Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms

Multilayer graphs provide a framework for representing multiple types of relations between entities, represented as nodes. In a multilayer graph each layer describes a specific type of relation among pairs of nodes that are shared across layers. For example, in multi-relational social networks, two layers might correspond to friendship relations and business relations, respectively. In temporal networks, each layer might correspond to a snapshot of the entire network at a sampled time instant. Multilayer graphs can be incorporated into in many signal processing and data mining techniques, including inference of mixture models [1], [2], tensor decomposition [3], information extraction [4], multi-view learning and processing [5], graph wavelet transforms [6], principal component analysis and dictionary learning [7], [8], anomaly detection [9], and community detection [10], [11], among others. The objective of multilayer graph clustering is to find a consensus cluster assignment on each node in the common node set by combining connectivity patterns in each layer.