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.

本研究提出了一种针对多层图所进行的聚类方法，其中采用了基于 Laplacian 正则化的非参数模型，并结合修改后的 Label Propagation 迭代方法，成功地进行了半监督学习，使得每一层所具有的信息内容更为丰富，聚类效果得到显著提高。

学习正确的层级：一种基于数据驱动的多层图半监督学习层聚合策略

Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for  Semi-Supervised Learning on Multilayer Graphs

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.

本文研究了如何对多层图进行聚类，引入了一种参数化的矩阵幂均值来合并不同层的拉普拉斯矩阵，并在随机块模型中分析它。我们证明了这种方法可以在不同设置下恢复地面真实聚类并在实际世界数据中验证。而对于大型图形计算矩阵幂均值可能非常昂贵，我们引入了一种计算其特征向量的数值方案，以便用于大型稀疏图形的情况。