Low Rank Representation on Grassmann Manifolds: An Extrinsic Perspective
This work addresses subspace clustering in computer vision, offering an incremental improvement for tasks like video and image analysis.
The paper tackles the problem of extending low-rank representation (LRR) to Grassmann manifolds for subspace clustering by proposing an extrinsic approach using tangent spaces, and experimental results on datasets like handwritten digits and videos show it outperforms existing methods.
Many computer vision algorithms employ subspace models to represent data. The Low-rank representation (LRR) has been successfully applied in subspace clustering for which data are clustered according to their subspace structures. The possibility of extending LRR on Grassmann manifold is explored in this paper. Rather than directly embedding Grassmann manifold into a symmetric matrix space, an extrinsic view is taken by building the self-representation of LRR over the tangent space of each Grassmannian point. A new algorithm for solving the proposed Grassmannian LRR model is designed and implemented. Several clustering experiments are conducted on handwritten digits dataset, dynamic texture video clips and YouTube celebrity face video data. The experimental results show our method outperforms a number of existing methods.