Eigenvector centrality mapping (ECM) is a popular technique for analyzing fMRI data of the human brain. It is used to obtain maps of functional hubs in networks of the brain in a manner similar to Google's PageRank algorithm. ECM attributes a score to the time course of each voxel that reflects its centrality within the network. Voxels that are strongly correlated with many other voxels that are themselves strongly correlated with other voxels receive high scores. Currently, there exist two different implementations ECM, one of which is very fast but limited to one particular type of correlation metric whose interpretation can be problematic. The second implementation supports many different metrics, but it is computationally costly and requires a very large main memory. Here we propose two new implementations of the ECM approach that resolve these issues. The first is based on a new correlation metric that we call "ReLU correlation (RLC)". The second method is based on matrix projections. We demonstrate the use of both techniques on standard fMRI data, as well as on high-resolution fMRI data acquired at 9.4 Tesla.
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