Nonlinear low-rank representation on Stiefel manifolds

Recently, the low-rank representation (LRR) has been widely used in computer vision and pattern recognition with great success owing to its effectiveness and robustness for data clustering. However, the traditional LRR mainly focuses on the data from Euclidean space and is not directly applicable to manifold-valued data. A way to extend the LRR model from Euclidean space to the Stiefel manifold, by incorporating the intrinsic geometry of the manifold, is proposed. Under LRR, an appropriate affinity matrix for data on the Stiefel manifold can be learned; subsequently data clustering can be efficiently performed on the manifold. Experiments on several directional datasets demonstrate its superior performance on clustering compared with the state-of-the-art approaches.