方向数据因其在环境工程、地球科学、信息、生物医学、能源等领域的广泛出现，引起了众多学者的关注。由于方向变量(directional variables)的结构分布特点，传统（线性）变量(linear variables)的统计建模和降维方法已不完全适用于此类变量。本项目将以方向变量与传统变量并存的高维数据为研究对象，拟研究（1）变量间的依存关系；（2）变量的特征提取。本项目将利用完全由数据驱动的非参数回归以及基于条件协方差矩阵的降维方法来解决上述两个问题。目标是在对方向变量与传统变量并存下的高维数据进行降维基础上，建立相应的多元非参数异方差回归模型，并编写相应程序包。本项目的成果将进一步完善非参数回归理论和高维数据降维方法，同时为环境污染监测、基因检测、图像纹理分析等实际问题的解决提供一种新途径。

Recently, directional data has appeared in environmental engineering, earth science, information, biomedical, energy and other areas, which has attracted the attention of many scholars. Due to the structure of the distribution of the direction variables, statistical modeling and dimension reduction methods for linear variables are no longer fully applicable to such variables. Based on the high-dimensional data with directional variables, this project will investigate dependency relationships among variables and select effective variables. Data-driven nonparametric regression and dimension reduction based on the conditions covariance matrix will be used to solve these two problems. Research goal is to firstly provide dimension reduction method for the high-dimensional data with directional variables and then construct the nonparametric regression models with directional variables and then complete the writing of packages. The outcome of this project will further improve the theory of nonparametric models and dimension reduction, while providing new ways for addressing environmental.pollution monitoring, genetic testing, image texture analysis and other practical problems.