Subspace Learning Based Low-Rank Representation

Subspace clustering has been a foundation problem in the field of computational vision and it has been widely applied in motion segmentation,image segmentation and face recognition,etc.In the past decades,researchers have presented various algorithms for subspace clustering.However,due to data missing,data corruption,uncertainty for the number of subspaces and the dimension of subspace and randomicity for the position between subspaces,subspace clustering is a challenging task.Numerous subspace segmentation methods have been proposed in the past two decades,and can be classified into four categories including algebraic approaches,statistical approaches,iterative approaches,and spectral clustering based approaches.Spectral clustering based approaches are very popular in recent years.There are two typical spectral clustering based methods,which include low rank representation(LRR)and sparse subspace clustering(SSC).And LRR and SSC have generated a number of literatures,such as LSR,SCLLR and SL3 C,etc.All of the above methods employ the self-representation of the data points in raw space to extract the similarity.However,better relationship will be explored if we use the self-representation of the data points in other subspace.So in this paper,we propose subspace learning based low rank representation to learn a subspace favoring the similarity extraction for the low rank representation.Different from the methods incorporating PCA in the model,since we simultaneously learn the subspace and obtain the low rank representation,the noise can not only be removed efficiently but also the better relationship between data can be obtained.We develop a principle for subspace learning in this paper,and this will be applied to mine data for subspace.Manifold clustering includes two branches: linear and nonlinear,and the linear case is subspace clustering.First,we develop our model only devoted to subspace segmentation.Then by extending the mapping from linear to nonlinear,our model can also be applied for nonlinear manifold clustering.Experiments on five databases such as Hopkins 155,Extended Yale B,CMU PIE,COIL-20 and USC SIPI demonstrate that our method is effective and outperform other state-of-the-art algorithms.