Mathematical Sciences: High Dimensional Data Analysis

建议：9505583 PI：李柯州研究所：加州大学洛杉矶分校题目：高维数据分析摘要：这项研究涉及探索高维数据中非线性的新统计方法的发展。两个工具，切片逆回归(SIR)和主海森方向(PHD)，已经开发了基于降维理论的基础上，研究人员的方法在高维领域。为了继续这一研究，研究人员研究了几个新问题，这些问题的结构比基本回归公式更复杂。研究主题包括将SIR/PHD推广到多个结果，基于PHD的树形结构方法的发展，数学/物理/计算机模型的可视化研究，以及非线性时间序列数据的分析。本研究采用动态图形学、计算和统计理论相结合的方法来研究高维数据。维度是当今人类科学领域最具挑战性的问题之一。这些研究成果的直接应用包括生物医学、社会经济或工业研究中的纵向数据分析，以及水文研究中的地下水建模。

Proposal: 9505583 PI: Ker-Chau Li Institution: UCLA Title: High Dimensional Data Analysis Abstract: The research concerns the development of new statistical methods for exploring nonlinearity in high dimensional data. Two tools, sliced inverse regression (SIR) and principal Hessian directions (PHD), have been developed based on a dimension reduction theory which underlies the investigator's approach in the high-Dimension area. To continue this line of research, the investigator studies several new problems which have more complicated structures than the basic regression formulation. The research topics include the generalization of SIR/PHD to multiple outcomes, development of PHD-based tree-structured methods, study of visualization for mathematical/physical/computer models, and analysis of nonlinear time series data. The research takes a combination of dynamic graphics, computation, and statistical theory to study high dimensional data. Dimensionality is one of the most challenging problems in maly scientific areas today. Immediate applications of these research results include analysis of longitudinal data in biomedical, socio-economic, or industrial studies, and groundwater modeling in hydrological studies.