# Multilayer Graph Clustering with Optimized Node Embedding

arXiv: https://arxiv.org/abs/2103.16534 · HTML: https://mlsanity.com/paper/2103.16534/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 14 of 14)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Spectral Inference Networks: Unifying Deep and Spectral Learning](https://mlsanity.com/paper/1806.02215/) (2018)
- [Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds](https://mlsanity.com/paper/1303.2221/) (2013)
- [Estimation of Graphical Models through Structured Norm Minimization](https://mlsanity.com/paper/1609.09010/) (2016)
- [Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms](https://mlsanity.com/paper/1708.02620/) (2017)
- [Multilayer Clustered Graph Learning](https://mlsanity.com/paper/2010.15456/) (2020)
- [OrthoNet: Multilayer Network Data Clustering](https://mlsanity.com/paper/1811.00821/) (2018)
- [Stochastic Gradient Descent for Spectral Embedding with Implicit Orthogonality Constraint](https://mlsanity.com/paper/1812.05721/) (2018)

## Abstract (arXiv)

We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem that involves a fidelity term to the layers of a given multilayer graph, and a regularization on the (single-layer) graph induced by the embedding. The fidelity term uses the contrastive loss to properly aggregate the observed layers into a representative embedding. The regularization pushes for a sparse and community-aware graph, and it is based on a measure of graph sparsification called "effective resistance", coupled with a penalization of the first few eigenvalues of the representative graph Laplacian matrix to favor the formation of communities. The proposed optimization problem is nonconvex but fully differentiable, and thus can be solved via the descent gradient method. Experiments show that our method leads to a significant improvement w.r.t. state-of-the-art multilayer graph clustering algorithms.