Mathematical Sciences: High Dimensional Data Analysis

项目申请：9505583 PI: Ker-Chau Li所在机构：UCLA题目：高维数据分析摘要：本研究涉及发展新的统计方法来探索高维数据中的非线性。两种工具，切片逆回归（SIR）和主要Hessian方向（PHD），已经基于降维理论开发，这是研究者在高维领域的方法的基础。为了继续这条研究路线，研究者研究了几个比基本回归公式结构更复杂的新问题。研究课题包括将SIR/PHD推广到多个结果，发展基于博士的树状结构方法，研究数学/物理/计算机模型的可视化，以及分析非线性时间序列数据。该研究将动态图形学、计算学和统计理论相结合来研究高维数据。维度是当今许多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.