Graph Neural Networks
Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening
Authors: Guoming Li, Jian Yang, Yifan Chen
Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise filtering paradigm, imposing a uniform filter across all nodes, yet recent findings suggest that this rigid paradigm struggles with heterophilic graphs. To overcome this, recent works have introduced node-wise filtering, which assigns distinct filters to individual nodes, offering enhanced adaptability. However, a fundamental gap remains: a comprehensive framework unifying these two strategies is still absent, limiting theoretical insights into the filtering paradigms. Moreover, through the lens of Contextual Stochastic Block Model, we reveal that a synthesis of graph-wise and node-wise filtering provides a sufficient solution for classification on graphs exhibiting both homophily and heterophily, suggesting the risk of excessive parameterization and potential overfitting with node-wise filtering. To address the limitations, this paper introduces Coarsening-guided Partition-wise Filtering (CPF). CPF innovates by performing filtering on node partitions. The method begins with structure-aware partition-wise filtering, which filters node partitions obtained via graph coarsening algorithms, and then performs feature-aware partition-wise filtering, refining node embeddings via filtering on clusters produced by k-means clustering over features. In-depth analysis is conducted for each phase of CPF, showing its superiority over other paradigms. Finally, benchmark node classification experiments, along with a real-world graph anomaly detection application, validate CPF's efficacy and practical utility. Code is available with the Github repository: https://github.com/vasile-paskardlgm/CPF.
Revolutionizing Graph Neural Networks with Partition-wise Filtering
This paper addresses critical limitations in existing Graph Neural Networks (GNNs), particularly concerning their efficacy on graphs exhibiting mixed homophily and heterophily. Traditional GNNs often employ a uniform 'graph-wise' filter across all nodes, which struggles with complex graph structures. While newer 'node-wise' filtering offers more adaptability, it risks excessive parameterization and overfitting. We introduce Coarsening-guided Partition-wise Filtering (CPF), a novel approach that unifies and optimizes filtering by operating on node partitions rather than individual nodes or the entire graph uniformly.
Key Innovations
- Unified Filtering Framework: CPF provides a comprehensive theoretical framework that integrates graph-wise and node-wise filtering paradigms, offering a more nuanced solution for diverse graph types.
- Structure-Aware Partitioning: The method first performs filtering on node partitions derived from graph coarsening, effectively capturing task-agnostic structural information.
- Feature-Aware Refinement: It then refines node embeddings by filtering on clusters produced by k-means clustering over features, aligning embeddings with downstream tasks.
- Optimized for Mixed Homophily/Heterophily: CPF is specifically designed to address graphs with varying homophily and heterophily, a common characteristic of real-world data, mitigating the overfitting risks of node-wise filtering.
Impact & Results
CPF demonstrates significant performance improvements across benchmark node classification tasks and a real-world graph anomaly detection application. Our experiments validate CPF’s efficacy and practical utility, highlighting its superiority over state-of-the-art methods in both homophilic and heterophilic contexts. This innovation streamlines GNN design, offering a more robust and scalable solution for complex graph-structured data analysis in enterprise AI applications.
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Average improvement on homophilic graphs
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Maximum improvement on heterophilic graphs
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CPF accuracy on Arxiv dataset
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CPF accuracy on Snap dataset
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
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Max Performance Improvement on Heterophilic Graphs
Coarsening-guided Partition-wise Filtering (CPF) Process
Input Graph Data G
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Structure-aware Partition-wise Filtering (Graph Coarsening)
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Node Partitions (Task-agnostic Structural Info)
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Feature-aware Partition-wise Filtering (k-means Clustering on Features)
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Refined Node Embeddings Z
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Downstream Tasks (e.g., Node Classification)
| Paradigm | Description | Pros | Cons |
|---|---|---|---|
| Graph-wise Filtering | Applies a uniform filter across all nodes. |
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| Node-wise Filtering | Assigns distinct filters to individual nodes. |
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| Partition-wise Filtering (CPF) | Filters operations on node partitions (structure-aware and feature-aware). |
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CPF in Graph Anomaly Detection
The paper validates CPF's practical utility in real-world graph anomaly detection (GAD), a critical task in fraud detection and cybersecurity. CPF demonstrates significant improvements, highlighting its robustness beyond standard node classification.
In GAD tasks, CPF achieved a 11.34% maximum improvement on YelpChi dataset, showcasing its effectiveness compared to general-purpose methods and even achieving comparable efficacy to specialized GAD filtering GNNs.
- Problem: Traditional GNNs often struggle with anomaly detection on real-world graphs due to their unique structural and feature characteristics.
- CPF's Approach: By leveraging partition-wise filtering, CPF better captures subtle anomalies and unusual patterns within node groups, which might be missed by uniform or overly granular node-wise filters.
- Results: On benchmark GAD datasets like YelpChi, Amazon, and T-Finance, CPF consistently delivered substantial enhancements, confirming its versatility and practical value in mission-critical enterprise applications.
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Estimated Annual Savings
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Your AI Implementation Roadmap
A structured approach to integrating Coarsening-guided Partition-wise Filtering into your enterprise, ensuring a smooth and successful transition.
Phase 1: Discovery & Strategy
(2-4 Weeks)
Initial consultations to understand your enterprise's graph data challenges and strategic objectives. Data audit and preliminary feasibility study for CPF integration.
Phase 2: Data Preparation & Coarsening
(4-8 Weeks)
Setting up infrastructure for graph data processing. Implementing and optimizing graph coarsening algorithms to create initial node partitions, tailored to your dataset characteristics.
Phase 3: Model Development & Training
(6-12 Weeks)
Developing and training CPF models, including structure-aware and feature-aware filtering components. Iterative tuning and validation on your specific enterprise datasets.
Phase 4: Deployment & Integration
(3-6 Weeks)
Seamless integration of the trained CPF models into your existing enterprise AI/ML pipelines. Comprehensive testing and performance monitoring in a live environment.
Phase 5: Optimization & Scaling
(Ongoing)
Continuous monitoring, performance optimization, and scaling of CPF for evolving data and business needs. Advanced feature development and iterative improvements.
Ready to Transform Your Enterprise with AI?
The estimated investment for this solution typically ranges from $75,000 to $250,000 USD, depending on the complexity of your graph data, data volume, and specific integration requirements. Schedule a direct consultation with our AI specialists to get a tailored proposal and precise estimate for your organization.
Coarsening-guided Partition-wise Filtering (CPF) represents a significant leap forward in Graph Neural Network (GNN) capabilities. By introducing a novel paradigm that filters on node partitions, CPF effectively unifies the benefits of both graph-wise and node-wise filtering, addressing critical limitations in handling graphs with mixed homophily and heterophily. Its superior performance across various benchmarks and real-world applications, including anomaly detection, validates its practical utility and efficiency. CPF offers a robust, scalable, and adaptable framework, setting a new standard for GNN design in complex enterprise AI environments.
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