Riemannian manifold has attracted an increasing amount of attention for visual classification tasks, especially for video or image set classification. Covariance matrices are the natural second-order statistics of image sets. However, nonsingular covariance matrices, known as symmetric positive defined (SPD) matrices, lie on the non-Euclidean Riemannian manifold (SPD manifold). Covariance discriminative learning (CDL) is an effective discriminative learning method that employs the Riemannian manifold in the SPD kernel space. However, in practice, the discriminative learning of CDL often suffers from the problems of poor generalization and overfitting caused by a finite number of training samples and noise corruption. Hence, we propose to address these problems by importing eigenspectrum regularization and graph-embedded frameworks. Discriminative learning with SPD manifold is generalized by the graph-embedded framework, which combines with eigenspectrum regularization in the SPD kernel space. Three local Laplacian graphs of graph-embedded framework and two eigenspectrum regularized models are incorporated to the proposed method. Comprehensive mathematical deduction of the proposed method is depicted with the “kernel tricks.” Experimental results on set-based face recognition and object categorization tasks reveal the effectiveness of the proposed method.

中文翻译：

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图像集分类的正则化图嵌入协方差判别学习

黎曼流形在视觉分类任务中，尤其是在视频或图像集分类中，吸引了越来越多的关注。协方差矩阵是图像集的自然二阶统计量。但是，称为非对称正定义（SPD）矩阵的非奇异协方差矩阵位于非欧氏黎曼流形（SPD流形）上。协方差判别学习（CDL）是一种有效的判别学习方法，它在SPD内核空间中采用黎曼流形。然而，在实践中，由于有限数量的训练样本和噪声破坏，CDL的判别式学习经常遭受泛化和拟合度差的问题。因此，我们建议通过引入特征谱正则化和图嵌入框架来解决这些问题。图嵌入框架概括了使用SPD流形的判别式学习，该框架结合了SPD内核空间中的本征谱正则化。该方法结合了图嵌入框架的三个局部拉普拉斯图和两个特征谱正则化模型。用“内核技巧”描述了所提出方法的综合数学推论。基于集合的人脸识别和目标分类任务的实验结果证明了该方法的有效性。用“内核技巧”描述了所提出方法的综合数学推论。基于集合的人脸识别和目标分类任务的实验结果证明了该方法的有效性。用“内核技巧”描述了所提出方法的综合数学推论。基于集合的人脸识别和目标分类任务的实验结果证明了该方法的有效性。