Topological Data Analysis in Graph Neural Networks: Surveys and Perspectives

For many years, topological data analysis (TDA) and deep learning (DL) have been considered separate data analysis and representation learning approaches, which have nothing in common. The root cause of this challenge comes from the difficulties in building, extracting, and integrating TDA construct...

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Published in:IEEE transaction on neural networks and learning systems Vol. 36; no. 6; pp. 9758 - 9776
Main Authors: Pham, Phu, Bui, Quang-Thinh, Thanh Nguyen, Ngoc, Kozma, Robert, Yu, Philip S., Vo, Bay
Format: Journal Article
Language:English
Published: United States IEEE 01.06.2025
Subjects:
Data analysis
Data mining
Data structures
Deep learning (DL)
Electronic mail
Feature extraction
graph filtration
graph neural network (GNN)
Graph neural networks
Learning systems
persistent homology (PH)
Representation learning
Surveys
Taxonomy
topological data analysis (TDA)
topological representation learning
ISSN:2162-237X, 2162-2388, 2162-2388
Online Access:Get full text
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Summary:For many years, topological data analysis (TDA) and deep learning (DL) have been considered separate data analysis and representation learning approaches, which have nothing in common. The root cause of this challenge comes from the difficulties in building, extracting, and integrating TDA constructs, such as barcodes or persistent diagrams, within deep neural network architectures. Therefore, the powers of these two approaches are still on their islands and have not yet combined to form more powerful tools for dealing with multiple complex data analysis tasks. Fortunately, we have witnessed several remarkable attempts to integrate DL-based architectures with topological learning paradigms in recent years. These topology-driven DL techniques have notably improved data-driven analysis and mining problems, especially within graph datasets. Recently, graph neural networks (GNNs) have emerged as a popular deep neural architecture, demonstrating significant performance in various graph-based analysis and learning problems. Explicitly, within the manifold paradigm, the graph is naturally considered as a topological object (e.g., the topological properties of the given graph can be represented by the edge weights). Therefore, integrating TDA and GNN is considered an excellent combination. Many well-known studies have recently presented the effectiveness of TDA-assisted GNN-based architectures in dealing with complex graph-based data representation analysis and learning problems. Motivated by the successes of recent research, we present systematic literature about this nascent and promising research direction in this article, which includes general taxonomy, preliminaries, and recently proposed state-of-the-art topology-driven GNN models and perspectives.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2024.3520147