人脸识别中线性判别分析的单参数正则化方法

A Single-Parameter-Regularized Method in Linear Discriminant Analysis for Face Recognition

将线性判别分析(LDA)应用于人脸识别中时,小样本问题常常出现,即,通常可获得的人脸训练样本个数远小于训练样本的维数,从而导致类内散布矩阵Sw奇异,于是得到病态的特征值问题。使用数学工具探讨了这一现象的实质。此外,提出了一种单参数正则化方法来解决小样本问题,该方法以满足tr(Swr)=tr(Sw)为条件,用一个可逆矩阵Srw去估计奇异的类内散布矩阵Sw。在使用小波变换对人脸像降维预处理后进行了该方法与传统LDA的对比实验。实验表明,该方法可大幅提高LDA的识别性能。

When Linear Discriminant Analysis （LDA） is applied to face recognition, the Small Sample Size Problem often occurs because the number of training samples is far smaller than the dimensionality of training sampies, which leads to a singular within - class scatter matrix S, and an ill - posed eigenvalue problem. In this paper, mathematical tools are used to explore the nature of this phenomenon. Moreover, a Single - Parameter - Regularized method is proposed to solve the Small Sample Size Problem. This method is to find an invertible matrix Sw^r to estimate the singular within - class scatter matrix Sw based on tr （ Sw^r ） = tr （ Sw ）. After the dimensionality - reduction pre - process of human face images using wavelet transform, the proposed method is compared with the traditional LDA experimentally. Experiment results show that the proposed method improves the recognition performance of LDA greatly.