分块多线性主成分分析及其在人脸识别中的应用研究

主成分分析(Principal Component Analysis,PCA)是人脸识别中一个经典的算法,但PCA方法在特征提取时考虑的是图像的整体信息,并没有考虑图像的局部信息,而分块PCA(Modular Principal Component Analysis,Modular PCA)则可以有效地提取图像中重要的局部信息,所以在人脸识别实验中获得了比传统PCA更好的识别效果。但PCA和Modular PCA都要进行图像的矢量化,这会破坏原始数据的空间结构,也有可能会导致"维数灾难"。多线性主成分分析(Multilinear Principal Component Analysis,Multilinear PCA)作为PCA在高维数据上的扩展,直接使用矩阵或者高阶的张量来获得有效特征,既可以避免"维数灾难",又可以体现直接将张量数据作为处理对象时保留原始数据较好基本结构信息的优点。在研究Modular PCA和Multilinear PCA的基础上,提出了分块多线性主成分分析(Modular Multilinear Principal Component Analysis,M2PCA)算法,用于识别人脸。在Yale、XM2VTS和JAFFE人脸数据库上进行了人脸识别实验,结果表明,在同等的分块条件下,所提出的方法的识别效果要优于Modular PCA的方法。

Modular Multilinear Principal Component Analysis and Application in Face Recognition

Though principal component analysis (PCA) is a classical method for face recognition,the PCA method extracts global features of the original images,and it does not consider the local discriminant features.In contrast,Modular PCA method extracts the important local discriminant features,and it achieves better performance than the PCA method in face recognition.However,vectorization in PCA or modular PCA often causes "curse of dimensionality".In order to extract features from matrix or higher-order tensor objects directly,multilinear principal component analysis (Multilinear PCA) is developed.Multilinear PCA can avoid "curse of dimensionality",meanwhile it will not destroy the original data structure.Inspired by Modular PCA and Multilinear PCA,we proposed a new method called modular multilinear principal component analysis (M²PCA) for face recognition.Experiments were conducted on the Yale,XM2VTS and JAFFE databases respectively,and experimental results indicate that,under the same condition of sub-blocks,the proposed method is obviously superior to the general Modular PCA.