Adaptive total-variation for non-negative matrix factorization on manifold

Non-negative matrix factorization (NMF) has been widely applied in information retrieval and computer vision. However, its performance has been restricted due to its limited tolerance to data noise, as well as its inflexibility in setting regularization parameters. In this paper, we propose a novel sparse matrix factorization method for data representation to solve these problems, termed Adaptive Total-Variation Constrained based Non-Negative Matrix Factorization on Manifold (ATV-NMF). The proposed ATV can adaptively choose the anisotropic smoothing scheme based on the gradient information of data to denoise or preserve feature details by incorporating adaptive total variation into the factorization process. Notably, the manifold graph regularization is also incorporated into NMF, which can discover intrinsic geometrical structure of data to enhance the discriminability. Experimental results demonstrate that the proposed method is very effective for data clustering in comparison to the state-of-the-art algorithms on several standard benchmarks.