  In presence of sparse noise we propose kernel regression for predicting
output vectors which are smooth over a given graph. Sparse noise models the
training outputs being corrupted either with missing samples or large
perturbations. The presence of sparse noise is handled using appropriate use of
$\ell_1$-norm along-with use of $\ell_2$-norm in a convex cost function. For
optimization of the cost function, we propose an iteratively reweighted
least-squares (IRLS) approach that is suitable for kernel substitution or
kernel trick due to availability of a closed form solution. Simulations using
real-world temperature data show efficacy of our proposed method, mainly for
limited-size training datasets.
