For image-set based classification, sparse coding and collaborative representation have gained a lot of attention due to their robustness and effectiveness. However, most existing methods focus on collaborative representation in Euclidean space. It still remains a research gap to handle this problem from Geometry-Aware perspective and interpret the mechanism of collaborative representation on nonlinear manifold. In this paper, we propose a novel method named probabilistic collaborative representation on Grassmann manifold for image set classification, which is interpreted from a probabilistic viewpoint. Specifically, we regard each image set as a point on Grassmann manifold inspired by its non-Euclidean geometry and then perform collaborative representation on the space of symmetric matrices, which enables us to explain the internal mechanism of classification and derive a closed form solution. Moreover, classification criterion is designed to further improve the performance of the proposed method. Experimental results on four databases (i.e. Honda/UCSD, YaleB, Youtube Celebrities and ETH-80) for face recognition task and object recognition task demonstrate the robustness and effectiveness of our proposed method.

对于基于图像集的分类，稀疏编码和协作表示由于其鲁棒性和有效性而备受关注。但是，大多数现有方法都集中在欧几里得空间中的协作表示。从Geometry-Aware角度处理此问题并解释非线性流形上的协同表示机制仍然存在研究空白。在本文中，我们提出了一种基于格拉斯曼流形的概率协同表示方法，用于图像集分类。具体来说，我们将每个图像集视为格拉斯曼流形上非欧几里德几何形状启发的一个点，然后在对称矩阵的空间上进行协作表示，这使我们能够解释分类的内部机制并得出封闭形式的解决方案。此外，设计分类标准以进一步提高所提出方法的性能。在四个数据库（即Honda / UCSD，YaleB，Youtube Celebrities和ETH-80）上进行面部识别任务和对象识别任务的实验结果证明了该方法的鲁棒性和有效性。