# TopoEmbedX: A General Framework for Representation Learning on Topological Domains

arXiv: https://arxiv.org/abs/2609.37884 · HTML: https://mlsanity.com/paper/2609.37884/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 27 of 27)

- [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)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Computing Graph Neural Networks: A Survey from Algorithms to Accelerators](https://mlsanity.com/paper/2010.00130/) (2020)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [NetLSD: Hearing the Shape of a Graph](https://mlsanity.com/paper/1805.10712/) (2018)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [Billion-scale Network Embedding with Iterative Random Projection](https://mlsanity.com/paper/1805.02396/) (2018)
- [Graph Neural Networks for Communication Networks: Context, Use Cases and Opportunities](https://mlsanity.com/paper/2112.14792/) (2021)
- [TopoX: A Suite of Python Packages for Machine Learning on Topological Domains](https://mlsanity.com/paper/2402.02441/) (2024)
- [Fast Sequence-Based Embedding with Diffusion Graphs](https://mlsanity.com/paper/2001.07463/) (2020)
- [Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction](https://mlsanity.com/paper/2203.01703/) (2022)
- [Simplex2Vec embeddings for community detection in simplicial complexes](https://mlsanity.com/paper/1906.09068/) (2019)
- [Signal processing on simplicial complexes](https://mlsanity.com/paper/2106.07471/) (2021)
- [Subgraph Frequencies: Mapping the Empirical and Extremal Geography of Large Graph Collections](https://mlsanity.com/paper/1304.1548/) (2013)
- [Generative Hypergraph Models and Spectral Embedding](https://mlsanity.com/paper/2207.13895/) (2022)

## Abstract (arXiv)

Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationships. These structures appear in many modern datasets and require specialized methods for generating meaningful embeddings. In this paper, we introduce TopoEmbedX, a unified framework for embedding a wide range of topological domains into Euclidean spaces. The package brings together several existing topological embedding algorithms---DeepCell, Cell2Vec, CellDiff2Vec, HOLE, and HOGLEE---and introduces five new algorithms: ComplexNetMF, ComplexRep, ComplexRandNE, ComplexWalklets, and ComplexHeat. These algorithms extend well-known graph embedding techniques to higher-order settings using the augmented Hasse graph of a topological domain. TopoEmbedX provides a clear, consistent, and easy-to-use framework for topological representation learning. Experiments show that the embeddings generated by TopoEmbedX support tasks such as classification and regression across multidimensional data.