Research On The Improvement Of Sparse Subspace Clustering

Sparse subspace clustering(SSC)algorithm,the first one to introduce sparse representation into subspace clustering problem,founds a new pattern for the subspace clustering,and has led to the satisfactory results in many applications.SSC is implemented in two phases:learning a sparse affinity matrix through alternating direction method of multipliers and performing spectral clustering on the affinity matrix.However,SSC is suboptimal,because it can not commendably cluster together the correlated data within cluster,as well as explicitly capture the natural relationship between the affinity matrix and the segmentation of the data.Therefore,the improvement based on sparse subspace clustering has received considerable attention in recent years.Motivated by some of the existed algorithm,combinatorial algorithms are presented in this paper.The main improvements include the following three aspects:Firstly,structured and weighted sparse subspace clustering(SWSSC)is combined via exploitation of a joint optimization framework in structured sparse subspace clustering(S3C)and a spatial constraint of data,and the weakness of local constraints is remedied.In the experiment of synthetic data clustering,the effectiveness of the improved algorithm can be proved and it can be applied to color image classification.Secondly,structured and low-rank sparse subspace clustering(SLRSSC)is produced by combining a joint optimization model in S3C with minimizing a weighted sum of nuclear norm in low-rank sparse subspace clustering(LRSSC),which enhance the connection of relevant data.Thirdly,structured adaptive subspace clustering(ASSC)is proposed by using trace Lasso in correlation adaptive subspace segmentation(CASS)instead of l1 norm as regularization constraint and a joint optimization framework in S3C,it can adaptively segment subspace and lead to more dense intra-cluster and more sparse inter-cluster.Experiments on synthetic data,Extended Yale B as well as color image classification and segmentation demonstrate the effectiveness of ASSC approach.