Orthogonal graph regularized non-negative matrix factorization under sparse constraints for clustering

The standard NMF algorithm is not suitable for sampling data from low-dimensional manifolds embedded in high-dimensional environmental spaces, as the geometric information hidden in feature manifolds and sample manifolds is rarely learned. In order to obtain better clustering performance based on NMF, manifold and orthogonal constraint, a new type of model named Orthogonal Graph regularized Non-negative Matrix Factorization model under Sparse Constraints (OGNMFSC) is proposed. Firstly, this type of model constructs a nearest neighbor graph to encode the geometric information of the data space, in order to obtain more discriminative ability by preserving the structure of the graph. Secondly, this type of model adds orthogonal constraints to achieve better local representation and significantly reduce the inconsistency between the original matrix and the basis vectors. Thirdly, by adding sparse constraints to obtain a sparser representation matrix, the clustering performance of the model can be improved. The main conclusion of this paper is that two effective algorithms have been generated to solve the model, which not only provides theoretical convergence proof for these two algorithms, but also demonstrates significant clustering performance in experiments compared to classical models such as K-means, PCA, NMF, Semi-NMF, NMFSC, ONMF, GNMF, NeNMF.