Convex Hull Collaborative Representation Learning on Grassmann Manifold with  \(L_1\) Norm Regularization

Collaborative representation learning mechanism has recently attracted great interest in computer vision and pattern recognition. Previous image set classification methods mainly focus on deriving collaborative representation models on Euclidean space. However, the underlying manifold geometry structure of the image set is not well considered. In this paper, we propose a novel manifold convex hull collaborative representation framework with \(L_1\) norm regularization from geometry-aware perspective. Our model achieves the goal of inheriting the highly expressive representation capability of the Grassmann manifold, while also maintaining the flexible nature of the convex hull model. Notably, the collaborative representation mechanism emphasizes the exploration of connections between different convex hulls on Grassmann manifold. Besides, we regularize the collaborative representation coefficients by using the \(L_1\) norm, which exhibits superior noise robustness and satisfies the data reconstruction requirements. Extensive experiments and comprehensive comparisons demonstrate the effectiveness of our method over other image set classification methods.