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

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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.