Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphs
Not on the map. Why?
Abstract (arXiv)
Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 18 of its 35 references that are in the map. First posted on arXiv 17 Aug 2024.
Builds on
18 of 35 references.
References · 18
- 2017Graph Attention Networkscited by 8,854
- 2017Inductive Representation Learning on Large Graphscited by 6,284
- 2018How Powerful are Graph Neural Networks?cited by 4,355
- 2019EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphscited by 443
- 2022ROLAND: Graph Learning Framework for Dynamic Graphscited by 131
- 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
- 2020Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A surveycited by 123
- 2019Neural Execution of Graph Algorithmscited by 118
- 2017Deep Learning with Topological Signaturescited by 113
- 2020Line Graph Neural Networks for Link Predictioncited by 89
- 2021Topological Graph Neural Networkscited by 86
- 2019Graph Filtration Learningcited by 68
6 more
- 2019Persistence Homology of Networks: Methods and Applicationscited by 30
- 2021Topological Relational Learning on Graphscited by 27
- 2021How to transfer algorithmic reasoning knowledge to learn new algorithms?cited by 22
- 2022Neural Approximation of Graph Topological Featurescited by 16
- 2020Can neural networks learn persistent homology features?cited by 11
- 2023Line Graph Neural Networks for Link Weight Predictioncited by 7
Built on by
Citing papers per year: 2025: 2.
2 papers.