结合零空间法和F-LDA的人脸识别算法

线性判别分析（LDA）是一种常用的线性特征提取方法。传统LDA应用于人脸识别时主要存在两个问题：1）小样本问题，即由于训练样本不足引起矩阵奇异； 2)优化准则函数并不直接与识别率相关。提出了一种新的能同时解决以上两个问题的基于LDA的人脸识别算法。首先，通过重新定义样本的类内散布矩阵和类间散布矩阵，提出了一种新的零空间法。然后把这种新的零空间法与F LDA（Fractional LDA）算法相结合，得到一种对人脸识别更有效的特征提取方法。实验结果表明，这种新算法具有较高的识别率。

Face recognition combining the null space approach and the fractional LDA

Linear discriminant analysis is one of the most popular linear projection techniques for feature extraction.The traditional LDA-based methods suffer from two main disadvantages: 1) the small sample size(SSS) problem;2) their optimization criteria are not directly related to the classification accuracy.A new LDA-based technique was proposed,which could overcome the above shortcomings.First, by redefining the within class scatter matrix and the between class scatter matrix,a new null space method was presented.Then,combined the new null space method with F-LDA(fractional LDA) algorithm,a completely new feature extraction algorithm for face recognition was given.The experimental results show that the new LDA-based feature extraction algorithm improves the performance of face recognition significantly.