  This paper studies distributed diffusion adaptation over clustered multi-task
networks in the presence of impulsive interferences and Byzantine attacks. We
develop a robust resilient diffusion least mean Geman-McClure-estimation
(RDLMG) algorithm based on the cost function used by the Geman-McClure
estimator, which can reduce the sensitivity to large outliers and make the
algorithm robust under impulsive interferences. Moreover, the mean sub-sequence
reduced method, in which each node discards the extreme value information of
cost contributions received from its neighbors, can make the network resilient
against Byzantine attacks. In this regard, the proposed RDLMG algorithm ensures
that all normal nodes converge to their ideal states with cooperation among
nodes. A statistical analysis of the RDLMG algorithm is also carried out in
terms of mean and mean-square performances. Numerical results evaluate the
proposed RDLMG algorithm in applications to multi-target localization and
multi-task spectrum sensing.
