Adaptive networks solve distributed optimization problems in which all agents of the network are interested to collaborate with their neighbors to learn a similar task. Collaboration is useful when all agents seek a similar task. However, in many applications, agents may belong to different clusters that seek dissimilar tasks. In this case, nonselective collaboration will lead to damaging results that are worse than noncooperative solution. In this paper, we contribute in problems that several clusters of interconnected agents are interested in learning multiple tasks. To address multitask learning problem, we consider an information theoretic criterion called correntropy in a distributed manner providing a novel adaptive combination policy that allows agents to learn which neighbors they should cooperate with and which other neighbors they should reject. In doing so, the proposed algorithm enables agents to recognize their clusters and to achieve improved learning performance compared with noncooperative strategy. Stability analysis in the mean sense and also a closed-form relation determining the network error performance in steady-state mean-square-deviation is derived. Simulation results illustrate the theoretical findings and match well with theory. KEYWORDSadaptive network, correntropy criterion, distributed processing, multitask learning 1 1232

Spectrum sensing is a significant issue in cognitive radio networks which enables estimation of the frequency spectrum and hence provides frequency reuse. In the large-scale cognitive radio networks, secondary users cannot share a common spectrum since the coverage area of primary users is limited. In this study, the authors suggest a diffusion adaptive learning algorithm based on correntropy cooperation policy, which first categorises received data of secondary users into several groups, and then learns a common spectrum inside each group. The mean-square performance of proposed algorithm is analysed and supported by simulations. Experimental results show that, in a multitask cognitive network, the proposed algorithm can achieve a better mean-square deviation learning performance both in transient and steady-state regimes in comparison with other conventional algorithms.

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In this paper, we investigate the transient performance of the proposed distributed multitask learning algorithm that is developed based on maximum correntropy criterion. In the first stage, we derive the proposed multitask learning algorithm in which the correntropy-based combination matrix determines which sensors should collaborate together and which sensors should stop the collaboration. In the second stage, according to the variance relation of the error vector, we derive a closed-form relation that shows the transition of mean-square-deviation learning performance. We also find the lower and upper bounds of the step size that ensure the stability of the multitask learning algorithm. The theoretical finding of the transient performance is shown to fit a well match with simulation results. KEYWORDS adaptive network, correntropy criterion, distributed signal processing, multitask learning, transient analysis Int J Adapt Control Signal Process. 2018;32:229-247.wileyonlinelibrary.com/journal/acs

Abstract-A distributed adaptive algorithm for estimation of sparse unknown parameters in the presence of nonGaussian noise is proposed in this paper based on normalized least mean fourth (NLMF) criterion. At the first step, local adaptive NLMF algorithm is modified by zero norm in order to speed up the convergence rate and also to reduce the steady state error power in sparse conditions. Then, the proposed algorithm is extended for distributed scenario in which more improvement in estimation performance is achieved due to cooperation of local adaptive filters. Simulation results show the superiority of the proposed algorithm in comparison with conventional NLMF algorithms.