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

这项建议涉及在以Grassmann流形和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。这项工作包括在几何错误分类检测方面的应用，以及开发算法以利用最近在空间相关的高斯时间序列检测方面的工作。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。例如，这包括对舒伯特最适合的品种的理论描述。研究结果将应用于数据集，包括昆虫的自动识别、脑计算机接口、统计信号处理、景观中的树叶多样性、通过高光谱图像的自动识别、声学阵列、超分辨率以及视频序列中的动作识别。研究人员提出了新的几何和统计工具来对感兴趣的模式进行分类。该研究项目为学生提供了独特的多学科体验和教育研究整合。研究的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库，目的是增进国家在几何数据分析方面的专门知识。这个资料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.