Graph Neural Networks
OCN: Effectively Utilizing Higher-Order Common Neighbors for Better Link Prediction
Common Neighbors (CNs) and their higher-order variants are important pairwise features widely used in state-of-the-art link prediction methods. However, existing methods often struggle with the repetition across different orders of CNs and fail to fully leverage their potential. We identify that these limitations stem from two key issues: redundancy and over-smoothing in high-order common neighbors. To address these challenges, we design orthogonalization to eliminate redundancy between different-order CNs and normalization to mitigate over-smoothing. By combining these two techniques, we propose Orthogonal Common Neighbor (OCN), a novel approach that significantly outperforms the strongest baselines by an average of 7.7% on popular link prediction benchmarks. A thorough theoretical analysis is provided to support our method. Ablation studies also verify the effectiveness of our orthogonalization and normalization techniques. Code is available at: https://github.com/qingpingmo/OCN
Executive Impact: OCN's Core Advantages
OCN addresses key challenges in link prediction by leveraging higher-order common neighbors. It tackles redundancy through orthogonalization and over-smoothing via normalization, achieving state-of-the-art performance with an average 7.7% improvement on benchmarks. Its efficiency and scalability are also highlighted.
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Deep Analysis & Enterprise Applications
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Orthogonalization Explained
Orthogonalization is crucial for eliminating redundancy between different orders of Common Neighbors (CNs). By applying a Gram-Schmidt like process, OCN ensures that higher-order CNs provide truly novel information, rather than just repeating what lower-order CNs already capture. This enhances the model's ability to learn complex pairwise structures and improves generalization. The paper also proposes a polynomial trick for faster, approximated orthogonalization.
Key Insight:
Eliminates redundancy in higher-order common neighbors, enabling models to capture distinct structural relationships.
Normalization for Over-Smoothing
Over-smoothing in higher-order CNs can make all node pairs appear similar, leading to a loss of distinctiveness. OCN addresses this by dividing the coefficient of each node by the number of k-hop walks it participates in. This 'path-based normalization' mitigates the issue by ensuring that frequently appearing common neighbors do not overly influence link features, thus preserving the uniqueness of pairwise representations.
Key Insight:
Counters over-smoothing by weighting common neighbors based on their participation in k-hop walks, maintaining distinctiveness.
OCN's Architectural Flow
OCN's architecture integrates MPNN with orthogonalized and normalized common neighbors. The process involves first running MPNN on the original graph to generate initial node representations. Then, higher-order common neighbors are computed, orthogonalized, and normalized. Finally, these processed common neighbor features guide the pooling of MPNN features to predict links. This MPNN-then-SF framework combines scalability with enhanced expressivity.
Enterprise Process Flow
MPNN on Original Graph
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Compute Higher-Order CNs
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Orthogonalize CNs (Redundancy)
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Normalize CNs (Over-smoothing)
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Pool MPNN Features with Processed CNs
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Predict Link Likelihood
Performance Benchmarking
OCN demonstrates state-of-the-art performance across various popular link prediction benchmarks, including Open Graph Benchmark datasets. It significantly outperforms existing models like NCNC, NCN, and BUDDY, achieving an average improvement of 7.7%. Ablation studies confirm the effectiveness of both orthogonalization and normalization components, highlighting their critical roles in the overall performance gains.
| Metric | OCN | NCNC | BUDDY |
|---|---|---|---|
| Cora HR@100 | 89.82±0.91 | 89.65±1.36 | 88.00±0.44 |
| Citeseer HR@100 | 93.62±1.30 | 93.47±0.95 | 92.93±0.27 |
| Pubmed HR@100 | 83.96±0.51 | 81.29±0.95 | 74.10±0.78 |
| Collab HR@50 | 72.43±3.75 | 70.59±0.29 | 65.94±0.58 |
| PPA HR@100 | 69.79±0.85 | 32.38±2.58 | 49.85±0.20 |
| Citation2 MRR | 88.57±0.06 | 84.92±0.29 | 87.56±0.11 |
| DDI HR@20 | 97.42±0.34 | 90.88±3.13 | 78.51±1.36 |
Notes:
- OCN consistently outperforms other leading models across most datasets.
- Normalization and orthogonalization are key contributors to OCN's superior performance.
- Higher-order common neighbors are effectively leveraged in OCN, unlike previous methods.
Scalability & Efficiency
OCN and its polynomial filter variant, OCNP, demonstrate better scalability compared to methods like SEAL and Neo-GNN, especially on larger datasets. While OCN has comparable or slightly higher memory overhead than NCN, OCNP significantly reduces computational complexity, making it more efficient in terms of both inference speed and memory consumption. This ensures practical applicability for real-world large-scale graphs.
Case Study: Scalability & Efficiency
Impact: OCN and OCNP exhibit strong scalability and efficiency, making them suitable for large-scale graph datasets, with OCNP offering reduced computational overhead.
OCN and its polynomial filter variant, OCNP, demonstrate better scalability compared to methods like SEAL and Neo-GNN, especially on larger datasets. While OCN has comparable or slightly higher memory overhead than NCN, OCNP significantly reduces computational complexity, making it more efficient in terms of both inference speed and memory consumption. This ensures practical applicability for real-world large-scale graphs.
Quantify Your AI Impact
Estimate the potential operational savings and efficiency gains for your enterprise by integrating advanced link prediction models like OCN.
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Your Path to Advanced Link Prediction
A phased approach to integrating OCN into your enterprise, ensuring a smooth transition and maximum impact.
Phase 1: Discovery & Strategy
Assess current link prediction needs, data readiness, and define success metrics. Develop a tailored implementation strategy.
Phase 2: Pilot & Integration
Deploy OCN on a subset of your data. Integrate with existing systems and validate initial performance.
Phase 3: Optimization & Scaling
Refine model parameters, expand deployment across relevant workflows, and monitor ongoing performance for continuous improvement.
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