Adaptive graph-regularized fixed rank representation for subspace segmentation

Low-rank representation (LRR) has shown its great power in subspace segmentation tasks. However, by using matrix factorization skill, fixed-rank representation dominates LRR in many subspace segmentation applications. In this paper, based on the depth analyses on fixed-rank representation (FRR), we propose a new graph-regularized FRR method which is termed adaptive graph-regularized fixed-rank representation (AGFRR). Different from the existing methods which use the original data set to build the graph regularizer for a reconstruction coefficient matrix, AGFRR uses one of the matrix factor of a reconstruction matrix to construct the graph regularizer for the reconstruction matrix itself. We claim that the constructed graph regularizer can discover the manifold structure of a given data set more faithfully. Hence, AGFRR is more suitable for revealing the nonlinear subspace structures of data sets than FRR. Moreover, an optimization algorithm for solving AGFRR problem is also provided. Finally, the subspace segmentation experiments on both synthetic and real-world data sets show that AGFRR is superior to the existing LRR and FRR-related algorithms.