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

本提案涉及以Grassmann和Flag流形为特征的大数据云中知识发现的理论和算法的发展。这项工作包括几何错误分类检测的应用，以及利用最近在空间相关高斯时间序列检测方面的工作开发算法。研究人员提出了一个数学框架，以计算格拉斯曼和Flag流形上的数据云的统计数据为中心。这包括，例如，舒伯特最佳拟合变化的理论表征。研究结果将应用于包括昆虫自动识别、脑机接口、统计信号处理、景观树叶多样性、通过高光谱图像自动识别、声学阵列、超分辨率和视频序列动作识别等数据集。拟议的跨学科研究计划解决了与处理和从大量数据中提取有意义信息相关的研究中的主要挑战。研究者提出了新的几何和统计工具来分类感兴趣的模式。该研究项目为学生提供了独特的多学科经验和研究整合的教育。研究目标包括优化信号中特征和异常的检测、表征和分类。一个广泛性质的数据集存储库，目的是促进国家在几何数据分析方面的专业知识。该存储库将促进对一系列科学兴趣感兴趣的算法的开发。

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.