Multi-view Clustering Based On Non-negative Matrix Factorization

Non-negative matrix factorization based methods are very important in the application of clustering.After extensive research on non-negative matrix factorization,in this paper we propose a multi-view clustering method which is based on concept factorization.This method considers the correlation by jointly optimizing the graph matrix to make full use of the data correlation among different views,and can automatically learn the weights of different views.Firstly,we discuss the significance and current research of multi-view data clustering,and give the flow chart of multi-view clustering methods which are based on matrix factorization.In addition,we summarize several variations of non-negative matrix factorization and basis multi-view clustering methods which are based on non-negative matrix factorization.Secondly,after extensive research on non-negative matrix factorization and concept factorization,we propose a multi-view clustering concept factorization framework which both considers graph and weight information.This framework overcomes the limitation that non-negative matrix factorization cannot deal with negative numbers,so it can be applied into all kinds of datasets.In this framework,we can preserve the local geometrical structure during the dimension reduction process by using a learned graph matrix.This framework can also learn the weights of different views automatically,which reduces the cost of setting each weight separately.Next,we present the objective function corresponding to the multi-view clustering framework,design a kind of novel updating rules to seek the optimal solution of the objective function,and then describe the detail algorithm of the proposed method.Besides,we have proved the convergence of the objective function theoretically when using the updating rules to solve the optimization problem.Finally,we show how to set the parameters and conduct lots of experiments to demonstrate the superiority of the proposed method.In total,we select nine multi-view datasets,three evaluation metrics and seven comparing algorithms.Furthermore,we show the effectiveness of the proposed method in terms of the sensitivity of parameter and the convergence.