mlsanityData to 7 Oct 2026

Persistent Homology and Graphs Representation Learning

arXiv 2102.12926 ↗First posted 25 Feb 2021cs.LG cs.CG cs.CVcited by 5

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Abstract (arXiv)

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we consider the case when these embeddings are real-valued. By viewing these embeddings as scalar functions on a domain of interest, we can utilize the tools available in persistent homology to study the topological information encoded in these representations. Our construction effectively defines a unique persistence-based graph descriptor, on both the graph and node levels, for every node representation algorithm. To demonstrate the effectiveness of the proposed method, we study the topological descriptors induced by DeepWalk, Node2Vec and Diff2Vec.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 15 of its 44 references that are in the map. First posted on arXiv 25 Feb 2021.

Builds on

15 of 44 references.

References · 15

  1. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,346
  2. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
  3. 2014DeepWalk: Online Learning of Social Representationscited by 1,543
  4. 2017Representation Learning on Graphs: Methods and Applicationscited by 456
  5. 2017Network Representation Learning: A Surveycited by 101
  6. 2019Graph Representation Learning: A Surveycited by 75
  7. 2020Cell Complex Neural Networkscited by 66
  8. 2016Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplificationcited by 22
  9. 2018Functional Summaries of Persistence Diagramscited by 19
  10. 2020Fast Sequence-Based Embedding with Diffusion Graphscited by 14
  11. 2021TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Imagescited by 12
  12. 2017Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homologycited by 8
3 more
  1. 2015Statistical Analysis of Persistence Intensity Functionscited by 6
  2. 2017Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubescited by 4
  3. 2018Graph Based Analysis for Gene Segment Organization In a Scrambled Genomecited by 2

Built on by

Cited by year

Citing papers per year: 2022: 3; 2023: 0; 2024: 1; 2025: 1.

5 papers.

  1. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  2. 2022On the Surprising Behaviour of node2veccited by 2
  3. 2022Reliable Malware Analysis and Detection using Topology Data Analysiscited by 1
  4. 2022Alleviating neighbor bias: augmenting graph self-supervise learning with structural equivalent positive samplescited by 1
  5. 2025Positional Encoding meets Persistent Homology on Graphscited by 1