Kernel Orthogonal Nonnegative Matrix Factorization: Application To Multispectral Document Image Decomposition

As a nonlinear extension of the standard nonnegative matrix factorization (NMF), kernel-based variants have demonstrated to be more effective for discovering meaningful latent features from raw data. However, many existing kernel methods allow only obtaining the basis matrix in the projected feature space, which prevents its inverse mapping back to the original space as requested in many applications. In this work, we propose a new kernel orthogonal NMF method that does not suffer from the pre-image issue. We incorporate the orthogonality constraint as an optimization problem over the Stiefel manifold to improve the sparsity and the model's clustering properties. We solve the proposed model with an efficient optimization approach based on the alternating direction method of multipliers (ADMM) scheme and the projected gradients method. We validate our model on the task of blind decomposition of real-world Multispectral (MS) document images. Our experiments demonstrate the competitiveness of our proposed model in comparison to the state-of-the-art techniques.