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, ℓ 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.

Keywords

• non-negative matrix factorization
• data representation
• clustering