fMRI Analysis with Sparse Weisfeiler-Lehman Graph Statistics

Abstract

fMRI analysis has most often been approached with linear methods. However, this disregards information encoded in the relationships between voxels. We propose to exploit the inherent spatial structure of the brain to improve the prediction performance of fMRI analysis. We do so in an exploratory fashion by representing the fMRI data by graphs. We use the Weisfeiler-Lehman algorithm to efficiently compute subtree features of the graphs. These features encode non-linear interactions between voxels, which contain additional discriminative information that cannot be captured by a linear classifier. In order to make use of the efficiency of the Weisfeiler-Lehman algorithm, we introduce a novel pyramid quantization strategy to approximate continuously labeled graphs with a sequence of discretely labeled graphs. To control the capacity of the resulting prediction function, we utilize the elastic net sparsity regularizer. We validate our method on a cocaine addiction dataset showing a significant improvement over elastic net and kernel ridge regression baselines and a reduction in classification error of over 14%. Source code is also available at https://gitorious.org/wlpyramid .