CIF: Small: Low-Dimensional Structure Learning for Tensor Data with Applications to Neuroimaging

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Advances in information technology are making it possible to collect increasingly massive amounts of multidimensional, multi-modal data across a diverse range of disciplines including bioinformatics, neuroscience, and the social sciences. One particular area where such multidimensional, multi-modal, and often nonlinear data is collected is neuroscience, in particular human brain connectomics. Connectomics aims to offer a comprehensive framework to describe neuronal connectivity by constructing networks from multi-modal and multi-subject, as well as both temporal and spatial, data. These high dimensional datasets pose a challenge to the signal processing community to develop data reduction methods that can exploit their rich structure in order to extract meaningful summarizations. Over the past several decades a tremendous amount of work has focused on the analysis and compression of high dimensional point-cloud datasets via low-dimensional manifold and subspace techniques. Although the research on low-dimensional structure learning from vector-type data is well developed, the direct application of these methods to higher order data poses significant challenges, including both increased computational complexity, and their inability to capture the couplings across different modes. This research addresses these problems through a tensor-based framework for data reduction and low-dimensional structure learning with a particular focus on reducing dynamic functional connectivity networks (dFCNs) into physiologically meaningful network components.The investigators develop two complementary approaches to address this high order data reduction problem: 1) Robust low-rank+sparse linear structure learning algorithms for tensors; 2) Multi-scale, locally linear adaptive tensor decomposition algorithms for compressing and learning structure from tensor data. Finally, this tensor based framework is applied to dFCNs constructed from electroencephalogram (EEG) data to assess well-known salience and control functional networks associated with affective regulation and cognitive control.