Weighted non-negative matrix factorization based on adaptive robust local sparse graph

As an efficient and intuitive dimension reduction algorithm, non-negative matrix factorization (NMF) has been widely employed in various fields. However, the existing NMF based methods have two disadvantages. Firstly, it treats each sample equally without considering the noise problem. Secondly, it does not restrict the coefficient matrix. Therefore, this paper proposes a novel weighted NMF algorithm based on adaptive robust local sparse graph (WNMF-ARLS), which includes the following superiorities compared with the other NMF-based algorithms: 1) The proposed method introduces a weighting regularization term, which distributes smaller weights to outliers and noise, and allocates larger weights to clean data. 2) Our method constructs a sparse local constraint graph to discover the data’s potential manifold structure. 3) Unlike most NMF algorithms based on graph regularization, in which the graphs remain unchanged and are pre-defined during the NMF process, the proposed method introduces sparse constraints and local constraints into the unified framework to adaptively construct the optimization graph. Lots of image clustering experiments are provided to illustrate the effectiveness and superiority of the proposed WNMF-ARLS algorithm. Experimental results also show that the clustering performance of the proposed method is significantly better than that of other comparison algorithms.