# TopER: Topological Embeddings in Graph Representation Learning

arXiv: https://arxiv.org/abs/2410.01778 · HTML: https://mlsanity.com/paper/2410.01778/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 85 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 30 of 50)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Directional Graph Networks](https://mlsanity.com/paper/2010.02863/) (2020)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Breaking the Limits of Message Passing Graph Neural Networks](https://mlsanity.com/paper/2106.04319/) (2021)
- [AutoGCL: Automated Graph Contrastive Learning via Learnable View Generators](https://mlsanity.com/paper/2109.10259/) (2021)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modeling](https://mlsanity.com/paper/2304.02806/) (2023)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Let Invariant Rationale Discovery Inspire Graph Contrastive Learning](https://mlsanity.com/paper/2206.07869/) (2022)
- [Understanding graph embedding methods and their applications](https://mlsanity.com/paper/2012.08019/) (2020)
- [Graph InfoClust: Leveraging cluster-level node information for unsupervised graph representation learning](https://mlsanity.com/paper/2009.06946/) (2020)
- [Graph Positional and Structural Encoder](https://mlsanity.com/paper/2307.07107/) (2023)

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

- [Diversity Curves for Graph Representation Learning](https://mlsanity.com/paper/2605.06466/) (2026)

## Abstract (arXiv)

Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting interpretability and practical visualization. In this work, we introduce Topological Evolution Rate (TopER), a novel, low-dimensional embedding approach grounded in topological data analysis. TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures, resulting in intuitive and interpretable visualizations of graph data. This approach not only enhances the exploration of graph datasets but also delivers competitive performance in graph clustering and classification tasks. Our TopER-based models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.