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TopoEmbedX: A General Framework for Representation Learning on Topological Domains

arXiv 2609.37884 ↗First posted 29 Sep 2026cs.LGcited by 0

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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.

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.

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27 of 47 references.

References · 27

  1. 2016node2vec: Scalable Feature Learning for Networkscited by 1,918
  2. 2014DeepWalk: Online Learning of Social Representationscited by 1,547
  3. 2017graph2vec: Learning Distributed Representations of Graphscited by 230
  4. 2017Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2veccited by 198
  5. 2022Graph neural networks for materials science and chemistrycited by 182
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  7. 2022Topological Deep Learning: Going Beyond Graph Datacited by 97
  8. 2019Topological Signal Processing over Simplicial Complexescited by 96
  9. 2018Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplaciancited by 86
  10. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 82
  11. 2020Computing Graph Neural Networks: A Survey from Algorithms to Acceleratorscited by 81
  12. 2021Graph Representation Learning in Biomedicinecited by 80
15 more
  1. 2021Topology-Aware Segmentation Using Discrete Morse Theorycited by 75
  2. 2020Cell Complex Neural Networkscited by 67
  3. 2021What are higher-order networks?cited by 66
  4. 2018A Topological Regularizer for Classifiers via Persistent Homologycited by 63
  5. 2018NetLSD: Hearing the Shape of a Graphcited by 52
  6. 2023Topology-Aware Uncertainty for Image Segmentationcited by 32
  7. 2018Billion-scale Network Embedding with Iterative Random Projectioncited by 25
  8. 2021Graph Neural Networks for Communication Networks: Context, Use Cases and Opportunitiescited by 22
  9. 2024TopoX: A Suite of Python Packages for Machine Learning on Topological Domainscited by 22
  10. 2020Fast Sequence-Based Embedding with Diffusion Graphscited by 14
  11. 2022Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstructioncited by 14
  12. 2019Simplex2Vec embeddings for community detection in simplicial complexescited by 13
  13. 2021Signal processing on simplicial complexescited by 12
  14. 2013Subgraph Frequencies: Mapping the Empirical and Extremal Geography of Large Graph Collectionscited by 8
  15. 2022Generative Hypergraph Models and Spectral Embeddingcited by 5

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