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

•A new wc-kernel to measure the correlation of brain regions, with weights learned in a data-driven manner to characterize specific contributions of different time points, is proposed.•A unified wc-kernel-based CNN framework to define functional connectivity networks and extract hierarchical connectivities for disease diagnosis is developed.•Achieving an accuracy of 84.6%, 88.0% and 57.0 for eMCI (early MCI) vs. HC (healthy control), AD vs. HC, and AD vs. lMCI (later MCI) vs. eMCI vs. HC classifications, respectively.