Probabilistic collaborative representation on Grassmann manifold for image set classification

• DOI: 10.1007/s00521-020-05089-x
• Publication Date: 2020-07-04T13:03:41Z
• Authors: Shuo Zhang; Dong Wei; Wenzhu Yan; Quansen Sun
• Keywords: Robustness; Manifold (fluid mechanics); Contextual image classification; Representation

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.