Nonnegative Matrix Factorization (NMF) is one of the most popular feature learning technologies in the field of machine learning and pattern recognition. It has been widely used and studied in the multi-view clustering tasks because of its effectiveness. This study proposes a general semi-supervised multi-view nonnegative matrix factorization algorithm. This algorithm incorporates discriminative and geometric information on data to learn a better-fused representation, and adopts a feature normalizing strategy to align the different views. Two specific implementations of this algorithm are developed to validate the effectiveness of the proposed framework: Graph regularization based Discriminatively Constrained Multi-View Nonnegative Matrix Factorization (GDCMVNMF) and Extended Multi-View Constrained Nonnegative Matrix Factorization (ExMVCNMF). The intrinsic connection between these two specific implementations is discussed, and the optimization based on multiply update rules is presented. Experiments on six datasets show that the effectiveness of GDCMVNMF and ExMVCNMF outperforms several representative unsupervised and semi-supervised multi-view NMF approaches.