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Topological Data Analysis in Graph Neural Networks: Surveys and Perspectives

拓扑数据分析 深度学习 计算机科学 代表(政治) 人工神经网络 功率图分析 图形 拓扑(电路) 机器学习 人工智能 理论计算机科学 数学 组合数学 算法 政治 法学 政治学
作者
Phu Pham,Quang‐Thinh Bui,Ngoc Thanh Nguyen,Róbert Kozma,Philip S. Yu,Bay Vo
出处
期刊:IEEE transactions on neural networks and learning systems [Institute of Electrical and Electronics Engineers]
卷期号:: 1-19 被引量:3
标识
DOI:10.1109/tnnls.2024.3520147
摘要

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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