基于改进分数阶SVD的块协作表示的小样本人脸识别算法

随着训练样本数目减少，传统人脸识别方法的性能会急剧下降，因此提出了改进的分数阶SVD（IFSVDR）的块协作表示算法，以提高小样本下人脸识别率。为了减少噪声对分类的干扰，对SVD算法进行改进，利用分数阶增大主要正交基权值，提高特征的判别力；对相对较小权值进行抑制，降低噪声的干扰。然后，将得到的特征图像用基于块的协作表示算法进行分类（PCRC）。相对传统稀疏分类算法，PCRC融合了集成学习，能更好地解决小样本问题，且CRC计算复杂度低于SRC。在扩展的Yale B和AR人脸数据库上的实验表明，本文提出的算法在单样本的情况下也有较高的识别率。

A small sample face recognition algorithm based on improved fractional order singular value decomposition and collaborative representation classification

With the reduction of training samples, the performance of traditional face recognition methods drops sharply. We propose an improved fractional order singular value decomposition (IFSVDR) method combined with patch based CRC (PCRC) framework. As the performance can be affected when training samples contain noise, we improve the SVD algorithm by using the fractional order to increase the weight of the main orthogonal basis, and decrease the weight of the relatively small basis to reduce the influence of noise on classification results. Then, we use the PCRC to classify the patches which are reconstructed by the IFSVDR. Compared with the classical sparse representation, the idea of ensemble learning enables the PCRC to deal with the small sample size problem. And the CRC has a lower computation complexity than the SRC. Experiments on the extended Yale B and AR face databases show that the proposed IFSVDR combining with the PCRC has a high recognition rate, even in the case of small sample.