Kernel Regression for Signals over Graphs

We propose kernel regression for signals over graphs. The optimal regression coefficients are learnt using a constraint that the target vector is a smooth signal over an underlying graph. The constraint is imposed using a graph-Laplacian based regularization. We discuss how the proposed kernel regression exhibits a smoothing effect, simultaneously achieving noise-reduction and graph-smoothness. We further extend the kernel regression to simultaneously learn the underlying graph and the regression coefficients. We validate our theory by application to various synthesized and real-world graph signals. Our experiments show that kernel regression over graphs outperforms conventional regression, particularly for small sized training data and under noisy training. We also observe that kernel regression reveals the structure of the underlying graph even with a small number of training samples. Index Terms Linear model, regression, kernels, machine learning, graph signal processing, graph-Laplacian. EDICS−NEG-SPGR, NEG-ADLE, MLR-GRKN.