Group Sparsity and Graph Regularized Semi-Nonnegative Matrix Factorization with Discriminability for Data Representation

Abstract: Semi-Nonnegative Matrix Factorization (Semi-NMF), as a variant of NMF, inherits the merit of parts-based representation of NMF and possesses the ability to process mixed sign data, which has attracted extensive attention. However, standard Semi-NMF still suffers from the following limitations. First of all, Semi-NMF fits data in a Euclidean space, which ignores the geometrical structure in the data. What’s more, Semi-NMF does not incorporate the discriminative information in the learned subspace. Last but not least, the learned basis in Semi-NMF is unnecessarily part based because there are no explicit constraints to ensure that the representation is part based. To settle these issues, in this paper, we propose a novel Semi-NMF algorithm, called Group sparsity and Graph regularized Semi-Nonnegative Matrix Factorization with Discriminability (GGSemi-NMFD) to overcome the aforementioned problems. GGSemi-NMFD adds the graph regularization term in Semi-NMF, which can well preserve the local geometrical information of the data space. To obtain the discriminative information, approximation orthogonal constraints are added in the learned subspace. In addition, `21 norm constraints are adopted for the basis matrix, which can encourage the basis matrix to be row sparse. Experimental results in six datasets demonstrate the effectiveness of the proposed algorithms.