Fig. 7: Lower bounds on the Jaccard reconstruction accuracy for the cross-reconstruction experiments in Fig. 5.
From: Learning low-rank latent mesoscale structures in networks
Subtracting both sides of the inequality (1) from 1 implies that the Jaccard reconstruction accuracy 1 − JD(G, Grecons;W) is lower-bounded by \(1-\frac{1}{2(k-1)}{{\mathbb{E}}}_{{{{{{{{\bf{x}}}}}}}}}\left[\parallel {A}_{{{{{{{{\bf{x}}}}}}}}}-{\hat{A}}_{{{{{{{{\bf{x}}}}}}}};W}{\parallel }_{1}\right]\). This lower bound also measures the accuracy of reconstructing mesoscale patches of G using latent motifs in W. In (a–d), we plot this lower bound for the same parameters as in Fig. 5b–e (i.e., k = 21 and r ∈ {6, 16, 25, 36, 49, 64, 81, 100}).
