous classification and mapping of fMRI data patterns. However, both methods have limitations. First, they suffer from the curse of dimensionality by solving classification and feature selection tasks directly in the whole feature space. Second, feature selections in both methods critically depend on sampled values of tuning parameters and they lack of a control over false selections. In this dissertation, I seek to address both limitations within a random subspace framework. The random subspace method is an effective approach to lessen the curse of dimensionality and explore data patterns from different local perspectives. It has been separately applied in classifications and feature selections with success. But no previous studies have attempted to integrate them together, possibly because of the high computational cost involved in using a double-loop cross validation scheme to avoid the parameter selection bias. In chapter 2, I seek to solve the methodological issues. I first extend an efficient method, only using a single K-fold cross validation procedure, to alleviate the parameter selection bias of an ensemble classifier formed by the random subspace method. The extension allows independent tuning of base classifiers, making feature selection more adaptive to the local data structure. I then integrate a random probe method into the random subspace framework to control false selections. A threshold is derived based on the distribution of scores of permuted artificial variables. In chapter 3 and 4, using extensive simulations, I empirically evaluate the developed random subspace framework with applications to LREN and RFESVM, respectively. I find that (1) the developed random subspace framework can boost performance of both LREN and RFESVM in classifications and feature selections; (2) the random probe method can effectively control false selection rates; (3) the proposed novel feature scoring method is capable of ranking informative features based on their individual discriminative capacities; (4) the random subspace framework is able to correctly determine informative features’ discrimination directions.