Compression-based inference of network motif sets
Fig 2
Greedy optimization algorithm.
(A) Illustration of a single step of the greedy stochastic algorithm. The putative compression ΔL(G, θ, s) that would be obtained by contracting each of the subgraphs in the minibatch is calculated, and the subgraph contraction resulting in the highest compression is selected (highlighted in blue). (B) Example of motif set inferred in the connectome of the right hemisphere of the mushroom bodies (MB right) of the Drosophila larva. (C) Evolution of the codelength during a single algorithm run. The algorithm is continued until no more subgraphs can be contracted. The representation θ* = θt with the shortest codelength is selected; here, after the 31st iteration (indicated by a vertical black dashed line). The horizontal orange dashed line indicates the codelength of the corresponding simple graph model without motifs (see Motif-free reference codes). (D) The algorithm is run a hundred times for each dyadic base model and the most compressing model is selected. Histograms represent the codelengths of models with motifs after each run of the greedy algorithm; colors correspond to the different base models (blue: ER model, orange: configuration model, pink: reciprocal ER model, yellow: reciprocal configuration model, see Fig 1B and Table 1); vertical dashed lines represent the codelengths of models without motifs, and the black dashed line indicates the codelength of the shortest-codelength model—here the configuration model with motifs.