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

信息技术的进步使收集包括生物信息学、神经科学和社会科学在内的各种学科的越来越大量的多维、多模式数据成为可能。收集这种多维、多模式、通常是非线性数据的一个特殊领域是神经科学，特别是人脑连接学。连接学旨在通过从多模式和多主题以及时间和空间数据构建网络来提供一个全面的框架来描述神经元的连接。这些高维数据集对信号处理领域提出了挑战，即开发能够利用其丰富的结构来提取有意义的摘要的数据约简方法。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来分析和压缩高维点云数据集。虽然从矢量型数据中学习低维结构的研究已经很成熟，但将这些方法直接应用到高阶数据中会带来巨大的挑战，包括计算复杂性增加，以及无法捕获不同模式之间的耦合。该研究通过基于张量的数据约简和低维结构学习框架来解决这些问题，重点是将动态功能连通网络(DFCN)归结为具有生理意义的网络组件。研究人员开发了两种互补的方法来解决这一高阶数据约简问题：1)张量的稳健的低阶+稀疏线性结构学习算法；2)从张量数据中压缩和学习结构的多尺度局部线性自适应张量分解算法。最后，将这种基于张量的框架应用于从脑电(EEG)数据构建的dFCNs，以评估与情感调节和认知控制相关的众所周知的突显和控制功能网络。

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.