Improving non-negative matrix factorization via ranking its bases

As a considerable technique in image processing and computer vision, Nonnegative Matrix Factorization (NMF) generates its bases by iteratively multiplicative update with two initial random nonnegative matrices W and H, that leads to the randomness of the bases selection. For this reason, the potentials of NMF algorithms are not completely exploited. To address this issue, we present a novel framework which uses the feature selection techniques to evaluate and rank the bases of the NMF algorithms to enhance the NMF algorithms. We adopted the well known Fisher criterion and Least Reconstruction Error criterion, which is proposed by us, as two instances to show how that works successfully under our framework. Moreover, in order to avoid the hard combinatorial optimization issue in ranking procedure, a de-correlation constraint can be optionally imposed to the NMF algorithms for giving a better approximation to the global optimum of the NMF projections. We evaluate our works in face recognition, object recognition and image reconstruction on ORL and ETH-80 databases and the results demonstrate the enhancement of the state-of-the-art NMF under our framework.