Abstract: Non-negative matrix factorization (NMF) algorithm can find a non-negative and linear matrix representation and retains the essential characteristics of the original data,it has been successfully applied to many fields.The classical NMF algorithm and its variant algorithms mostly use the mean square error function to measure the reconstruction error,which has been shown to be effective in many tasks,but it still faces some difficulties in dealing with noise-containing data.The Huber loss function performs the same penalty for the smaller residual as the mean square error loss function,and the penalty for the larger residual is linearly grown,so the Huber loss function is more robust than the mean square error loss function.It has been proved that the L_2,1 norm sparse regularization term is a feature selection function in the classification and clustering model of machine learning.Therefore,combining the advantages of the two,a non-negative matrix factorization clustering model based on Huber loss function and incorporating L_2,1 norm regularization term is proposed,and an effective optimization procedure based on projected gradient method to update variables is given.Compared with the classical NMF multi-clustering algorithm on multiple sets of datasets,the experimental results show the effectiveness of the proposed algorithm.

Key words: L_2,1 norm, Huber loss function, Nonnegative matrix factorization, Projected gradient method