Tensor network factorizations: Relationships between brain structural connectomes and traits.

Advanced brain imaging techniques make it possible to measure individuals' structural connectomes in large cohort studies non-invasively. Given the availability of large scale data sets, it is extremely interesting and important to build a set of advanced tools for structural connectome extraction and statistical analysis that emphasize both interpretability and predictive power. In this paper, we developed and integrated a set of toolboxes, including an advanced structural connectome extraction pipeline and a novel tensor network principal components analysis (TN-PCA) method, to study relationships between structural connectomes and various human traits such as alcohol and drug use, cognition and motion abilities. The structural connectome extraction pipeline produces a set of connectome features for each subject that can be organized as a tensor network, and TN-PCA maps the high-dimensional tensor network data to a lower-dimensional Euclidean space. Combined with classical hypothesis testing, canonical correlation analysis and linear discriminant analysis techniques, we analyzed over 1100 scans of 1076 subjects from the Human Connectome Project (HCP) and the Sherbrooke test-retest data set, as well as 175 human traits measuring different domains including cognition, substance use, motor, sensory and emotion. The test-retest data validated the developed algorithms. With the HCP data, we found that structural connectomes are associated with a wide range of traits, e.g., fluid intelligence, language comprehension, and motor skills are associated with increased cortical-cortical brain structural connectivity, while the use of alcohol, tobacco, and marijuana are associated with decreased cortical-cortical connectivity. We also demonstrated that our extracted structural connectomes and analysis method can give superior prediction accuracies compared with alternative connectome constructions and other tensor and network regression methods.