Edge-Likelihood Refinement for Overlapping Community Detection in Multiplex Networks

چکیده مقاله

Overlapping community detection in multiplex networks requires membership estimates that can retain participation in more than one group while accounting for layer-specific connectivity. This paper presents Edge-Likelihood Refinement (ELR), a compact refinement procedure that starts from a spectral membership estimate and updates a shared simplex-valued membership matrix according to a Bernoulli edge likelihood. Each network layer has its own symmetric communi-ty-affinity matrix, while both observed and absent links contribute to the objective. This design makes a mixed member-ship useful only when it better explains the multilayer adjacency patterns. On ten predefined synthetic multiplex networks with 120 nodes, three layers, and three communities, ELR achieved mean overlapping normalized mutual information and overlap-node F1 scores of 0.924 and 0.934. A fuzzy-modularity baseline obtained 0.701 and 0.044, and its matched-start variant obtained an overlap-node F1 of 0.081. ELR improved only modestly over its spectral initializer, whose overlap-node F1 was 0.928, but preserved its strong overlap recovery. The results support ELR as a practical likelihood-based re-finement step under the tested assumptions.