Kernel nonnegative matrix factorization without the pre-image problem

The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with nonlinear NMF. In this paper, we propose an efficient nonlinear NMF, which is based on kernel machines. As opposed to previous work, the proposed method does not suffer from the pre-image problem. We propose two iterative algorithms: an additive and a multiplicative update rule. Several extensions of the kernel-NMF are developed in order to take into account auxiliary structural constraints, such as smoothness, sparseness and spatial regularization. The relevance of the presented techniques is demonstrated in unmixing a synthetic hyperspectral image.