基于极小准则的完备正交判别局部保持算法

摘要

A complete orthogonal discriminant locality preserving method based on minimal criterion is proposed on the theory of unsupervised discriminant projection. According to the space information among samples belonging to the same class, the proposed method redefines the within-class and between scatter matrix. Then, according to the objective function of unsupervised discriminant projection, the new objective function is derived, which can address the small sample size problem by being projected into total scatter matrix non-null space. The algorithmic procedure of the proposed method based on QR decomposition is given. Finally, experimental results on face database demonstrate the effectiveness of the proposed method.%以无监督判别投影算法为理论基础,提出了一种基于极小准则的完备正交判别局部保持投影算法.算法首先根据同类样本的空间信息重新定义了类内局部保持散度矩阵与类问局部保持散度矩阵,然后借鉴无监督判别投影算法的目标函数,推导出一个基于极小准则的目标函数,该目标函数通过投影到总体散度矩阵的非零空间中有效地解决小样本问题,最后给出了该算法基于QR分解的正交投影矩阵的求解方法.人脸库上的实验结果表明了所提方法的有效性.