PDEs对单向二维CCA的影响  

Effects of PDEs on One-directional Two-dimensional CCA

作　　者：陈柯鑫 范丽亚[1] CHEN Kexin;FAN Liya(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2021年第2期14-25,95,共13页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(11801248);山东省自然科学基金项目(ZR2016AM24,ZR2018BF010)资助。

摘　　要：累计贡献率(CCR)决定着降维子空间的维度,贡献率越高,维度越大,计算成本也越高,但对图像的识别精度来说却并不一定越好。利用单向二维典型相关分析(2D-CCA)进行图像特征抽取时面临的CCR如何选取问题,目前还没有一个有效的解决方案。偏微分方程组(PDEs)与一维典型相关分析(CCA)的算法结合并没有解决CCA存在的会破坏图像的空间结构,丢失图像的判别信息以及造成“维数灾难”等问题。为解决上述问题,提出了将PDEs与单向2D-CCA结合的一体化学习算法,着重研究了PDEs对2D-CCA中CCR的影响。在AR数据集、FRGCv数据集上的实验以及对比实验的结果表明PDEs的进化不仅可以弱化2D-CCA中CCR的选择,甚至不用考虑CCR的选择,原则上不超过5次的进化可达到最优识别精度,且识别精度明显优于基于PDEs的一维CCA算法。The CCR determines the dimension of the reduced subspace,the higher the contribution rate is,the larger the dimension is and the higher the calculation cost is.However,it is not necessarily better for the image recognition accuracy.The selection problem of cumulative contribution rate(CCR)has to faced by using one-directional two-dimensional canonical correlation analysis(2D-CCA)for image feature extraction,and there is no effective solution at present.The combination of PDEs and one-dimensional canonical correlation analysis(CCA)does not solve the problems of CCA,such as destroying the spatial structure of the image,losing the discrimination information of the image and causing the"dimension disaster".To solve the above problems,an integrated learning algorithm combining PDEs with one-directional 2D-CCA is proposed,and the influence of PDEs on CCR in 2D-CCA is emphatically studied.The experimental results on AR dataset and FRGCv dataset and comparative experiments show that the evolution of PDEs can not only weaken the choice of CCR in 2D-CCA,but also do not need to consider the choice of CCR.In principle,no more than five evolutions can achieve the best recognition accuracy,and the recognition accuracy is obviously better than that of one-dimensional CCA algorithm based on PDEs.

关 键 词：图像识别 二维典型相关分析 偏微分方程 累积贡献率 进化次数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]