Algorithm 1: diffusion Logarithm-Correntropy Algorithm

Initialize: Start with $\left\{w_{l,-1}=0\right\}$ for all l, initialize $w_{k,0}$ for each node

k,step-size $\mu$, and cooperative coefficients $c_{lk}$. Set $\alpha >0$, $\sigma >0$.

for $t=1:T$

for each node k:

Adaptation.

${\xi }_{l,i}=exp\left(-\frac{{\left(e_{l,i}\right)}^2}{2{\sigma }^2\left({\left(w_{l,i-1}\right)}^2+1\right)}\right)$

${\tau }_{l,i=}\left(exp\left(-\frac{{\left(e_{l,i}\right)}^2}{2{\sigma }^2\left({\left(w_{l,i-1}\right)}^2+1\right)}\right).\frac{e_{l,i}\left(u_{l,i}+d_{l,i}{w}_{l,i}\right)}{{\sigma }^2{\left({\left(w_{l,i-1}\right)}^2+1\right)}^2}\right)$.

${\phi }_{k,i}={\phi }_{k,i-1}-\mu \frac{\partial H\left(e_{k,i}\right)}{\partial w_{k,i-1}}={\phi }_{k,i-1}-\mu \left({\tau }_{l,i}+\frac{{\tau }_{l,i}}{1+\alpha {\xi }_{l,i}}\right)$

Communication.

Transmit the intermediate ${\phi }_{k,i}$ to all neighbors in $N_k$.

Combination.

$w_{k,i}=\sum _{l\in N_k}{c}_{lk}{\phi }_{l,i}$

$N_k$ are the neighbor nodes of node k in the communication subnetwork.