RIA: The Canonical Correlations: Numerical Algorithms and Extensions

RIA：规范相关性：数值算法和扩展

• 批准号: 9308399
• 负责人: Hongyuan Zha
• 金额: $ 7.17万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9308399&HistoricalAwards=false
• 关键词: RIA; Canonical; Correlations; Numerical; Algorithms

The goal of this research is to carry out the analysis of structured (e.g.Toeplitz) matrix pairs and to analyze the convergence behavior of the numerical algorithm connection with constructing efficient preconditioners. Numerical algorithms are developed for updating and downdating problems associated with canonical correlations when data points are added or deleted. Theories and algorithms are developed for the following extensions of canonical correlations: canonical correlations with a general bilinear form, canonical correlations with linear equality constraints, canonical correlations of several data sets. This research is expected to yield new concepts in matrix decompositions and numerical linear algebra and statistical computation, and facilitate and further spread the use of canonical correlation analysis in the general scientific community.

本研究的目的是开展 分析结构化（如Toeplitz）矩阵对，并分析数值算法的收敛行为 与构建高效的预处理器有关。 数值算法的开发与典型的相关性，当数据点被添加或删除的更新和更新问题。 典型相关的理论和算法的下列扩展：典型相关的一般双线性形式，典型相关的线性等式约束，典型相关的几个数据集。 这项研究预计将产生新的概念，矩阵分解和数值线性代数和统计计算，并促进和进一步推广典型相关分析在一般科学界的使用。