Multi-view Clustering Via Double Constraints Non-negative Matrix Factorization

Clustering is an important part in machine learning and many efficient clustering algorithms have been proposed. With the development of the Internet, data can be obtained more and more easily. The same samples are often described from different characteristics. It becomes an essential issue how to improve the clustering performance by utilizing the multi-view information, which makes multi-view clustering develop fast.Non-negative matrix factorization is widely deployed and easy to implement, which makes NMF based clustering algorithms attract a lot of attentions. With the success of NMF in clustering, a large number of scholars have applied NMF to multi-view clustering. NMF based multi-view clustering algorithms inherit the advantages of NMF and improve the accuracy and stability of clustering. NMF based multi-view clustering algorithms also have the following drawbacks. First, the solution of NMF based multi-view algorithm is not unique. Second, the standard orthogonal basis matrix is not obtained for each view. Finally, the locally geometrical structure is not preserved.To overcome the three drawbacks, we propose a multi-view clustering algorithm via double constraints NMF(DCNMF). Orthogonality is utilized to make the solution unique. Matrix multiplication is used in our framework to obtain the standard orthogonal basis. Meanwhile the high computational complexity caused by orthogonality is avoided. Moreover, to preserve the locally geometrical structure between views, graph regularization is utilized. We provide an update rule for the parameter of the graph regularization to balance the reconstruct error and regularization, besides, it accelerates the convergence of our algorithms. Experimental results and theoretical proofs assure the validity and efficiency of our algorithms. Finally the experimental results show that our algorithms can obtain a good clustering result effectively.