Non-Negative Pre-Image in Machine Learning for Pattern Recognition

Moreover, in order to have a physical interpretation, some constraints should be incorporated in the signal or image processing technique, such as the non-negativity of the solution. This paper deals with the non-negative pre-image problem in kernel machines, for nonlinear pattern recognition. While kernel machines operate in a feature space, associated to the used kernel function, a pre-image technique is often required to map back features into the input space. We derive a gradient-based algorithm to solve the pre-image problem, and to guarantee the non-negativity of the solution. Its convergence speed is significantly improved due to a weighted stepsize approach. The relevance of the proposed method is demonstrated with experiments on real datasets, where only a couple of iterations are necessary.