New Dimension Reduction Approaches for Modern Scientific Data with High Dimensionality and Complex Structure

高维复杂结构现代科学数据降维新方法

• 批准号: 1106668
• 负责人: Lexin Li
• 金额: $ 10万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-15 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106668&HistoricalAwards=false
• 关键词: New; Dimension; Reduction; Approaches; Modern

With the recent explosion of scientific data, and its unprecedented size and complexity, dimension reduction is becoming a central ingredient in any modern statistical analysis. This project aims to couple dimension reduction methodology with current statistical learning techniques, which results in an entirely new class of flexible and effective dimension reduction solutions for modern data with both high dimensionality and complex structure. From the coupling, the investigator establishes a framework for dimension reduction that incorporates prior information regarding the known structural relationships between the variables. Within this framework, the investigator plans to develop a family of dimension reduction solutions so that the results are more readily interpretable and accurate. Such a framework is to greatly facilitate the analysis of neuroimaging, climate, and genomic data where prior structural information is often available. Modern technologies routinely produce massive amounts of data and such a data deluge now engulfs every branch of science and public life. As a result, scientific progress now heavily depends on the ability to process and analyze complex high-dimensional data. At the heart of these analyses are methods that reduce the dimensionality of the data, sometimes dramatically, by identifying a small set of variables that are important, or obtaining a few combinations of the original measurements. This project aims to develop a host of novel dimension reduction methods to address these pressing challenges in high-dimensional data analysis. The proposed research is expected to make significant contributions on two fronts: enabling scientists to quickly and effectively extract useful information from massive data, and at the same time, benefiting the discipline of statistics with advances in theory, methods and applications.

随着最近科学数据的爆炸性增长，以及其前所未有的大小和复杂性，降维正成为任何现代统计分析的核心要素。该项目旨在将降维方法与当前的统计学习技术相结合，从而为高维和复杂结构的现代数据带来一种全新的灵活有效的降维解决方案。通过耦合，调查者建立了降维框架，该框架结合了关于变量之间的已知结构关系的先验信息。在这个框架内，研究人员计划开发一系列降维解决方案，使结果更易于解释和准确。这样的框架将极大地促进神经成像、气候和基因组数据的分析，在这些数据中，先前的结构信息通常是可用的。现代技术经常产生海量数据，这样的数据洪流现在吞没了科学和公共生活的每个分支。因此，科学进步现在在很大程度上依赖于处理和分析复杂高维数据的能力。这些分析的核心是通过确定一小部分重要变量或获得原始测量的几个组合来降低数据维度的方法，有时会显著降低数据的维度。该项目旨在开发一系列新的降维方法来解决高维数据分析中的这些紧迫挑战。预计拟议的研究将在两个方面做出重大贡献：使科学家能够快速有效地从海量数据中提取有用的信息，同时使统计学科在理论、方法和应用方面的进步受益。