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

arXiv: https://arxiv.org/abs/2306.00152 · HTML: https://mlsanity.com/paper/2306.00152/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 62 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization](https://mlsanity.com/paper/1905.01332/) (2019)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [Community Detection in Multiplex Networks](https://mlsanity.com/paper/1910.07646/) (2019)
- [Nonlinear Higher-Order Label Spreading](https://mlsanity.com/paper/2006.04762/) (2020)
- [New Analysis and Results for the Frank-Wolfe Method](https://mlsanity.com/paper/1307.0873/) (2013)
- [Towards Gradient Free and Projection Free Stochastic Optimization](https://mlsanity.com/paper/1810.03233/) (2018)
- [Random Walks on Multiplex Networks](https://mlsanity.com/paper/1306.0519/) (2013)
- [Frank-Wolfe and friends: a journey into projection-free first-order optimization methods](https://mlsanity.com/paper/2106.10261/) (2021)
- [MGCN: Semi-supervised Classification in Multi-layer Graphs with Graph Convolutional Networks](https://mlsanity.com/paper/1811.08800/) (2018)
- [Towards effective visual analytics on multiplex and multilayer networks](https://mlsanity.com/paper/1501.01666/) (2015)
- [Evolutionary games on multilayer networks: A colloquium](https://mlsanity.com/paper/1504.04359/) (2015)
- [The multilayer connectome of Caenorhabditis elegans](https://mlsanity.com/paper/1608.08793/) (2016)
- [Active set complexity of the Away-step Frank-Wolfe Algorithm](https://mlsanity.com/paper/1912.11492/) (2019)
- [Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs](https://mlsanity.com/paper/1910.13951/) (2019)
- [mGNN: Generalizing the Graph Neural Networks to the Multilayer Case](https://mlsanity.com/paper/2109.10119/) (2021)
- [Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products](https://mlsanity.com/paper/2007.05239/) (2020)
- [Avoiding bad steps in Frank Wolfe variants](https://mlsanity.com/paper/2012.12737/) (2020)
- [A Variance-aware Multiobjective Louvain-like Method for Community Detection in Multiplex Networks](https://mlsanity.com/paper/2106.13543/) (2021)
- [Hyper-diffusion on multiplex networks](https://mlsanity.com/paper/2205.10291/) (2022)
- [Multilink Communities of Multiplex Networks](https://mlsanity.com/paper/1706.09011/) (2017)
- [Multilayer patent citation networks: A comprehensive analytical framework for studying explicit technological relationships](https://mlsanity.com/paper/2203.14479/) (2022)

## Abstract (arXiv)

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.