# A Simple Way to Learn Metrics Between Attributed Graphs

arXiv: https://arxiv.org/abs/2209.12727 · HTML: https://mlsanity.com/paper/2209.12727/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 26 Sep 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1906.02174/) (2019)
- [A Survey on Metric Learning for Feature Vectors and Structured Data](https://mlsanity.com/paper/1306.6709/) (2013)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [Orthogonal Estimation of Wasserstein Distances](https://mlsanity.com/paper/1903.03784/) (2019)
- [Wasserstein-based Graph Alignment](https://mlsanity.com/paper/2003.06048/) (2020)
- [Distance Metric Learning for Graph Structured Data](https://mlsanity.com/paper/2002.00727/) (2020)
- [Hierarchical and Unsupervised Graph Representation Learning with Loukas's Coarsening](https://mlsanity.com/paper/2007.03373/) (2020)

## Built on by (most cited first, 1 of 1)

- [Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernels](https://mlsanity.com/paper/2402.03838/) (2024)

## Abstract (arXiv)

The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to improve performance of classification or clustering methods. However, due to difficulties in establishing computable, efficient and differentiable distances between attributed graphs, few metric learning algorithms adapted to graphs have been developed despite the strong interest of the community. In this paper, we address this issue by proposing a new Simple Graph Metric Learning - SGML - model with few trainable parameters based on Simple Graph Convolutional Neural Networks - SGCN - and elements of Optimal Transport theory. This model allows us to build an appropriate distance from a database of labeled (attributed) graphs to improve the performance of simple classification algorithms such as k-NN. This distance can be quickly trained while maintaining good performances as illustrated by the experimental study presented in this paper.