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Dimension Reduction and Data Reduction: Foundations for Visualization
The FODAVA (Foundations of Data Analysis and Visualization) Lead research team at the Georgia Institute of Technology provides unified expertise in the critical areas for providing leadership of the FODAVA effort, including machine learning and computational statistics, information visualization, massive-dataset algorithms and data structures, and optimization theory. The team is focused on the fundamental theory and approaches to make breakthroughs in data representations and transformations. The work is directed along the two main axes of scale reduction, data reduction and dimension reduction, to allow human analysts to absorb and penetrate modern large-scale high-dimensional datasets cognitively and visually.
In the area of dimension reduction, the team is extending the theory of automatic feature selection by sparse recovery, developing effective methods for manifold dimension reduction in terms of differential operators, developing new scalable manifold methods using convex-concave saddle-point approaches, and creating dimension reduction methods which incorporate constraints that increase their understandability, such as preserving the data's cluster structure. In the area of data reduction, the team is developing multi-resolution data approximation schemes using hierarchical data structures and multipole-like expansions, approaches for analyzing data of heterogeneous data quality using convolution kernel approaches, and approaches for automatic anomaly cleaning and detection using Lp estimation. The results of this research impact the theory and practice of data analysis, as well as that of information visualization, in particular through the Visual Analytics Digital Library, integration of the resulting methodologies into existing visual analytics systems, and a series of workshops. Undergraduates, under-represented groups, and graduate students are educated in this new interdisciplinary area respectively through Georgia Tech's Threads model, FACES effort, and innovative PhD introductory course emphasizing cross-disciplinary research and new PhD program in Computational Science and Engineering.