Diffusion Least-Mean Squares With Adaptive Combiners: Formulation and Performance Analysis

By Noriyuki Takahashi, Isao Yamada, Ali H. Sayed. IEEE Transactions on Signal Processing, 2010

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Adaptive Networks (2014, background): “Itis explained in [1] and [11] that, while such selections may be appropriate in some applications, they can nevertheless lead to degraded performance in the context of adaptation and learning over networks [139].”
Diffusion Adaptation Strategies for Distributed Optimization and Learning Over Networks (2011, background): “Second, despite the fact that nodes influence each other’s behavior, we are able to quantify the performance of every node in the network and to derive closed-form expressions for the mean-square performance at small step-sizes — see (106)–(108).”
Adaptation, Learning, and Optimization over Networks (2014, background): “Following [32, 209, 231, 233], the block maximum norm of x is denoted by ‖x‖b,∞ and is defined as ‖x‖b,∞ Δ = max 1≤k≤N ‖xk‖ (F.”
Diffusion Adaptation over Networks (2012, methodology): “I of [18] and the matrix M in Lemma 2 of [33] are block diagonal, the ‖ · ‖b,∞ norm should replace the ‖ · ‖ρ norm used there, as in the proof that led to (606) and as already done in [54].”
Robust Distributed Diffusion Recursive Least Squares Algorithms With Side Information for Adaptive Networks (2018, methodology): “The Metropolis rule [49] used for computing the combination coefficients {cm,k} in combination step is expressed as: ⎧ ⎪⎨”