CDS&E-MSS: Algebraic and Geometric Tools and Algorithms for the Analysis of Data Clouds and Large Data Arrays

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This proposal concerns the development of theory and algorithms for knowledge discovery in large data clouds characterized on Grassmann and Flag manifolds. This work includes applications to the detection of geometric misclassifications as well as the development of algorithms to exploit recent work on the detection of spatially-correlated Gaussian time-series. The investigators propose a mathematical framework centered on computing statistics for data clouds on Grassmann and Flag manifolds. This includes, for example, a theoretical characterization of a Schubert Variety of Best Fit. The results of the research will be applied to data sets that include, e.g., automatic identification of insects, the brain computer interface, statistical signal processing, foliage diversity in landscapes, automatic identification through hyperspectral imagery, acoustic arrays, super-resolution, and action recognition in video sequences.The proposed interdisciplinary research program addresses a major challenge in research related to the processing and extraction of meaningful information from large collections of data. The investigators' propose new geometric and statistical tools for classifying patterns of interest. The research program provides students with a unique multidisciplinary experience and research integration in education. Goals of the research include optimizing the detection, characterization and classification of features and anomalies in signals. A Data Set Repository of a broad nature for the purpose of furthering national expertise in Geometric Data Analysis. This repository will facilitate the development of algorithms ofinterest to a range of scientific interests.