Enterprise AI Analysis
ArnoldiGCL: Graph Contrastive Learning via Learnable Arnoldi-Based Guided Spectral Chebyshev Polynomial Filters
Authors: Mustafa Coşkun, Abdelkader Baggag, Mehmet Koyutürk
Graph Contrastive Learning (GCL) emerged as a powerful paradigm in self-supervised graph representation learning. While earlier applications of GCL rely on homophily assumptions, spectral graph neural networks (GNNs) enhance the effectiveness of GCL on heterophilic graphs by incorporating both low-pass and high-pass filters. However, due to numerical considerations, existing approaches oversimplify low-pass and high-pass filters by modeling them as basic linear operations, failing to capture complex topological relationships. Here, we propose ArnoldiGCL, a novel algorithm that enables the application of complex spectral filters for Graph Contrastive Learning (GCL). Using Arnoldi orthonormalization-based Chebyshev interpolation, ArnoldiGCL overcomes the difficulties posed by ill-conditioned Vandermonde systems that arise in the modeling of complex filters. By introducing learnable filters, our method generates diverse spectral views and effectively captures nuanced graph structures. Theoretical analysis demonstrates that ArnoldiGCL accurately interpolates complex filters, thus forming a solid foundation for contrastive learning on graphs with complex structures. Extensive experiments on real-world datasets confirm that ArnoldiGCL significantly outperforms state-of-the-art GCL algorithms on both homophilic and heterophilic graphs, showcasing its robustness and versatility. The code for ArnoldiGCL is available as open source at: https://github.com/mustafaCoskunAgu/ArnoldiGCL
Executive Impact at a Glance
ArnoldiGCL's advancements in graph contrastive learning offer significant opportunities for enterprises handling complex, interconnected data, driving more accurate insights and decision-making.
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Performance Increase on Heterophilic Graphs
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Improved Numerical Stability in Filter Approximation
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Versatility Across Graph Homophily Levels
Deep Analysis & Enterprise Applications
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Challenges in Graph Representation Learning
Graph Contrastive Learning (GCL) is a powerful self-supervised learning paradigm, but traditional methods often assume graph homophily and struggle with heterophilic graphs. Existing spectral GNN approaches in GCL simplify filter designs, limiting their ability to capture complex non-linear topological relationships due to numerical stability issues with polynomial interpolation.
ArnoldiGCL's Novel Approach
ArnoldiGCL introduces a novel framework that enables the application of complex, non-linear spectral filters within GCL. It uses Arnoldi orthonormalization-based Chebyshev interpolation to overcome ill-conditioned Vandermonde systems, ensuring stable and accurate filter approximation. This allows for learning diverse spectral views and capturing nuanced graph structures effectively.
Transforming Enterprise Graph Analysis
ArnoldiGCL significantly outperforms state-of-the-art GCL algorithms on a wide range of real-world datasets, including both homophilic and heterophilic graphs. By providing a robust and versatile approach to spectral filtering, it establishes a solid foundation for self-supervised graph learning, particularly in contexts with complex and non-linear node relationships.
12.7%
Higher Accuracy on Heterophilic Graph Classification
Arnoldi-Based Filter Approximation Process
Define Complex Filter (e.g., Band-Pass)
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Sample Filter at Chebyshev Nodes
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Construct System via Arnoldi Orthonormalization
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Compute Accurate Polynomial Coefficients
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Apply Filter to Graph for Diverse Views
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Case Study: Robust Representation Learning Across Graph Topologies
Challenge: Traditional Graph Contrastive Learning (GCL) methods often falter on complex real-world datasets characterized by both homophily (nodes connect to similar nodes) and heterophily (nodes connect to dissimilar nodes). The underlying assumption of homophily limits their ability to accurately capture nuanced relationships in diverse network structures, leading to suboptimal node representations and downstream task performance.
ArnoldiGCL Solution: ArnoldiGCL addresses this by enabling the precise and stable approximation of arbitrary nonlinear spectral filters. By integrating Arnoldi orthonormalization with Chebyshev polynomial interpolation, it overcomes the numerical difficulties of ill-conditioned systems. This allows for the dynamic learning of both low-pass and high-pass filters, as well as more sophisticated band-pass and band-rejection filters, which are crucial for modeling complex, multi-scale topological patterns inherent in heterogeneous graphs.
Impact: The ability of ArnoldiGCL to adaptively learn and apply complex spectral filters results in significantly enhanced performance across a wide spectrum of graph types. From citation networks (homophilic) to social networks (mixed) and dating networks (heterophilic), ArnoldiGCL generates richer, more discriminative node embeddings. This translates to improved accuracy in critical enterprise applications such as fraud detection, customer segmentation, and drug discovery, where understanding intricate relationships within vast, heterogeneous graphs is paramount to success and competitive advantage. Enterprises can leverage ArnoldiGCL to unlock deeper insights from their graph-structured data, driving more informed strategic decisions.
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