Kernel Structure Constrained Low-rank Representation

As the explosion of the high-dimensional data,effective analysis and processing about them is important to many problems.Hence,the approach of high-dimensional data clustering analysis is very necessary.Subspace clustering method is one of the effective approaches.Thereinto,spectral clustering-based approaches are very popular techniques.Low-rank representation(LRR)and sparse subspace clustering(SSC)are two representative methods of this kind.However,these methods still have some shortcomings,for e xample,the theoretical guarantee on the performance of LRR requires the condition that the subspaces are independent and the data sampling is sufficient.In order to handle the more general case,structure-constrained low-rank representation(SC-LRR)is proposed for disjoint subspace segmentation to extend LRR.However,in many real-world problems,the data points can be well approximated by a mixture of manifolds instead of only subspaces.This problem is more difficult,but has greater significance.Kernelizing the subspace clustering methods is an important idea for the multi-manifold data.However,the kernelization of some methods is nontrivial,for example,although SC-LRR provides theoretical guarantee on disjoint subspaces,its kernelization will suffer from some technical problems.In this paper,we present kernel structure constrained low-rank representation(KSCLRR)by designing the special iteration of 2,1 norm and provide the related theoretical analysis.Experimental results confirm the effectiveness of KSCLRR for manifold clustering.