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...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 regressionclassification 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LLRCDA比现有方法更具有优越性。展开更多
In this article, we start by a review of the circle group? [1] and its topology induced [1] by the quotient metric, which we later use to define a topological structure on the unit circle . Using points on? under the ...In this article, we start by a review of the circle group? [1] and its topology induced [1] by the quotient metric, which we later use to define a topological structure on the unit circle . Using points on? under the complex exponential map, we can construct orthogonal projection operators. We will show that under this construction, we arrive at a topological group, denoted? of projection matrices. Together with the induced topology, it will be demonstrated that? is Hausdorff and Second Countable forming a topological manifold. Moreover, I will use an example of a group action on? to generate subgroups of?.展开更多
文摘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 regressionclassification 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LLRCDA比现有方法更具有优越性。
文摘In this article, we start by a review of the circle group? [1] and its topology induced [1] by the quotient metric, which we later use to define a topological structure on the unit circle . Using points on? under the complex exponential map, we can construct orthogonal projection operators. We will show that under this construction, we arrive at a topological group, denoted? of projection matrices. Together with the induced topology, it will be demonstrated that? is Hausdorff and Second Countable forming a topological manifold. Moreover, I will use an example of a group action on? to generate subgroups of?.
