Designing weighted correlation kernels in convolutional neural networks for functional connectivity based brain disease diagnosis

Functional connectivity networks (FCNs) based on functional magnetic resonance imaging (fMRI) have been widely applied to analyzing and diagnosing brain diseases, such as Alzheimer's disease (AD) and its prodrome stage, i.e., mild cognitive impairment (MCI). Existing studies usually use Pearson correlation coefficient (PCC) method to construct FCNs, and then extract network measures (e.g., clustering coefficients) as features to learn a diagnostic model. However, the valuable observation information in network construction (e.g., specific contributions of different time points), as well as high-level and high-order network features are neglected in these studies. In this paper, we first define a novel weighted correlation kernel (called wc-kernel) to measure the correlation of brain regions, by which weighting factors are learned in a data-driven manner to characterize the contributions of different time points, thus conveying the richer interaction information among brain regions compared with the PCC method. Furthermore, we build a wc-kernel based convolutional neural network (CNN) (called wck-CNN) framework for learning the hierarchical (i.e., from local to global and also from low-level to high-level) features for disease diagnosis, by using fMRI data. Specifically, we first define a layer to build dynamic FCNs using our proposed wc-kernels. Then, we define another three layers to sequentially extract local (brain region specific), global (brain network specific) and temporal features from the constructed dynamic FCNs for classification. Experimental results on 174 subjects (a total of 563 scans) with rest-state fMRI (rs-fMRI) data from ADNI database demonstrate the efficacy of our proposed method.