Kernelized Low Rank Representation on Grassmann Manifolds
This work addresses subspace clustering for computer vision tasks, but it is incremental as it extends an existing method to a new mathematical space.
The authors tackled the problem of clustering subspaces on Grassmann manifolds by generalizing low rank representation (LRR) from Euclidean space to a kernelized framework, and experimental results on datasets like handwritten digits and face clips showed that the proposed methods outperformed state-of-the-art subspace clustering methods.
Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to generalize LRR on Euclidean space onto an LRR model on Grassmann manifold in a uniform kernelized framework. The new methods have many applications in computer vision tasks. Several clustering experiments are conducted on handwritten digit images, dynamic textures, human face clips and traffic scene sequences. The experimental results show that the proposed methods outperform a number of state-of-the-art subspace clustering methods.