  In generalized graph signal processing (GGSP), the signal associated with
each vertex in a graph is an element from a Hilbert space. In this paper, we
study GGSP signal reconstruction as a kernel ridge regression (KRR) problem. By
devising an appropriate kernel, we show that this problem has a solution that
can be evaluated in a distributed way. We interpret the problem and solution
using both deterministic and Bayesian perspectives and link them to existing
graph signal processing and GGSP frameworks. We then provide an online
implementation via random Fourier features. Under the Bayesian framework, we
investigate the statistical performance under the asymptotic sampling scheme.
Finally, we validate our theory and methods on real-world datasets.
