Generalized Sparse Classifiers for Decoding Cognitive States in fMRI

Abstract

Abstract. The high dimensionality of functional magnetic resonance imaging (fMRI) data presents major challenges to fMRI pattern classification. Directly applying standard classifiers often results in overfitting, which limits the generalizability of the results. In this paper, we propose a new group of classifiers, "Generalized Sparse Classifiers" (GSC), to alleviate this overfitting problem. GSC draws upon the recognition that numerous standard classifiers can be reformulated under a regression framework, which enables state-of-theart regularization techniques, e.g. elastic net, to be directly employed. Building on this regularized regression framework, we exploit an extension of elastic net that permits general properties, such as spatial smoothness, to be integrated. GSC thus facilitates simultaneous sparse feature selection and classification, while providing greater flexibility in the choice of penalties. We validate on real fMRI data and demonstrate how explicitly modeling spatial correlations inherent in brain activity using GSC can provide superior predictive performance and interpretability over standard classifiers.

Generalized Sparse Regularization with Application to fMRI Brain Decoding

“…We refer to our approach as generalized sparse regularization (GSR). In contrast to [7] and [9], we show that GSR is applicable to a much broader set of sparse linear models than just the LASSO regression model. The adaptability of GSR to such a wide range of models stems from how any l 2 norm penalty can be merged into an l 2 data fitting loss through a simple augmentation trick.…”

“…Learning parsimonious models by imposing sparsity also simplifies result interpretation [1], which is of utmost importance in most medical studies. Since the advent of the least absolute shrinkage and selection operator (LASSO) regression model [1], where Tibshirani showed that penalizing the l 1 norm induces sparsity in the regression coefficients, numerous powerful variants were subsequently proposed [2][3][4][5][6][7][8][9]. Zou and Hastie, for instance, proposed the elastic net penalty [2], which retains the sparse property of LASSO but additionally encourages correlated…”

“…Recent years witnessed a surging interest in exploiting sparsity [1][2][3][4][5][6][7][8][9] to handle the ever-increasing scale and complexity of current medical image analysis problems [10,11]. Oftentimes, one is faced with exceedingly more predictors than samples.…”

“…By varying the choice of weights, Generalized LASSO facilitates numerous applications, such as trend filtering, wavelet smoothing, and outlier detection [7]. In a previous work [9], we proposed an extension of LASSO that also enables such modeling flexibility but is much simpler to optimize. Specifically, we proposed adding a generalized ridge penalty (l 2 norm of a weighted combination of the model parameters) to the LASSO regression model and showed that the resulting optimization problem can be efficiently minimized with existing LASSO solvers [12][13][14][15].…”

“…In this paper, we propose a simple yet effective approach for incorporating prior knowledge into a wide collection of sparse linear models, as motivated by our previous work [9]. We refer to our approach as generalized sparse regularization (GSR).…”