第14卷第5期 智能系统学报 Vol.14 No.5 2019年9月 CAAI Transactions on Intelligent Systems Sep.2019 D0:10.11992/tis.201808007 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.TP.20181223.1553.002.html 面向局部线性回归分类器的判别分析方法 朱换荣，郑智超，孙怀江 (南京理工大学计算机科学与工程学院，江苏南京210094) 摘要：局部线性回归分类器(locality-regularized linear regression classification,.LLRC)在人脸识别上表现出了高 识别率以及高效性的特点，然而原始特征空间并不能保证LLRC的效率。为了提高LLRC的性能，提出了一种 与LLRC相联系的新的降维方法，即面向局部线性回归分类器的判别分析方法(locality-regularized linear regres- sion classification based discriminant analysis,LLRC-DA)。LLRC-DA根据LLRC的决策准则设计目标函数，通过最 大化类间局部重构误差并最小化类内局部重构误差来寻找最优的特征子空间。此外，LLRC-DA通过对投影矩 阵添加正交约束来消除冗余信息。为了有效地求解投影矩阵，利用优化变量之间的关系，提出了一种新的迹比 优化算法。因此LLRC-DA非常适用于LLRC。在FERET和ORL人脸库上进行了实验，实验结果表明LLRC DA比现有方法更具有优越性。 关键词：局部线性回归分类器：维数约简；正交投影；迹比问题；人脸识别；特征提取；判别分析；线性回归分 类器 中图分类号：TP391文献标志码：A文章编号：1673-4785(2019)05-0959-07 中文引用格式：朱换荣，郑智超，孙怀江.面向局部线性回归分类器的判别分析方法.智能系统学报，2019,14(5)： 959-965. 英文引用格式：ZHU Huanrong,ZHENG Zhichao,SUN Huaijiang.Locality-regularized linear regression classification-based dis- criminant analysis JI.CAAI transactions on intelligent systems,2019,14(5):959-965. Locality-regularized linear regression classification-based discriminant analysis ZHU Huanrong,ZHENG Zhichao,SUN Huaijiang (College of Computer Science and Technology,Nanjing University of Science and Technology,Nanjing 210094,China) Abstract:Locality-regularized linear regression classification (LLRC)based face recognition achieves high accuracy and high efficiency.However,the original feature space cannot guarantee the efficiency of LLRC.To improve the per- formance of LLRC,this study proposes a new dimensionality reduction method called locality-regularized linear regres- sion classification-based discriminant analysis (LLRC-DA).which is directly associated with LLRC.The objective func- tion of LLRC-DA is designed according to the classification rule of LLRC.In LLRC.interclass local reconstruction er- rors are maximized and simultaneously,intraclass local reconstruction errors are minimized to identify the optimal fea- ture subspace.In addition,LLRC-DA eliminates redundant information using an orthogonal constraint,imposed on the projection matrix.To effectively obtain the solutions of the projection matrix,we exploit the relationship between op- timal variables and propose a new trace ratio optimization method.Hence,LLRC-DA suits LLRC well.Extensive exper- imental results obtained from the FERET and ORL face databases demonstrate the superiority of the proposed method than state-of-the-art methods. Keywords:locality-regularized linear regression classification;dimensionality reduction;orthogonal projections,trace ratio problem:face recognition:feature extraction:discriminant analysis:linear regression classification 收稿日期：2018-08-09.网络出版日期：2018-12-26 基金项目：国家自然科学基金项目(61772272). 维数约简是帮助我们理解数据特征结构的有 通信作者：朱换荣.E-mail:zhuhuanrong@foxmail.com 效工具，被广泛地应用于人脸识别到、图像检DOI: 10.11992/tis.201808007 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.TP.20181223.1553.002.html 面向局部线性回归分类器的判别分析方法 朱换荣，郑智超，孙怀江 （南京理工大学 计算机科学与工程学院，江苏 南京 210094） 摘 要：局部线性回归分类器 (locality-regularized linear regression classification，LLRC) 在人脸识别上表现出了高 识别率以及高效性的特点，然而原始特征空间并不能保证 LLRC 的效率。为了提高 LLRC 的性能，提出了一种 与 LLRC 相联系的新的降维方法，即面向局部线性回归分类器的判别分析方法 (locality-regularized linear regres￾sion classification based discriminant analysis，LLRC-DA)。LLRC-DA 根据 LLRC 的决策准则设计目标函数，通过最 大化类间局部重构误差并最小化类内局部重构误差来寻找最优的特征子空间。此外，LLRC-DA 通过对投影矩 阵添加正交约束来消除冗余信息。为了有效地求解投影矩阵，利用优化变量之间的关系，提出了一种新的迹比 优化算法。因此 LLRC-DA 非常适用于 LLRC。在 FERET 和 ORL 人脸库上进行了实验，实验结果表明 LLRC￾DA 比现有方法更具有优越性。 关键词：局部线性回归分类器；维数约简；正交投影；迹比问题；人脸识别；特征提取；判别分析；线性回归分 类器 中图分类号：TP391 文献标志码：A 文章编号：1673−4785(2019)05−0959−07 中文引用格式：朱换荣, 郑智超, 孙怀江. 面向局部线性回归分类器的判别分析方法 [J]. 智能系统学报, 2019, 14(5): 959–965. 英文引用格式：ZHU Huanrong, ZHENG Zhichao, SUN Huaijiang. Locality-regularized linear regression classification-based dis￾criminant analysis[J]. CAAI transactions on intelligent systems, 2019, 14(5): 959–965. Locality-regularized linear regression classification-based discriminant analysis ZHU Huanrong，ZHENG Zhichao，SUN Huaijiang (College of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China) Abstract: Locality-regularized linear regression classification (LLRC) based face recognition achieves high accuracy and high efficiency. However, the original feature space cannot guarantee the efficiency of LLRC. To improve the per￾formance of LLRC, this study proposes a new dimensionality reduction method called locality-regularized linear regres￾sion classification-based discriminant analysis (LLRC-DA), which is directly associated with LLRC. The objective func￾tion of LLRC-DA is designed according to the classification rule of LLRC. In LLRC, interclass local reconstruction er￾rors are maximized and simultaneously, intraclass local reconstruction errors are minimized to identify the optimal fea￾ture subspace. In addition, LLRC-DA eliminates redundant information using an orthogonal constraint, imposed on the projection matrix. To effectively obtain the solutions of the projection matrix, we exploit the relationship between op￾timal variables and propose a new trace ratio optimization method. Hence, LLRC-DA suits LLRC well. Extensive exper￾imental results obtained from the FERET and ORL face databases demonstrate the superiority of the proposed method than state-of-the-art methods. Keywords: locality-regularized linear regression classification; dimensionality reduction; orthogonal projections; trace ratio problem; face recognition; feature extraction; discriminant analysis; linear regression classification 维数约简是帮助我们理解数据特征结构的有 效工具，被广泛地应用于人脸识别[ 1 - 3 ] 、图像检 收稿日期：2018−08−09. 网络出版日期：2018−12−26. 基金项目：国家自然科学基金项目 (61772272). 通信作者：朱换荣. E-mail：zhuhuanrong@foxmail.com. 第 14 卷第 5 期 智 能 系 统 学 报 Vol.14 No.5 2019 年 9 月 CAAI Transactions on Intelligent Systems Sep. 2019