Latent Factor Analysis of High-Dimensional Brain Imaging Data
Recent advances in neuroimaging study, especially functional magnetic resonance imaging (fMRI), has become an important tool in understanding the human brain. Human cognitive functions can be mapped with the brain functional organization through the high-resolution fMRI scans. However, the high-dimensional data with the increasing number of scanning tasks and subjects pose a challenge to existing methods that wasn’t optimized for high-dimensional imaging data. In this thesis, I develop advanced data-driven methods to help utilize more available sources of information in order to reveal more robust brain-behavior relationship. In the ﬁrst chapter, I provide an overview of the current related research in fMRI and my contributions to the ﬁeld. In the second chapter, I propose two extensions to the connectome-based predictive modeling (CPM) method that is able to combine multiple connectomes when building predictive models. The two extensions are both able to generate higher prediction accuracy than using the single connectome or the average of multiple connectomes, suggesting the advantage of incorporating multiple sources of information in predictive modeling. In the third chapter, I improve CPM from the target behavioral measure’s perspective. I propose another two extensions for CPM that are able to combine multiple available behavioral measures into a composite measure for CPM to predict. The derived composite measures are shown to be predicted more accurately than any other single behavioral measure, suggesting a more robust brainbehavior relationship. In the fourth chapter, I propose a nonlinear dimensionality reduction framework to embed fMRI data from multiple tasks into a low-dimensional space. This framework helps reveal the common brain state in the multiple available tasks while also help discover the differences among these tasks. The results also provide valuable insights into the various prediction performance based on connectomes from different tasks. In the ﬁfth chapter, I propose an another hyerbolic geometry-based brain graph edge embedding framework. The framework is based on Poincar´e embedding and is able to more accurately represent edges in the brain graph in a low-dimensional space than traditional Euclidean geometry-based embedding. Utilizing the embedding, we are able to cluster edges of the brain graph into disjoint clusters. The edge clusters can then be used to deﬁne overlapping brain networks and the derived metrics like network overlapping number can be used to investigate functional ﬂexibility of each brain region. Overall, these work provide rich data-driven methods that help understand the brain-behavioral relationship through predictive modeling and low-dimensional data representation.