Multi-view Clustering Based On Tensor Self-representation Learning

With the rapid development of big data era and electronic information technology,multi-view data is often found in different fields of scientific research and in various practical applica-tions.Compared with single-view data,multi-view data is useful for learning tasks because it can provide more information useful for clustering and classification learning tasks,therefore,multi-view learning has been an important research direction in areas such as artificial intel-ligence and data mining.In recent years,multi-view clustering algorithms based on tensor singular value decomposition(t-SVD),which make full use of the low-rank property of tensor data,can explore the intrinsic connection and essential structure among multi-view data more efficiently and thoroughly,and have achieved impressive results in improving the clustering performance of the algorithms.However,the existing tensor nuclear norm low-rank constraint methods based on t-SVD ignores the difference in contribution between the different singular values,which leads to a significant degradation of the algorithm's clustering accuracy and sta-bility when dealing with noisy(containing light,occlusion)data.Aiming at this problem,this paper,in order to improve the shortcomings of the low-rank constraint on the tensor nuclear norm,proposes two more efficient and robust algorithmic models.The specific works in this paper is as follows:The tensor nuclear norm based on t-SVD ignores the difference in contribution between different singular values,which leads to degradation in the clustering performance of the algo-rithm,in order to solve this problem,in this paper,we propose a multi-view clustering model(WTN-MVC)based on the weighted tensor nuclear norm low-rank constraint.The model uses a weighted tensor nuclear norm to impose a low-rank constraint on the tensor,assigning dif-ferent weights to each singular value and effectively exploiting the a priori information on the difference in contribution between different singular values.Based on this,the proposed model is effectively optimized using the alternating update method(ADMM),and the complete op-timization algorithm is given.The clustering results on different data sets all show that the proposed model in this paper significantly improves the clustering performance.Although the multi-view clustering model(WTN-MVC)based on the weighted tensor nuclear norm low-rank constraint embeds the priori knowledge of the difference in singular value contribution,it only imposes a low-rank constraint on the subspace tensor and ignores the sparsity of the self-represented coefficient matrix under each view.In response to the problems of the WTN-MVC model,in this paper,we propose a multi-view clustering model(SWTN-MVC)based on the weighted tensor nuclear norm and sparse representation.It usesl₁norm to describe the local structure of high-dimensional data by applying sparse constraints to the self-representation coefficient matrix of each view,and the stability and accuracy of the clustering algorithm is further improved by constraining the self-representing coefficient ma-trix simultaneously with low-rank and sparse representations.At the same time,this chapters of this paper gives a complete and effective optimization algorithm,and the model is exten-sively experimented on different datasets.The clustering results of different datasets are all significantly better than the clustering results of the same type of algorithms.