Dual-graph regularized non-negative matrix factorization with sparse and orthogonal constraints

Semi-supervised Non-negative Matrix Factorization (NMF) can not only utilize a fraction of label information, but also effectively learn local information of the objectives, such as documents and faces. Semi-supervised NMF is an efficient technique for dimensionality reduction of high dimensional data. In this paper, we propose a novel semi-supervised NMF, called Dual-graph regularized Non-negative Matrix Factorization with Sparse and Orthogonal constraints (SODNMF). Dual-graph model is added into semi-supervised NMF, and the manifold structures of the data space and the feature space are taken into account simultaneously. In addition, the sparse constraint is used in SODNMF, which can simplify the calculation and accelerate the processing speed. The most important is that SODNMF makes use of bi-orthogonal constraints, which can avoid the non-correspondence between images and basic vectors. Therefore, it can effectively enhance the discrimination and the exclusivity of clustering, and improve the clustering performance. We give the objective function, the iterative updating rules and the convergence proof. Empirical experiments demonstrate encouraging results of our novel algorithm in comparison to four algorithms within some state-of-the-art algorithms through a set of evaluations based on three real datasets.