The Power Mean Laplacian for Multilayer Graph Clustering
This provides a method for clustering multilayer graphs, which is incremental as it builds on existing Laplacian-based approaches.
The paper tackles the problem of clustering multilayer graphs by introducing a one-parameter family of matrix power means to merge Laplacians from different layers, showing it can recover ground truth clusters in both synthetic and real-world data.
Multilayer graphs encode different kind of interactions between the same set of entities. When one wants to cluster such a multilayer graph, the natural question arises how one should merge the information different layers. We introduce in this paper a one-parameter family of matrix power means for merging the Laplacians from different layers and analyze it in expectation in the stochastic block model. We show that this family allows to recover ground truth clusters under different settings and verify this in real world data. While computing the matrix power mean can be very expensive for large graphs, we introduce a numerical scheme to efficiently compute its eigenvectors for the case of large sparse graphs.