Estimating signals over graphs via multi-kernel learning

Estimating functions on graphs finds well-documented applications in machine learning and, more recently, in signal processing. Given signal values on a subset of vertices, the goal is to estimate the signal on the remaining ones. This task amounts to estimating a function (or signal) over a graph. Most existing techniques either rely on parametric signal models or require costly cross-validation. Leveraging the framework of multi-kernel learning, a data-driven nonparametric approach is developed here. Instead of a single kernel, the algorithm relies on a dictionary of candidate kernels and efficiently selects the most suitable ones by minimizing a convex criterion using a group Lasso module. Numerical tests demonstrate the superior estimation performance of the novel approach over competing alternatives.