FODAVA-Lead: Dimension Reduction and Data Reduction: Foundations for Visualization

佐治亚理工学院的FODAVA（数据分析和可视化基础）领导研究团队在关键领域提供统一的专业知识，以提供FODAVA工作的领导，包括机器学习和计算统计，信息可视化，大规模数据集算法和数据结构，以及优化理论。该团队专注于在数据表示和转换方面取得突破的基础理论和方法。这项工作沿着两个主要的尺度约简，数据约简和维数约简方向进行，使人类分析师能够在认知和视觉上吸收和渗透现代大规模高维数据集。在降维领域，该团队通过稀疏恢复扩展了自动特征选择理论，根据微分算子开发了有效的流形降维方法，使用凸凹鞍点方法开发了新的可扩展流形方法，并创建了包含约束的降维方法，增加了它们的可理解性，例如保留数据的簇结构。在数据约简领域，该团队正在开发使用分层数据结构和多极扩展的多分辨率数据近似方案，使用卷积核方法分析异构数据质量数据的方法，以及使用Lp估计自动异常清理和检测的方法。这项研究的结果影响了数据分析的理论和实践，以及信息可视化的理论和实践，特别是通过视觉分析数字图书馆，将所得方法集成到现有的视觉分析系统中，以及一系列研讨会。本科生、弱势群体和研究生分别通过佐治亚理工学院的Threads模式、FACES努力、强调跨学科研究的创新博士入门课程和新的计算科学与工程博士课程，在这个新的跨学科领域接受教育。

FODAVA-Lead: Dimension Reduction and Data Reduction: Foundations for VisualizationThe 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.