Tensor Based Multi-view Subspace Clustering

In multi-view data,each view has its own specific attributes for a particular task.At the same time,different views often contain supplementary information that can be uti-lized to fully describe the data sets,making the subspace representation more accurate and reliable.Furthermore,the tensor-based multi-view subspace clustering method can cap-ture the higher-order correlation information and potential clustering information among different views on the basis of the traditional clustering model.Compared with traditional methods,multi-view subspace clustering based on tensor can effectively reduce the re-dundancy of learning subspace representation,leading to further improving the accuracy of clustering.This paper mainly focus on the multi-view subspace clustering based on different low-rank tensor constraints.Firstly,in this thesis,we propose a new tensor decomposition model,named O-Minus decomposition(OMD),which is utilized to process the multi-view subspace clustering tasks.At present,the the current methods based on low-rank tensor constraints have some problems,such as the lack of exploration of self-representation tensor due to the unbal-anced expansion matrix,and the inability to capture inter-view and intra-view information simultaneously.Therefore,our proposed model,which is based on the Tensor Ring(TR)architecture,has built an effective bridge between two weakly correlated factors between non-adjacent modes based on energy physics and other relevant knowledge.Based on this structure,we can simultaneously obtain the inter-view and intra-view information.In addition,OMD enhances the ability to capture the global low-rank information.In this paper,we use multiplier alternating direction method to solve the proposed OMD-MVC optimization model.Numerical experiments on six reference data sets demonstrate the superiority of the proposed method in clustering accuracy.Further,data structures embedded in self-presentation tensors may vary in different multi-view data sets,and application of specific tensor low-rank constraints may result in suboptimal clustering performance for various data.Thus,we proposed the Adaptively Topological Tensor Network(ATTN).Based on the fully connected tensor network,by determining the edge ranks from the information of the self-representation tensor,ATTN will give a better tensor representation with the data-driven strategy.Specifically,in multi-view tensor clustering,we analyze the higher-order correlations among different modes of self-representation tensors,and prune the links of the weakly correlated ones.Therefore,the obtained tensor network structure can be efficiently exploring the essential clustering information with different self-representation tensor structure.A greedy adaptive rank-increasing strategy is also applied to improve the capacity of capturing low rank structure.We apply ATTN on multi-view subspace clustering and utilize the alternating direction method of multipliers to solve it.Experiments show that multi-view subspace clustering based on ATTN has better performance on five multi-view datasets.