Combining sparseness and smoothness improves classification accuracy and interpretability

Sparse logistic regression (SLR) has been shown to be a useful method for decoding high-dimensional fMRI and MEG data by automatically selecting relevant feature dimensions. However, when applied to signals with high spatio-temporal correlations, SLR often over-prunes the feature space, which can result in overfitting and weight vectors that are difficult to interpret. To overcome this problem, we investigate a modification of ℓ₁-normed sparse logistic regression, called smooth sparse logistic regression (SSLR), which has a spatio-temporal "smoothing" prior that encourages weights that are close in time and space to have similar values. This causes the classifier to select spatio-temporally continuous groups of features, whereas SLR classifiers often select a scattered collection of independent features. We applied the method to both simulation data and real MEG data. We found that SSLR consistently increases classification accuracy, and produces weight vectors that are more meaningful from a neuroscientific perspective.