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In this paper, we consider the problem of estimating multiple parameter vectors over a sensor network in a multitasking framework and under temporally-correlated input conditions. For this, an efficient clustered multitask diffusion affine projection algorithm (APA) is proposed that enjoys both intra-cluster and inter-cluster cooperation via diffusion. It is, however, shown that while collaboration in principle is a useful step to enhance the performance of a network, uncontrolled mode of inter-cluster collaboration can at times be detrimental to its convergence performance, especially near steady-state. To overcome this, a controlled form of inter-cluster collaboration is proposed by means of a control variable which helps in maintaining the collaboration in right direction. The proposed controlled multitask strategy attains improved performance in terms of both transient and steady-state mean square deviation (MSD) vis-avis existing algorithms, as also confirmed by simulation studies. We carry out a detailed performance analysis of the proposed algorithm, obtain stability bounds for its convergence in both mean and mean-square senses, and derive expressions for the network level MSD. Simulation results reveal that the proposed scheme performs consistently well even in the absence of cluster information.

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.