Sparse logistic regression for whole-brain classification of fMRI data

Abstract

Multivariate pattern recognition methods are increasingly being used to identify multiregional brain activity patterns that collectively discriminate one cognitive condition or experimental group from another, using fMRI data. The performance of these methods is often limited because the number of regions considered in the analysis of fMRI data is large compared to the number of observations (trials or participants). Existing methods that aim to tackle this dimensionality problem are less than optimal because they either over-fit the data or are computationally intractable. Here, we describe a novel method based on logistic regression using a combination of L1 and L2 norm regularization that more accurately estimates discriminative brain regions across multiple conditions or groups. The L1 norm, computed using a fast estimation procedure, ensures a fast, sparse and generalizable solution; the L2 norm ensures that correlated brain regions are included in the resulting solution, a critical aspect of fMRI data analysis often overlooked by existing methods. We first evaluate the performance of our method on simulated data and then examine its effectiveness in discriminating between well-matched music and speech stimuli. We also compared our procedures with other methods which use either L1-norm regularization alone or support vector machine based feature elimination. On simulated data, our methods performed significantly better than existing methods across a wide-range of contrast-to-noise ratios and feature prevalence rates. On experimental fMRI data, our methods were more effective in selectively isolating a distributed fronto-temporal network that distinguished between brain regions known to be involved in speech and music processing. These findings suggest that our method is not only computationally efficient, but it also achieves the twin objectives of identifying relevant discriminative brain regions and accurately classifying fMRI data.

Improving Sparse Recovery on Structured Images with Bagged Clustering

“…Here, we focus on the logistic loss, log(1 + exp(−yXβ)), given that it is well-suited for classification settings. The corresponding classifier is a sparse logistic regression (SLR), used routinely in neuroimaging [7].…”

Generalized Sparse Regularization with Application to fMRI Brain Decoding

“…Recent research in this area of fMRI analysis has mainly focused on exploitation of sparsity-enforcing techniques, such as sparse logistic regression [16,17], elastic net [18], and group LASSO [19] among others [20], to mitigate the curse of dimensionality. However, merely enforcing sparsity does not promote spatial smoothness in classifier weight patterns [9], which deviates from how spatially proximal voxels tend to display similar level of brain activity [21].…”

Generalized Sparse Classifiers for Decoding Cognitive States in fMRI

“…Alternatively, principal component analysis (PCA) can be applied prior to classification [10]. However, neither of these strategies considers the collective discriminant information encoded by the voxel patterns, and thus may result in suboptimal feature selection [11][12][13].…”

“…Recently, powerful methods that simultaneously select discriminant voxels and estimate their weights for classification have been proposed [11][12][13]. These methods extend traditional classifiers by incorporating sparse regularization, which controls overfitting by encouraging zero weights to be assigned to irrelevant voxels.…”

“…weights assigned to isolated voxels), which limits interpretability and hence defeats the ultimate objective of fMRI studies [13]. To relax this highly-overlooked limitation, methods that include an additional ridge penalty to promote joint selection of correlated voxels have been proposed [12,13]. This refinement seems to produce less spatially-scattered weight patterns [13].…”