Community detection in multilayer degree corrected stochastic block models via DC-MASE

The degree-corrected multiple adjacency spectral embedding (DC-MASE) obtains a joint embedding from multilayer network data to estimate community memberships in the multilayer degree-corrected stochastic blockmodel (DC-SBM).

Overview

Given a collection of L adjacency matrices representing graphs with $n$ aligned vertices (e.g. multilayer networks), DC-MASE obtains a joint embedding matrix with n rows, where each row corresponds to a vertex in the networks. After this, communities are obtained by applying a clustering procedure (such as K-means) to partition the latent positions into K groups in order to estimate the memberships in the multilayer degree-corrected stochastic block model.

The joint embedding is calculated by performing a separate adjacency spectral embedding (ASE) for each graph, which consists in computing the eigendecomposition of each adjacency matrix, with a possible eigenvalue scaling, followed by a row-normalization step (such as dividing the rows by its L2 norm), and then performs a joint singular value decomposition of the concatenated row-normalized ASEs. A pictorial representation is presented below.

R Code

The R code in this repository implements DC-MASE and other methods to perform community detection in multilayer networks. To use this code, download all the content from the R/ folder. Some examples and simulation experiments from the paper are contained in this folder.

Data

The networks encode weighted edges representing the monthly number of flights between pairs of US airports. These data were obtained from the T-100 Segment (US Carriers Only) database US Bureau of Transportation Statistics (BTS). A post-processed version of this dataset is included in this repository. The DC-MASE algorithm is illustrated using these data.

References

Agterberg, J., Lubberts, Z., Arroyo, J., Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels,