Research On Weighted Sparse Low-rank Subspace Clustering Algorithm

Subspace clustering refers to cluster the high-dimensional data from different subspaces into the low-dimensional subspaces in which the data originally belongs to.As a method of clustering high-dimensional data,subspace clustering is widely used in pattern recognition and computer vision.Sparse subspace clustering mainly uses the sparse representation coefficient matrix of high-dimensional data to construct the affinity matrix,and then uses the spectral clustering method to obtain the final results.Based on the sparsity and low rank of the coefficient matrix,we try to seek for a model which can reveal the structure of the high-dimensional data.The contributions of this thesis are listed as follows:(1)A fractional-order function based reweighted l1 minimization framework is proposed.The framework introduces the fractional-order function into the original reweighted l1 minimization framework.In the subspace clustering problem,the l0 norm is utilized to capture the sparsity of the data,which is,however,a NP-hard problem.Then the l1 norm is widely used to replace the l0 norm.In this paper,a fractional-order function based reweighted l1 minimization framework is proposed which can better approximate l0 norm.In addition,the framework is introduced into SSC model and the fractional-order function based reweighted sparse subspace clustering model(FRSSC)is proposed.Experimental results on the motion segmentation and face clustering datasets prove that the model increases the accuracy.(2)A fractional-order function based reweighted nuclear norm minimization framework(FWNNM)is proposed.In the subspace clustering problem,rank is used to capture the global structure of the data.Nuclear norm is regarded as a convex relaxation of rank minimization problem,which is also a NP-hard problem.The FWNNM framework can better approximate the rank minimization problem than the original nuclear norm.In addition,the FWNNM framework is introduced into LRR model and weight constraints are imposed on the singular value of the coefficient matrix.Then the fractional-order function based reweighted nuclear norm minimization low rank representation is proposed.Experimental results on the motion segmentation and face clustering datasets prove that the good performance of the model.(3)Considering the sparsity and low rank simultaneously,reweighted l1 minimization framework is introduced into the LRSSC model and the fractional-order function based low rank sparse subspace clustering method(FRLRSSC)is proposed.We want to obtain the sparser coefficient matrix and ensure the global structure of the data at the same time.Experimental results on the motion segmentation dataset show that FRLRSSC model has good performance on the data which has more complex structure.