Orthogonal-Constrained Graph Non-Negative Matrix Factorization for Clustering

We propose a novel approach for clustering problem, which refers to as Graph Regularized Orthogonal Subspace Non Negative Matrix Factorization (GNMFOS). This type of model introduces both graph regularization and orthogonality as penalty terms into the objective function. It not only obtains the uniqueness of matrix decomposition but also improves the sparsity of decomposition and reduces computational complexity. Most importantly, using the idea of iteration under weak orthogonality, we construct an auxiliary function for the algorithm and obtain convergence proof to compensate for the lack of convergence proof in similar models. The experimental results show that compared with classical models such as GNMF and NMFOS, our algorithm significantly improves clustering performance and the quality of reconstructed images.