Advances in understanding the structural connectomes of human brain require improved approaches for the construction, comparison and integration of high-dimensional whole-brain tractography data from a large number of individuals. This article develops a population-based structural connectome (PSC) mapping framework to address these challenges. PSC simultaneously characterizes a large number of white matter bundles within and across different subjects by registering different subjects' brains based on coarse cortical parcellations, compressing the bundles of each connection, and extracting novel connection weights. A robust tractography algorithm and streamline post-processing techniques, including dilation of gray matter regions, streamline cutting, and outlier streamline removal are applied to improve the robustness of the extracted structural connectomes. The developed PSC framework can be used to reproducibly extract binary networks, weighted networks and streamline-based brain connectomes. We apply the PSC to Human Connectome Project data to illustrate its application in characterizing normal variations and heritability of structural connectomes in healthy subjects.

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.

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Statistical classification of actions in videos is mostly performed by extracting relevant features, particularly covariance features, from image frames and studying time series associated with temporal evolutions of these features. A natural mathematical representation of activity videos is in form of parameterized trajectories on the covariance manifold, i.e. the set of symmetric, positive-definite matrices (SPDMs). The variable execution-rates of actions implies variable parameterizations of the resulting trajectories, and complicates their classification. Since action classes are invariant to execution rates, one requires rate-invariant metrics for comparing trajectories. A recent paper represented trajectories using their transported square-root vector fields (TSRVFs), defined by parallel translating scaled-velocity vectors of trajectories to a reference tangent space on the manifold. To avoid arbitrariness of selecting the reference and to reduce distortion introduced during this mapping, we develop a purely intrinsic approach where SPDM trajectories are represented by redefining their TSRVFs at the starting points of the trajectories, and analyzed as elements of a vector bundle on the manifold. Using a natural Riemannain metric on vector bundles of SPDMs, we compute geodesic paths and geodesic distances between trajectories in the quotient space of this vector bundle, with respect to the reparameterization group. This makes the resulting comparison of trajectories invariant to their re-parameterization. We demonstrate this framework on two applications involving video classification: visual speech recognition or lip-reading and hand-gesture recognition. In both cases we achieve results either comparable to or better than the current literature.