Sequential Subspace Clustering Based On Sparse And Low-rank Representation

Sparse and low-rank representation based subspace clustering is an important technique to process and analyze image and video data,which has been widely used in machine learning,computer vision,etc.However,for sequential data,a main challenge in subspace clustering is to effectively exploit spatial-temporal information.Therefore,according to intraclass sample similarity and interclass sample difference of sequential data,three sequential subspace clustering methods are proposed in this paper.The detail is as follows:1.Robust sequential subspace clustering via l1 norm temporal graph is proposed.Firstly,the l1-norm temporal graph is designed to encode the temporal information underlying in sequential data.By using the l2 norm,it can enforce well temporal similarity of neighboring frames with a sample-dependent weight,and mitigate the effect of noises and outliers on subspace clustering because large errors mixed in the real data can be suppressed.Then,under the assumption of data self-expression,our clustering model is put forward by further integrating the classical sparse subspace clustering and the l1-norm temporal graph.To solve the proposed model,we introduce a new efficient proximity algorithm with convergence analysis.Finally,experimental results on both synthetic and real data demonstrate the efficacy of our method and its superior performance over the state-of-the-art methods.2.Sequential subspace clustering based on joint lp and l2,p-norms minimization is proposed.Firstly,by defining the sample-distance dependent weights,a l2,p-norm temporal graph is constructed to depict local similarity along the temporal direction.Secondly,the non-convex lp-norm(0<p<1)minimization usually delivers better results than that of convex l1-norm minimization,and it can also remove more links between semantically-unrelated samples,therefore,lp norm is adopted to measure the sparsity of representation matrix.Finally,the linearized alternating direction method is used to solve the optimization model,experimental results on video dataset,motion dataset and face dataset confirm the effectiveness of the proposed method.3.Sequential subspace clustering via integrating feature selection and spatial-temporal weights is proposed.Firstly,feature selection is used to select the sample relevant features to construct the spatial weights,a l1-norm spatial-temporal graph is designed to encode the spatial-temporal information underlying in sequential data.Then,considering that the linear dependence of sequential neighboring subspaces,in order to enhance block diagonal property of matrix,the weights of spatial-temporal constraint is constructed.Moreover,our clustering model is put forward by further integrating the low-rank representation,l1-norm spatialtemporal graph and weighted spatial-temporal constraint,and that linearized alternating direction method is adopted to optimize the model.Finally,experimental results on real datasets demonstrate that this method is effective and competitive.