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This paper proposes efficient batch-based and online strategies for kernel regression over graphs (KRG). The proposed algorithms do not require the input signal to be a graph signal, whereas the target signal is defined over the graph. We first use random Fourier features (RFF) to tackle the complexity issues associated with kernel methods employed in the conventional KRG. For batch-based approaches, we also propose an implementation that reduces complexity by avoiding the inversion of large matrices. Then, we derive two distinct online strategies using RFF, namely, the mini-batch gradient KRG (MGKRG) and the recursive least squares KRG (RLSKRG). The stochasticgradient KRG (SGKRG) is introduced as a particular case of the MGKRG. The MGKRG and the SGKRG are low-complexity algorithms that employ stochastic gradient approximations in the regression-parameter update. The RLSKRG is a recursive implementation of the RFF-based batch KRG. A detailed stability analysis is provided for the proposed online algorithms, including convergence conditions in both mean and mean-squared senses. A discussion on complexity is also provided. Numerical simulations include a synthesized-data experiment and real-data experiments on temperature prediction, brain activity estimation, and image reconstruction. Results show that the RFF-based batch implementation offers competitive performance with a reduced computational burden when compared to the conventional KRG. The MGKRG offers a convenient trade-off between performance and complexity by varying the number of mini-batch samples. The RLSKRG has a faster convergence than the MGKRG and matches the performance of the batch implementation.

This paper studies a clustered multitask diffusion least mean-square strategy that accounts for communication delays in the inter-and intra-cluster information exchanges. We conduct detailed performance analysis and establish convergence criteria, both in mean and mean-square senses, to investigate the effect of inter-node communication delays on the stability and estimation performance. In particular, we derive convergence conditions and closed-form expressions for transient and steadystate mean square deviation. The concepts are verified using simulation examples, which show a precise match between theoretical and experimental steady-state MSD results.

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