mlsanityData to 7 Oct 2026

Topological Node2vec: Enhanced Graph Embedding via Persistent Homology

arXiv 2309.08241 ↗First posted 15 Sep 2023stat.ML cs.LG math.ATcited by 5

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Abstract (arXiv)

Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the topology of the input graph. To resolve this we introduce a topological loss term to be added to the training loss of Node2vec which tries to align the persistence diagram (PD) of the resulting embedding as closely as possible to that of the input graph. Following results in computational optimal transport, we carefully adapt entropic regularization to PD metrics, allowing us to measure the discrepancy between PDs in a differentiable way. Our modified loss function can then be minimized through gradient descent to reconstruct both the geometry and the topology of the input graph. We showcase the benefits of this approach using demonstrative synthetic examples.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 35 of its 68 references that are in the map. First posted on arXiv 15 Sep 2023.

Builds on

35 of 68 references.

References · 35

  1. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,346
  2. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  3. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
  4. 2014DeepWalk: Online Learning of Social Representationscited by 1,543
  5. 2017Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Rankingcited by 332
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  7. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 219
  8. 2019Topology-Preserving Deep Image Segmentationcited by 198
  9. 2015On Wasserstein Two Sample Testing and Related Families of Nonparametric Testscited by 165
  10. 2017A Survey on Network Embeddingcited by 142
  11. 2019Topological Autoencoderscited by 124
  12. 2019Ripser: efficient computation of Vietoris-Rips persistence barcodescited by 115
23 more
  1. 2018Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithmcited by 111
  2. 2019A Topology Layer for Machine Learningcited by 79
  3. 2019Hyper-SAGNN: a self-attention based graph neural network for hypergraphscited by 69
  4. 2018A Topological Regularizer for Classifiers via Persistent Homologycited by 62
  5. 2020On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithmcited by 61
  6. 2019Sinkhorn Divergences for Unbalanced Optimal Transportcited by 52
  7. 2020Understanding graph embedding methods and their applicationscited by 50
  8. 2020word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings of Structured Datacited by 38
  9. 2020Debiased Sinkhorn barycenterscited by 34
  10. 2018Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transportcited by 32
  11. 2019A Framework for Differential Calculus on Persistence Barcodescited by 29
  12. 2020GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodescited by 26
  13. 2018Topology-Aware Surface Reconstruction for Point Cloudscited by 21
  14. 2019Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transportcited by 17
  15. 2022Topological Optimization with Big Stepscited by 15
  16. 2020The Effects of Randomness on the Stability of Node Embeddingscited by 14
  17. 2015Continuation of Point Clouds via Persistence Diagramscited by 13
  18. 2021Estimation and Quantization of Expected Persistence Diagramscited by 8
  19. 2022Approximating Persistent Homology for Large Datasetscited by 8
  20. 2021A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysiscited by 5
  21. 2021Optimisation of Spectral Wavelets for Persistence-based Graph Classificationcited by 2
  22. 2022On the Surprising Behaviour of node2veccited by 2
  23. 2022An Homogeneous Unbalanced Regularized Optimal Transport model with applications to Optimal Transport with Boundarycited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 1; 2026: 1.

5 papers.

  1. 2024Point-Level Topological Representation Learning on Point Cloudscited by 4
  2. 2024TopER: Topological Embeddings in Graph Representation Learningcited by 1
  3. 2025T3former: Temporal Graph Classification with Topological Machine Learningcited by 1
  4. 2023Estimation of embedding vectors in high dimensionscited by 0
  5. 2026Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithmscited by 0