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

在今天的许多学科中，与给定问题相关的多种和互补数据的可用性越来越高，主要挑战是从这些大量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，排列成矩阵或张量，为数据融合提供了一个有吸引力的解决方案，让它们完全相互作用并相互通知，并产生可直接解释的因子矩阵，其中产生的因子（组件）与感兴趣的量直接相关。本研究通过同质子空间的定义有效地总结了大型数据集的异质性，从而使子空间内的组件高度依赖，从而为大规模数据推理提供了一个强大的解决方案。这些方法的成功将通过从神经成像数据中识别同质的受试者亚组来证明，从而实现个性化医疗，其目标是为特定个体量身定制干预策略。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问题的核心，因此这套新工具将影响科学和技术的许多领域，包括医学成像、遥感、图像/视频处理、通信和社交网络等领域。独立向量分析（IVA）和耦合张量分解是处理时空数据的两种强大方法，它们通过不同的机制利用结构/依赖信息。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。这是通过使用IVA和耦合张量分解并行地开发问题的有效解决方案来完成的。然后，在第二阶段，根据方法和唯一性条件建立这两种方法之间的联系，以开发一种利用这两种方法的优势的方法。强调解决方案的唯一性和可解释性，并将其应用于具有挑战性的数据集，将确保方法以及开发的理论基础不仅完整，而且具有实际用途。这项工作的另一个重要方面是在两个不一定沟通的社区之间建立桥梁。这项工作将证明，统计和代数驱动的数据融合方法并不相互竞争，而是具有重要的互补方面，可以有效地利用。此外，清楚地了解它们的联系和差异，可以对所有方法进行公平的比较，清楚地突出它们的能力和局限性。这将有助于为不断发展的数据科学和机器学习领域奠定坚实而平衡的基础。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.