Network discovery via constrained tensor analysis of fMRI data

We pose the problem of network discovery which involves simplifying spatiotemporal data into cohesive regions (nodes) and relationships between those regions (edges). Such problems naturally exist in fMRI scans of human subjects. These scans consist of activations of thousands of voxels over time with the aim to simplify them into the underlying cognitive network being used. We propose supervised and semi- supervised variations of this problem and postulate a con- strained tensor decomposition formulation and a corresponding alternating least squares solver that is easy to implement. We show this formulation works well in controlled experiments where supervision is incomplete, superuous and noisy and is able to recover the underlying ground truth net- work. We then show that for real fMRI data our approach can reproduce well known results in neurology regarding the default mode network in resting-state healthy and Alzheimer affected individuals. Finally, we show that the reconstruction error of the decomposition provides a useful measure of the network strength and is useful at predicting key cognitive scores both by itself and with clinical information.