基于L-p范数的二维最大间距准则及其在人脸识别中的应用  

L-p norm basedon two-dimensional maximum margin criterion with application on face recognition

作　　者：张仕霞 金聪[1] 

机构地区：[1]华中师范大学计算机学院,武汉430079

出　　处：《电子测量技术》2017年第12期196-202,共7页Electronic Measurement Technology

基　　金：国家社会科学基金(13BTQ050)项目资助

摘　　要：在二维图像投影降维时,经常使用L-2范数和L-1范数构建降维模型,在一定程度上实现了降维的目标。但是这些方法只适用于单一范数,有很大局限。本文提出了一个新的方法,降维目标函数采用L-p范数(1≤p≤2),这种方法可以构建更加一般化的降维模型,适用于所有同类模型的求解,p=1和p=2可以视作这个模型的特殊情况。所提的方法比单一的L1或L2范数具有更强的灵活性,能够适应不同问题。本文采用目标函数为L-p范数的二维最大间距准则,同时定义了类内离散因子对原始数据降维。通过在ORL和Yale以及加噪数据库上的实验表明本文方法具有更好的鲁棒性和高效性。Among the dimensionality reduction methods of 2 Dimage,they often use L-2 norm and L-1 norm to construct the dimension reduction model,to a some extent,they realize the goal of dimension reduction.However,these methods only apply to the single norm,which is very limited.In this paper,we propose a new method,which uses L-p norm（1≤p≤2）instead of a single one.This method can construct a more generalized dimension reduction model and is suitable for all similar models.p=1 and p=2 can be regarded as a special case of this model.The proposed method is more flexible than a L1 or L2 norm and can adapt to different problems.In this paper,the objective function adopts the L-p norm of the two-dimensional maximum margin criterion,and the intra-class discrete factor is defined to reduce the original data.The experiments on ORL and Yale and noise reduction databases show better robustness and efficiency.

关 键 词：二维最大间距准则 特征提取 人脸识别 L-p范数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]