Non-Negative Matrix Factorization With Dual Constraints for Image Clustering

How to learn dimension-reduced representations of image data for clustering has been attracting much attention. Motivated by that the clustering accuracy is affected by both the prior-known label information of some of the images and the sparsity feature of the representations, we propose a non-negative matrix factorization (NMF) method with dual constraints in this paper. In our model, one constraint is used to keep the label feature and the other constraint is utilized to enhance the sparsity of the representations. Notably that these two constraints are embedded naturally into the traditional NMF model, refraining from the usage of the balance parameters which are hard to choose. Meantime, for solving the proposed model, the alternative iteration scheme is employed, and an efficient algorithm based on convex optimization is designed to conduct each iteration operation. It is proved that this algorithm achieves a nonlinear convergence rate, much faster than existing methods with linear rate. Simulation results demonstrate the advantages of the proposed method.