Multilayer Spectral Graph Clustering via Convex Layer Aggregation

TL;DR

This paper introduces a theoretical framework for multilayer spectral graph clustering using convex layer aggregation, analyzing phase transitions under a multilayer signal plus noise model to determine conditions for reliable clustering.

Contribution

It provides a novel phase transition analysis with bounds on noise levels for multilayer spectral clustering, validated through synthetic experiments.

Findings

Identifies a critical noise level for reliable cluster separation.

Provides analytical bounds that are exact for equal-sized clusters.

Validates phase transition analysis with synthetic multilayer graphs.

Abstract

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.