Abstract: Principal Component Analysis（PCA） is a classical method for dimension reduction. 2DPCA is able to extract features fast because it does not transform image matrices into vectors before extracting features. However, both PCA and 2DPCA are often not robust in the case of outliers since they are based on L2-norm. Moreover, the solution to PCA or 2DPCA is generally not sparse. A new method based on L1 norm with Lp-norm constraints is proposed. It can obtain the sparse solution when the parameter p approaches 1. This method is not only fast and convenient just like 2DPCA, but also generic and less sensitive to outliers. Besides, it is proved that this proposed method can obtain a local maximal solution. Some experiments are carried out on ORL and UMIST face data sets to demonstrate the effectiveness of the proposed method.

Key words: principal component analysis, face recognition, feature extraction, 2 Dimension Principal Component Analysis（2DPCA）, Lp-norm, ORL face data set

摘要： 主成分分析（PCA）是降维的一种经典方法。二维主成分分析（2DPCA）在特征抽取之前不需要将图像矩阵转化为向量形式，所以能快速地提取特征。但是基于L2范数的PCA和2DPCA在遇到异常值时的表现不稳定而且得到的向量通常不是稀疏的。提出了一种基于L1范数的且受Lp范数约束的2DPCA方法（2DPCA-Lp）。当参数p接近1时，它可以得到稀疏的解。该方法既具有2DPCA的快速方便性，又是泛化的并且对异常值较不敏感。同时也证明该方法可以取得一个局部最大化的解。通过在ORL和UMIST人脸库上的实验表明了该方法的有效性。

关键词: 主成分分析, 脸识别, 特征提取, 二维主成份分析, Lp范数, ORL人脸库