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

信息技术的进步使得在生物信息学、神经科学和社会科学等不同学科中收集越来越多的多维、多模态数据成为可能。收集这种多维、多模态和通常非线性数据的一个特定领域是神经科学，特别是人脑连接组学。连接组学的目标是提供一个全面的框架来描述神经元的连接，通过构建网络，从多模态和多主题，以及时间和空间，数据。这些高维数据集对信号处理社区提出了挑战，以开发可以利用其丰富结构的数据简化方法，以提取有意义的摘要。在过去的几十年里，大量的工作集中在通过低维流形和子空间技术分析和压缩高维点云数据集。虽然从向量类型数据中进行低维结构学习的研究已经很发达，但将这些方法直接应用于高阶数据带来了重大挑战，包括增加计算复杂性，以及无法捕获不同模式之间的耦合。本研究通过一个基于张量的数据约简和低维结构学习的框架来解决这些问题，特别关注将动态功能连接网络（dFCN）约简为具有生理意义的网络组件，研究者开发了两种互补的方法来解决这个高阶数据约简问题：1）鲁棒的张量低秩稀疏线性结构学习算法; 2）多尺度、局部线性自适应张量分解算法，用于从张量数据压缩和学习结构。最后，这个张量为基础的框架被应用到dFCNs构造从脑电图（EEG）数据，以评估著名的显着性和控制功能网络与情感调节和认知控制。

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.