Weighted Non-negative Matrix Factorization for Image Recovery and Representation

Non-negative matrix factorization and its variants cannot learn an effective subspace from the dataset corrupted by outliers. In this article, we propose a robust non-negative matrix factorization approach, called weighted non-negative matrix factorization, which can both recover the corrupted data space and learn a more effective subspace from the corrupted data space. In the proposed method, introducing a weighted graph, which uses Boolean values to mark noise points, while a clean data space and subspace can be achieved by the unlabel data points. The proposed problem can be formulated as a nonconvex optimization problem, which can be optimized by the multiplicative update methods. Taking the face data polluted by Salt and Pepper noise as an example, the effectiveness of the proposed method in image recovery and low-dimensional representations learning is verified.