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

FODAVA-LEAD：降维和数据降维：可视化的基础佐治亚理工学院的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、海量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本理论和方法。在降维方面，该团队扩展了稀疏恢复的自动特征选择理论，开发了基于微分算子的流形降维的有效方法，利用凸凹鞍点方法开发了新的可伸缩的流形降维方法，并创建了包含增加其可理解性的约束的降维方法，例如保持数据的簇结构。在数据简化领域，该小组正在开发使用分层数据结构和类似多极展开的多分辨率数据近似方案、使用卷积核方法分析具有不同数据质量的数据的方法以及使用LP估计自动清理和检测异常的方法。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、将由此产生的方法融入现有的视觉分析系统以及一系列讲习班。本科生、代表不足的群体和研究生分别通过佐治亚理工学院的线程模式、面临努力和创新的博士入门课程在这个新的跨学科领域接受教育，该课程强调跨学科研究和计算科学和工程方面的新博士课程。

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.