Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings (2006.13009v2)

Abstract: In this paper, we propose an end-to-end graph learning framework, namely Iterative Deep Graph Learning (IDGL), for jointly and iteratively learning graph structure and graph embedding. The key rationale of IDGL is to learn a better graph structure based on better node embeddings, and vice versa (i.e., better node embeddings based on a better graph structure). Our iterative method dynamically stops when the learned graph structure approaches close enough to the graph optimized for the downstream prediction task. In addition, we cast the graph learning problem as a similarity metric learning problem and leverage adaptive graph regularization for controlling the quality of the learned graph. Finally, combining the anchor-based approximation technique, we further propose a scalable version of IDGL, namely IDGL-Anch, which significantly reduces the time and space complexity of IDGL without compromising the performance. Our extensive experiments on nine benchmarks show that our proposed IDGL models can consistently outperform or match the state-of-the-art baselines. Furthermore, IDGL can be more robust to adversarial graphs and cope with both transductive and inductive learning.

• The paper introduces IDGL, a novel framework that iteratively refines graph structures and node embeddings to improve predictive accuracy on challenging benchmarks.
• It leverages an anchor-based approximation in its IDGL-Anch variant to reduce computational complexity and enhance scalability in graph processing.
• Extensive experiments demonstrate that IDGL outperforms state-of-the-art GNN methods, providing increased robustness against adversarial and noisy conditions.

Iterative Deep Graph Learning for Enhanced Graph Neural Network Performance

The paper presents a framework, named Iterative Deep Graph Learning (IDGL), designed to advance Graph Neural Networks (GNNs) by iteratively learning optimal graph structures alongside their corresponding embeddings. The essence of IDGL lies in its dual-interaction philosophy: improvement of graph structures arises from refined node embeddings, and vice versa. This iterative interplay continues until the constructed graph aligns sufficiently well with the optimization target for a downstream prediction task.

To further illustrate adaptability and efficiency, the paper introduces IDGL-Anch, a variant leveraging anchor-based approximation to reduce complexity, ensuring scalability without sacrificing performance. Notably, IDGL demonstrates increased resilience to adversarial graph modifications and maintains robust functionality across both transductive and inductive learning scenarios, as substantiated by experimental benchmarks encompassing nine datasets.

Core Contributions

1. Iterative Graph Structure Learning: IDGL represents a novel methodology, uniquely iterating between refining the graph structure and node embeddings. This iterative enhancement dynamically adjusts based on convergence criteria specific to each mini-batch.
2. Anchor-Based Scalability: By employing anchor-based approximation, IDGL-Anch reduces memory and computational demands, achieving linear time complexity related to the number of graph nodes, a substantial improvement over traditional quadratic complexity.
3. Strong Empirical Performance: Extensive empirical evaluation shows that IDGL consistently meets or surpasses state-of-the-art methods across varied datasets, demonstrating its efficacy in both optimizing predictive accuracy and addressing the challenges of noisy or incomplete graphs.

Detailed Analysis

The IDGL framework distinguishes itself by recasting the graph learning challenge into a similarity metric learning problem, incorporating a multi-head self-attention mechanism to construct graphs with enhanced feature sparsification. It employs weighted cosine similarity combined with $\varepsilon$-neighborhood graph sparsification to ensure non-negativity and manageably sparse adjacency matrices. This innovative viewpoint supports learning graph topology that caters specifically to the complexities of the target task, diverging from previous methods which neglected downstream task dependence.

In terms of graph regularization, the paper emphasizes the necessity of controlling smoothness, connectivity, and sparsity within learned graphs. By employing techniques like the Dirichlet energy for smoothness and additional sparsity penalizations, IDGL ensures high fidelity of the emergent graph structure. This graph regularization loss synergizes with task-specific prediction loss to guide joint optimization, positioning IDGL advantageously compared to methods that overlook structural graph learning.

Experimental Validation

IDGL and its scalable counterpart, IDGL-Anch, are demonstrated to outperform a variety of existing GNN architectures on a range of tasks, particularly in settings where the initial graph data is noisy, incomplete, or completely absent. IDGL's robustness against adversarial alterations, as seen in experiments involving synthetic edge perturbations, highlights the framework’s robustness, a critical feature for practical implementation in real-world graph-based applications.

Future Prospects

The potential real-world applications of this research span numerous domains where optimal graph structure and embeddings are vital, such as social network analysis, drug discovery, and natural language processing. Moreover, future work could address scenarios with noise prevalent across graph topology and node features alike, expanding IDGL's applicability in more diverse and challenging environments.

In conclusion, IDGL stands as a significant advancement in the field of GNNs, combining innovative methodological design with practical efficacy and scalability, paving the way for more robust, adaptable applications in graph-based learning systems. The theoretical insights and extensive experimental validation presented within this framework underscore its potential to set a new threshold in graph structure learning.