中文摘要：

将图像集合表示为格拉斯曼流形上的点能够获得更好的识别性能。传统格拉斯曼流形上的判别分析方法仅考虑了带标签样本的统计信息,忽略了无标签样本。鉴于此,基于流形正则化思想,提出了一个新的格拉斯曼流形上的半监督判别分析方法（SDAGM）,将其应用于图像集合的识别问题。通过构建近邻图刻画格拉斯曼流形上的所有样本局部几何结构,并使其作为正则化项添加到格拉斯曼流形上的判别分析目标函数中,本文方法不但考虑标签信息,而且利用了一致性假设。标准数据集上的实验结果表明了SDAGM的有效性。

英文摘要：

Recent research has shown that a better recognition performance can be attained through representing image sets as points on Grassmannian manifolds. However, the conventional discriminant analysis methods based on such manifolds take into account only the statistical information of labeled samples and suffer from ignoring unlabeled samples. To address this issue,a new method based on manifold regularization, called semi-supervised discriminant Analysis on Grassmannian Manifold（SDAGM）, is presented and applied to the image sets recognition problem. In SDAGM, a nearest neighbor graph is constructed to capture the local geometrical structure of all samples on the Grassmannian manifold and incorporates them into the objective function of discriminant analysis on Grassmannian manifold as a regularization term. Not only does the proposed algorithm consider the label information, but it also uses a consistency assumption. The feasibility and effectiveness of SDAGM are verified on several standard data sets with promising results.