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

在监测、联网和传感技术迅速发展的基础上，所收集的大多数现代数据本质上都是多层面的，也就是说，每一个数据都受到各种因素的影响。例如，遥感视频中的像素是时间、颜色（波长）和空间位置的函数。另一个当代的例子来自广泛使用的评级和推荐系统，其中评级取决于用户、用户人口统计、被评级的产品和时间。事实上，这是许多其他应用程序的情况，如蜂窝网络性能统计，地球科学的地球物理系统，以及互动学习和协作环境中的教育统计。这项研究解决了推进数据科学的需要，为这些复杂和大规模的多维数据提供可靠和可扩展的信息采集和处理。特别是，研究建立和调查一个新的线性和多线性代数框架来建模多维数据。使用这个框架，可以利用良好的向量空间方法的主体，并使它们以原则性的方式处理多维数据，以实现比当前方法多几个数量级的性能增益。 该研究还解决了在部署大规模应用程序的框架中出现的挑战，并研究了数值和内存有效的算法。研究和教育的整合是通过新的跨领域课程开发，继续本科生辅导，并通过研究成果与现有的本科课程整合。更广泛的影响是通过一些合作努力实现的，涉及，塔夫茨互动学习和协作环境（InterLACE）计划，布里格姆和妇女？s医院和AT T研究。

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.