基于广义矩阵指数的判别局部保持投影方法

Discriminant Locality Preserving Projections Method Based on the Generalized Matrix Exponential

【目的】局部保持投影(LPP)是一种经典的非线性数据降维方法。在LPP方法基础上人们提出了判别局部保持投影方法(DLPP),并取得了良好的效果,但DLPP方法存在小样本问题,针对该问题提出了广义矩阵指数判别局部保持投影(GEDLPP)算法。【方法】基于矩阵函数的性质,使用广义矩阵指数函数来重构DLPP,即为GEDLPP算法。【结果】提出的算法有两个优点:一是解决了DLPP方法的小样本问题;二是GEDLPP所隐含的非线性映射拉伸了不同类别样本之间的距离,从而提高了模式分类的能力。【结论】在COIL-20数据库,Yale,Extended Yale B和CMU-PIE人脸数据集上的实验结果表明:与最近提出的解决DLPP小样本问题的改进方法相比,GEDLPP的识别率优于其他方法。

[Purposes]Locality Preserving Projections(LPP)is a classic non-linear dimensionality reduction method,which has paid much attention by researchers.Based on the LPP method,people have proposed the Discriminant Locality Preserving Projections method(DLPP),and achieved good results.However,the DLPP method has the small-sample-size(SSS)problem.[Methods]Based on the nature of matrix exponential function,the generalized matrix exponential function is used to reconstruct the DLPP method,and a new dimensionality reduction method is proposed,called General Exponential Discriminant Locality Preserving Projections(GEDLPP).[Findings]The GEDLPP method has two advantages.First,it addresses the SSS problem of the DLPP.Second,the non-linear mapping implied by GEDLPP enlarges the distance between samples of different categories,thereby improving the performance of pattern classification.[Conclusions]The experimental results on COIL-20 database,Yale,extended Yale B and CMU-PIE face datasets show that,compared with the recently proposed improved method to solve the SSS problem of the DLPP,the recognition rate of GEDLPP is superior to state-of-art methods.