Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for
  Semi-Supervised Learning on Multilayer Graphs
Sara Venturini Andrea Cristofari Francesco Rinaldi Francesco Tudisco
Clustering (or community detection) on multilayer graphs poses several
additional complications with respect to standard graphs as different layers
may be characterized by different structures and types of information. One of
the major challenges is to establish the extent to which each layer contributes
to the cluster assignment in order to effectively take advantage of the
multilayer structure and improve upon the classification obtained using the
individual layers or their union. However, making an informed a-priori
assessment about the clustering information content of the layers can be very
complicated. In this work, we assume a semi-supervised learning setting, where
the class of a small percentage of nodes is initially provided, and we propose
a parameter-free Laplacian-regularized model that learns an optimal nonlinear
combination of the different layers from the available input labels. The
learning algorithm is based on a Frank-Wolfe optimization scheme with inexact
gradient, combined with a modified Label Propagation iteration. We provide a
detailed convergence analysis of the algorithm and extensive experiments on
synthetic and real-world datasets, showing that the proposed method compares
favourably with a variety of baselines and outperforms each individual layer
when used in isolation.