利用标准化LDA进行人脸识别

线性判别分析（LDA）是一种较为普遍的用于特征提取的线性分类方法。提出一种基于LDA的人脸识别方法－－标准化LDA，该方法克服了传统LDA方法的缺点，重新定义了样本类间离散度矩阵，在原始定义的基础上增加一个由类间距离决定的可变权函数，使得在选择投地，能够更好地分开各个类的样本；同时，它采用一种合理而有效的方法解决矩阵奇异的问题，即保留样本类内离散度矩阵的零空间，因为这个空间包含了最具有判别能力的信息。在这个零空间里，寻找对应于样本类间离散度矩阵的较大特征值的特征向量作为最后降维的转换矩阵。实验结果显示，在人脸识别中，与传统LDA相比，该方法有更好的识别率。标准化LDA也可以用于其他图像识别问题。

Normalized LDA Method for Face Recognition

Linear Discriminant Analysis (LDA) is one of the most popular linear classification techniques for feature extraction. A new approach of Normalized-LDA is introduced to overcome the drawbacks existing in the traditional LDA method. It redefines the between-class scatter by adding a weight function according to the between-class distance. Therefore, it can separate the classes as much as possible. At the same time, it projects the between-class scatter into the null space of within-class scatter that contains the most discriminant information. Hence, the transformation matrix composed with the largest eigenvectors of the transferred between-class scatter can maximize the Fisher Criteria. Experimental results show this method achieves better performance of face recognition in comparison with the traditional LDA method. It can also be applied to other problems of image recognition.