Learning adaptive Grassmann neighbors for image-set analysis

Abstract

Representing image sets as subspaces on Grassmann manifold and leveraging the Riemannian geometry of this space has proven to be highly effective in various visual recognition tasks. However, the computational cost associated with operating on Riemannian manifolds, especially of high-dimensional ones, poses a significant limitation to the applicability of existing techniques. Moreover, the image sets with labels are scarce and valuable in real-world scenarios, where the manual annotation is time-consuming and costly. To tackle these issues, in this paper, we propose an unsupervised Grassmannian dimensionality reduction method for image set classification and clustering, which simultaneously performs local structure learning and dimensionality reduction under the subspace view. Specifically, instead of relying on the pre-defined similarity matrix that obtained from raw data and may contain much noise, we adaptively learn the local structures from the projected low-dimensional Grassmann manifold. The refined structures then provide more discriminative power to learn the accurate manifold-to-manifold mapping. To better preserve the global structure of the data, this mapping is constrained to satisfy the orthogonal condition. In addition, our model can be compatible with F-norm OLPP for Grassmann manifold when the squared F-norm is transformed into projection metric. A re-weighted iterative scheme is carefully developed to optimize the problem. Experimental results on several benchmark datasets for image set classification and clustering tasks clearly demonstrate that our model consistently outperforms baselines, yielding significant improvements.