Multiplex graph matching matched filters

Abstract

We consider the problem of detecting a noisy induced multiplex template network in a larger multiplex background network. Our approach, which extends the graph matching matched filter framework of Sussman et al. (IEEE Trans Pattern Anal Mach Intell 42(11):2887–2900, 2019) to the multiplex setting, utilizes a multiplex analogue of the classical graph matching problem to use the template as a matched filter for efficiently searching the background for candidate template matches. The effectiveness of our approach is demonstrated both theoretically and empirically, with particular attention paid to the potential benefits of considering multiple channels in the multiplex framework.

Bisected graph matching improves automated pairing of bilaterally homologous neurons from connectomes

“…We also found that BGM outperforms GM for any combination of network layers for both connectomes. These results highlight the advantages of combining BGM with a previously described extension of graph matching [30] when multiple edge types are available, as the highest accuracy on both datasets came from using both contralateral connections and multiple edge types.…”

“…For each combination of layers, BGM always showed an increase in mean matching accuracy over GM (p-values < 0.005 for all of these comparisons, two-sided Mann-Whitney U test). On both datasets, the best results came from using BGM (this work) in concert with the multiplex graph matching proposed in Pantazis et al [30].…”

“…Matching A to some other multiplex network (which has the same edge types 1, …, K ), A RR , thus amounts to matching each of their constituent adjacency matrices. Pantazis et al [30] formalized this notion by writing the objective function as …”

“…With this formulation, the graph matching problem can be seen as a special case of the bisected graph matching problem, since the objective function in Equation 2.2 reduces to that of Equation 2.1 in the special case where A LR and A RL are both the zero matrix. Note that this problem is also distinct from the multiplex graph matching problem described in Pantazis et al [30], as the contralateral subgraphs require only a permutation of their rows or their columns (not both) to maintain the correct structure of the adjacency matrix.…”

“…To match neurons based on connectivity using this multiplex network information, one can generalize the graph matching problem to a multiplex graph matching problem. Pantazis et al [30] proposed a generalization of the FAQ algorithm to solve this problem. This multiplex graph matching scheme can easily be combined with the bisected graph matching proposed in this work, again by simply modifying the graph matching objective function and its gradient to account for these multiple connection types (see Section 7.2 for more details).…”