Adaptive multitask network based on maximum correntropy learning algorithm

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.