Abstract: Because the Small Sample Size (SSS) problem usually leads to singularity of the within-class scatter matrix, there will be an ill-posed problem in solving the generalized character equation. An improved algorithm based on former ones was proposed. It introduced mirror image to enlarge sample capacity and adopted the method of the null space of the within-class scatter matrix Sw to get the best solution of Fisher criterion. Experimental results on ORL face database and Yale face database show that the proposed algorithm is more effective than traditional Linear Discriminant Analysis (LDA), Independent Components Analysis (ICA) and 2-Dimensional Symmetric Principal Component Analysis (2DSPCA).

Key words: Linear Discriminant Analysis (LDA), Small Sample Size (SSS) problem, mirror image, null space, between-class scatter matrix, within-class scatter matrix

摘要： 小样本问题的存在使得类内离散度矩阵为奇异阵,因此求解线性判别分析(LDA)算法的广义特征方程存在病态奇异问题。为解决此问题,在已有算法的基础上,引入镜像图像来扩大样本容量,并采用零空间的方法求得Fisher准则函数的最优解。通过在ORL和Yale标准人脸库上的实验结果表明,人脸识别效果优于传统LDA方法、独立成分分析(ICA)方法以及二维对称主成分分析(2DSPCA)方法。

关键词: 线性判别分析, 小样本问题, 镜像图像, 零空间, 类间离散度, 类内离散度