Research Of Self-Expressiveness Based Subspace Clustering Methods

The complexities of data are reflected not only in higher dimensions of data,but also in the fact that the data has a multi-view representation obtained from many sources or with different feature construction methods.Self-expressiveness based subspace clustering methods are one of the most important methods for high dimensional data clustering.Multi-view subspace clustering methods are extensions of subspace clustering methods on multi-view data.Since the past decade,methods of subspace clustering and multi-view subspace clustering have been widely applied in many scientific problems,e.g.,motion segmentation,image processing.The subspace clustering algorithm based on low-rank representation(LRR)cannot handle large-scale data effectively,and distributed low-rank subspace clustering algorithm(DFC-LRR)cannot handle the high-dimensional data directly.This paper proposes a divide-and-conquer method-based low-rank tensor representation subspace clustering algorithm,the proposed algorithm extends the traditional vector representation-based subspace clustering algorithms to higher-order tensor data,and proposes a divide-and-conquer algorithm for solving tensor optimization problems.To deal with high-dimensional data directly,DFC-TLRR transforms high-dimensional data to higher-order tensor,then introduces t-product in the selfrepresentation of data.Subsequently,the low-rank submodule representations are obtained through a divide-and-conquer method.Lastly,we get the similarity matrix of data by a sparse processing.Experimental results on the Extended Yale B,COIL20,and UCSD datasets show that the proposed algorithm outperforms DFC-LRR in clustering accuracy,and distributed computing can reduce the running time.Most of the existing multi-view subspace clustering methods only explore the consistency or complementarity between different views,lack a comprehensive consideration of both,and without considering the contribution degree of views.To solve this issue,a consistent manifold constrained sparse multi-view subspace clustering algorithm(CMSMSC)is proposed.On the one hand,the proposed algorithm learns the weights for the subspace representation matrixes of different views dynamically and adaptively,then calculates the consistent subspace representation matrix of all views by linear weighting method.A regularization term of the weights is developed to smoothen the distribution of the weights and enhance the complementarity of information across multiple views.On the other hand,the proposed algorithm establishes local geometric relationship between instances in the original highdimensional space by using multi-view local linear embedding model in advance,and this information is subsequently introduced in our model by constructing a graph regularization term of the consistent subspace representation,which not only effectively preserves the local geometric structure about the original data in the low-dimensional subspace,but also ensures the consistency of subspace representation across different views.Experiments on six real datasets corresponding to different application scenarios show that our algorithm has excellent robustness and clustering performance compared with other comparison algorithms.