Cevikalp Hakan, Neamtu Marian, Wilkes Mitch, Barkana Atalay
Department of Electrical Engineering and Computer Science, Vanderbilt University, Box 131, Station B, Nashville, TN 37235, USA.
IEEE Trans Pattern Anal Mach Intell. 2005 Jan;27(1):4-13. doi: 10.1109/tpami.2005.9.
In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the within-class scatter matrix is singular and the Linear Discriminant Analysis (LDA) method cannot be applied directly. This problem is known as the "small sample size" problem. In this paper, we propose a new face recognition method called the Discriminative Common Vector method based on a variation of Fisher's Linear Discriminant Analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the within-class scatter matrix of the samples in the training set while the other uses the subspace methods and the Gram-Schmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher's Linear Discriminant criterion given in the paper. Our test results show that the Discriminative Common Vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability.
在人脸识别任务中，样本空间的维度通常大于训练集中样本的数量。因此，类内散布矩阵是奇异的，线性判别分析（LDA）方法不能直接应用。这个问题被称为“小样本量”问题。在本文中，我们针对小样本量情况，基于Fisher线性判别分析的一种变体，提出了一种新的人脸识别方法，称为判别公共向量方法。给出了两种不同的算法来提取表示人脸数据库训练集中每个人的判别公共向量。一种算法使用训练集中样本的类内散布矩阵，而另一种算法使用子空间方法和Gram-Schmidt正交化过程来获得判别公共向量。然后，将判别公共向量用于新面孔的分类。所提出的方法为最大化本文给出的修正Fisher线性判别准则提供了一个最优解。我们的测试结果表明，判别公共向量方法在识别准确率、效率和数值稳定性方面优于其他方法。
