Collaborative Research:CISE-ANR:CIF:Small:Learning from Large Datasets - Application to Multi-Subject fMRI Analysis

在当今的许多学科中，与给定问题相关的多个和互补的数据的可用性越来越高，而主要的挑战是从这些大量的数据集中提取和有效地总结相关信息。这些数据集的联合分解以矩阵或张量的形式排列，通过让它们相互充分交互和通知并产生可直接解释的因子矩阵，为数据融合提供了一种有吸引力的解决方案，其中产生的因子(分量)直接与感兴趣的量相关联。这项研究将通过定义齐次子空间来有效地总结大型数据集中的异构性，从而为从大规模数据中进行推理提供强有力的解决方案，以致子空间中的组件高度依赖。这些方法的成功将通过从神经成像数据中识别受试者的同质亚组来展示，从而使个性化医疗成为可能，其目标是为给定的个人量身定做干预策略。有效地总结大规模数据集中的信息是当今许多具有挑战性的问题的核心，因此新的工具集将影响许多科学和技术领域，包括医学成像、遥感、图像/视频处理、通信和社交网络。独立向量分析(IVA)和耦合张量分解是处理时空数据的两种有效方法，每种方法都通过不同的机制利用结构/相关性信息。它们还提供了强大的唯一性保证，这是可解释性的关键。该项目利用IVA和耦合张量分解的互补优势，通过自动识别同质子空间以及这些子空间中的组件，开发了一个强大的框架，用于联合分析/融合大量数据集。这是通过最初开发有效的IVA和耦合张量分解问题的解决方案来实现的，并行工作。然后，在第二阶段，在方法和唯一性条件方面建立这两种方法之间的联系，以开发一种利用两种方法的优点的方法。强调解决方案的唯一性和可解释性，以及对具有挑战性的数据集的应用，将确保这些方法以及所开发的理论基础不仅是完整的，而且是实用的。这项工作的另一个重要方面是在不一定沟通的两个社区之间建立桥梁。这项工作将证明，统计和代数激励的数据融合方法不是相互竞争的，而是具有重要的互补方面，可以有效地加以利用。此外，清楚地了解它们的联系和区别，可以公平地比较所有方法，清楚地突出它们的能力和局限性。这将有助于为不断增长的数据科学和机器学习领域建立一个坚实和平衡的基础。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

In many disciplines today, there is an increasing availability of multiple and complementary data associated with a given problem, and the main challenge is extracting and effectively summarizing the relevant information from these large number of datasets. Joint decomposition of these datasets, arranged as matrices or tensors, provides an attractive solution to data fusion by letting them fully interact and inform each other and yields factor matrices that are directly interpretable, where the resulting factors (components) are directly associated with quantities of interest. This research will provide a powerful solution for inference from large-scale data by effectively summarizing the heterogeneity in large datasets through the definition of homogeneous subspaces such that components within a subspace are highly dependent. The success of the methods will be demonstrated through identification of homogeneous subgroups of subjects from neuroimaging data, thus enabling personalized medicine whose goal is to tailor intervention strategies for a given individual. Effectively summarizing information in large-scale datasets is at the heart of many of today's challenging problems, hence the new set of tools will impact numerous areas in science and technology, including those in medical imaging, remote sensing, image/video processing, communications, and social networks.Independent vector analysis (IVA) and coupled tensor factorizations are two powerful ways for working with spatio-temporal data, each exploiting the structural/dependence information through different mechanisms. They also provide strong uniqueness guarantees, which is key for interpretability. This project leverages the complementary strengths of IVA and coupled tensor decompositions to develop a powerful framework for joint analysis/fusion of a large number of datasets through automated identification of homogeneous subspaces along with the components within these subspaces. This is accomplished by initially developing effective solutions to the problem with IVA and with coupled tensor decompositions, working in parallel. Then, in a second stage, the connections between these two approaches are established, both in terms of methods and uniqueness conditions, to develop a methodology that leverages the strengths of both approaches. The emphasis on uniqueness and interpretability of the solutions together with an application to a challenging dataset will ensure that the methods, as well as the developed theoretical foundations, are not only complete but also practically useful. Another important aspect of the work is the establishing of bridges across two communities that do not necessarily communicate. The work will demonstrate that statistically and algebraically motivated approaches to data fusion are not in competition with each other but have important complementary aspects that can be effectively leveraged. In addition, a clear view of their connections as well as differences enables fair comparisons of all methods clearly highlighting their abilities together with their limitations. This will help establish a solid and well-balanced foundation for the growing fields of data science and machine learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.