Study of Diffusion Normalized Least Mean M-estimate Algorithms
This work addresses robust distributed learning for networks affected by impulsive noise, representing an incremental improvement with a sparse-aware variant.
The authors tackled the problem of robust distributed learning in networks with impulsive interference by proposing diffusion normalized least mean M-estimate algorithms based on the modified Huber function, achieving superior performance over existing diffusion algorithms in simulations across various impulsive noise scenarios.
This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to exploit the system's underlying sparsity to further improve the learning performance, a sparse-aware variant is also developed by incorporating the $l_0$-norm of the estimates into the update process. We then analyze the transient, steady-state and stability behaviors of the algorithms in a unified framework. In particular, we present an analytical method that is simpler than conventional approaches to deal with the score function since it removes the requirements of integrals and Price's theorem. Simulations in various impulsive noise scenarios show that the proposed algorithms are superior to some existing diffusion algorithms and the theoretical results are verifiable.