Multilayer Spectral Graph Clustering via Convex Layer Aggregation
This work addresses clustering challenges in multilayer graphs, which is incremental as it builds on existing spectral methods with theoretical extensions.
The paper tackles the problem of clustering nodes in multilayer graphs by proposing a convex layer aggregation method, and establishes a phase transition analysis showing a critical noise level for reliable cluster separation with exact bounds for identical cluster sizes.
Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theoretical framework for multilayer spectral graph clustering of the nodes via convex layer aggregation. Under a novel multilayer signal plus noise model, we provide a phase transition analysis that establishes the existence of a critical value on the noise level that permits reliable cluster separation. The analysis also specifies analytical upper and lower bounds on the critical value, where the bounds become exact when the clusters have identical sizes. Numerical experiments on synthetic multilayer graphs are conducted to validate the phase transition analysis and study the effect of layer weights and noise levels on clustering reliability.