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

FODAVA负责人：降维和数据简化：可视化的基础FODAVA（数据分析和可视化的基础）在技术的格鲁吉亚研究所的领导研究团队提供了统一的专业知识，在关键领域提供FODAVA工作的领导，包括机器学习和计算统计，信息可视化，数据集算法和数据结构，以及优化理论。 该团队专注于基础理论和方法，以在数据表示和转换方面取得突破。 该工作沿着规模缩减的两个主轴，即数据缩减和维度缩减，让人类分析人员能够在认知和视觉上吸收和渗透现代大规模高维数据集。在维度缩减领域，该团队正在扩展通过稀疏恢复进行自动特征选择的理论，开发基于微分算子的流形维度缩减的有效方法，使用凹凸鞍点方法开发新的可扩展流形方法，并创建降维方法，其中包含增加其可理解性的约束，例如保留数据的聚类结构。在数据简化领域，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的方法，以及使用Lp估计进行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，特别是通过可视化分析数字图书馆，将所得方法集成到现有的可视化分析系统中，以及一系列研讨会。 本科生，代表性不足的群体和研究生分别通过格鲁吉亚理工学院的线程模型，FACES努力和创新的博士入门课程，强调跨学科研究和计算科学与工程的新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.