CAREER: Advancing Multidimensional Data Science via New Algebraic Models and Scalable Algorithms

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Building upon the rapid advancements in monitoring, networking and sensing technologies, most modern data collected are inherently multidimensional in nature, that is, each datum is influenced by a variety of factors. For example, a pixel in a remote sensing video is a function of time, color (wavelength) and spatial location. Another contemporary example comes from the widely used rating and recommendation systems, where a rating depends on the user, user demographic, product being rated and time. In fact, this is the case for numerous other applications such as cellular network performance statistics, geophysical systems for earth sciences, and education statistics in interactive learning and collaboration environments. This research addresses the need to advance data science for reliable and scalable information acquisition and processing for these complex and large-scale multidimensional data. In particular, the research builds and investigates a novel linear and multilinear algebraic framework to model multidimensional data. Using this framework one can tap into the well-developed body of vector space methods and adapt them to process multidimensional data in a principled manner to realize orders of magnitude performance gains over current methods. The research also addresses the challenges, which arise in deploying the framework for large-scale applications and investigates numerical and memory efficient algorithms. Integration of research and education is enabled through new cross-cutting curriculum development, continued undergraduate mentoring, and through integration of the research outcomes with existing undergraduate curriculum. The broader impacts are realized through a number of collaborative efforts involving, Tufts Interactive Learning and Collaboration Environment (InterLACE) program, Brigham and Women?s Hospital and AT&T research.