Figure 4
Improvement of the success ratio during the optimisation for embeddings obtained with Mercator8. We plot \(p_{\textrm{s}}(\{r_i,\theta _i\})\) defined in (2) as a function of the number of epochs for random sampling (red), degree dependent sampling (green), clogged source dependent sampling (blue) and clogged target dependent sampling (purple). The curves correspond to the median over 20 samples and the shaded region around the curves falls between the 40\(^{\textrm{th}}\) and 60\(^{\textrm{th}}\) percentiles. For better visibility, we marked both the starting values (before the optimisation) and the ending values (after 400 epochs) with ’x’ symbols. The results are shown for the network of political books (\(N=105\), \(L=441\)) in panel (a), for a PSO network with \(N=128\) nodes and \(L=618\) links in panel (b), a PSO network with \(N=256\) nodes and \(L=1178\) links in panel (c), the metabolic network (\(N=453\), \(L=2025\)) in panel (d), a PSO network with \(N=512\) nodes and \(L=2264\) links in panel (e), the unicodelang network (\(N=858\), \(L=1245\)) in panel (f), the network between fictional characters (\(N=796\), \(L=2823\)) in panel (g) and a PSO network with \(N=1024\) nodes and \(L=4402\) links in panel (h).
