项目面向主成分分析（Principal Component Analysis, PCA）这一重要的基础理论方法展开深入研究，认为一个好的主成分分析方法应该同时具备鲁棒性、归纳性、准确性、快速性。然而，虽然当前的PCA拓展方法众多，但是缺乏同时具备上述四个性质的通用框架。为此，项目以构建同时具备上述四个性质的PCA通用框架为最终研究目标，基于已具备鲁棒性和归纳性的PCA方法，研究自动去均值和Schatten-p范数来提升优化解的准确性；在此基础上，研究具有等价优化解和近似优化解的加速策略来提升优化效率，并给出有效的理论证明。本项目的研究成果可直接应用于前景-背景分割等高维数据中，能够促进和完善PCA方法的理论发展，也能启发同类研究。

The project is oriented to Principal Component Analysis (PCA), an important and basic research method, believing that a good principal component analysis method should be robust, inductive, accurate and fast. However, although there are many variants of PCA, there is a lack of generalization framework with the above four properties. In order to build a generalization framework of PCA that have those four properties mentioned above, this project will study the automatic mean removal and Schatten-p norm to improve the accuracy of optimization solution; will study the acceleration strategy with the equivlalent optimization solution and the approximated optimization solution to improve the optimization efficiency, and provide the effective theoretical proof. The research results of this project can be directly applied to high-dimensional data such as foreground-background segmentation, can promote and improve the theoretical development of PCA, and can also inspire the similar research.