Collaborative Research: CDS&E: Theoretical Foundations and Algorithms for L1-Norm-Based Reliable Multi-Modal Data Analysis

在现代科学和工程应用中，从不同的传感器模式收集大量数据，通常以高阶数组(张量)的形式存储，并联合分析以提取有关潜在现象的信息。这种联合张量分析可以利用数据模式之间的内在依赖关系，并允许显著增强的推理。张量分析的标准方法依赖于对已处理数据(离群值)中的严重腐蚀点敏感的公式。为了抵消现代数据分析中离群值的破坏性影响(及其依赖的应用程序)，该项目将研究新的理论和稳健的算法方法。所开发工具的性能优势将在数据分析、机器学习和计算机视觉领域的应用中进行评估。因此，这项研究渴望显著提高跨科学和工程领域的数据支持研究的可靠性。该项目将理论探索与用于数据分析和实验评估的实用算法解决方案相结合，不仅有可能为美国学术机构，也有可能为美国政府和行业建立重要的未来能力。因此，除了促进科学进步外，该项目还可以为国家繁荣和福利的进步做出贡献。此外，该项目下的研究活动将与教育相结合。参与的研究生和本科生将在优化理论、机器学习、计算机视觉和数据挖掘等领域获得重要经验。此外，该项目计划包括多个STEM外展活动，并通过吸收来自代表性不足群体的学生来支持STEM的多样性。在本项目中，将研究L1范数张量分析的理论基础，重点是其计算难度和精确解。然后，基于这些新的基础，将探索高效实用的L1范数张量分析算法，以及可扩展和分布式的软件实现。这些理论和算法研究有望极大地促进当前未被探索的L1范数张量分析领域的知识，并为抗离群点的多模式数据处理提供高度有效的方法。接下来，PI将在数据分析、机器学习和计算机视觉领域的关键问题上使用新开发的算法工具。此外，该项目下的研究活动将与教育相结合。参与的研究生和本科生将在优化理论、机器学习、计算机视觉和数据挖掘等领域获得重要经验。此外，该项目计划包括多项STEM外展活动，并通过吸收来自代表性不足群体的学生来支持STEM的多样性。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 modern applications of science and engineering, large volumes of data are collected from diverse sensor modalities, commonly stored in the form of high-order arrays (tensors), and jointly analyzed in order to extract information about underlying phenomena. This joint tensor analysis can exploit inherent dependencies across data modalities and allow for markedly enhanced inference. Standard methods for tensor analysis rely on formulations that are sensitive to heavily corrupted points among the processed data (outliers). To counteract the destructive impact of outliers in modern data analysis (and thereto relying applications), this project will investigate new theory and robust algorithmic methods. The performance benefits of the developed tools will be evaluated in applications from the fields of data analytics, machine learning and computer vision. Thus, this research aspires to increase significantly the reliability of data-enabled research across science and engineering. Combining theoretical explorations, with practical algorithmic solutions for data analysis and experimental evaluations, this project has the potential to build significant future capacity not only for U.S. academic institutions but also for the U.S. government and industry. Thus, apart from promoting the progress of science, this project could contribute to advances in the national prosperity and welfare. In addition, research activities under this project will be integrated with education. Participating students, at both graduate and undergraduate levels, will gain important experience in optimization theory, machine learning, computer vision, and data mining, among other areas. Moreover, the project plan includes multiple STEM outreach activities and supports diversity in STEM by involving students from underrepresented groups.In this project, the theoretical underpinnings of L1-norm tensor analysis will be investigated, with a focus on its computational hardness and exact solution. Then, based on these new foundations, efficient/practical algorithms for L1-norm tensor analysis will be explored, together with scalable and distributed software implementations. These theoretical and algorithmic investigations are expected to advance significantly the knowledge in the currently under-explored area of L1-norm tensor analysis and deliver highly impactful methodologies for outlier-resistant multimodal data processing. Next, the PIs will employ the newly developed algorithmic tools in key problems from the fields of data analytics, machine learning and computer vision. In addition, research activities under this project will be integrated with education. Participating students, at both graduate and undergraduate levels, will gain important experience in optimization theory, machine learning, computer vision, and data mining, among other areas. Moreover, the project plan includes multiple STEM outreach activities?and supports diversity in STEM by involving?students from underrepresented groups.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.