Neural Common Neighbor with Completion: A Scalable and Powerful Link Prediction Model

Core Concepts

Neural Common Neighbor (NCN) uses learnable pairwise representations to boost link prediction performance, and Neural Common Neighbor with Completion (NCNC) further improves NCN by addressing the problem of graph incompleteness.

Abstract

The paper proposes two key contributions:

Neural Common Neighbor (NCN):

Existing link prediction models use manual and inflexible pairwise features, which limits their performance.
NCN replaces the manual pairwise features with learnable representations produced by a Message Passing Neural Network (MPNN).
NCN outperforms recent strong baselines by large margins while maintaining scalability.

Addressing Graph Incompleteness:

The incompleteness of the input graph is ubiquitous in link prediction tasks and can lead to distribution shifts between the training and test sets, as well as loss of common neighbor information.
To alleviate this problem, the authors propose two intervention methods:

Common Neighbor Completion (CNC): Iteratively completes unobserved links using a link prediction model.
Target Link Removal (TLR): Removes the target links from the input graph.

Combining CNC and TLR with NCN, the authors propose Neural Common Neighbor with Completion (NCNC), which achieves state-of-the-art performance in link prediction tasks.

Stats

The number of common neighbors between training and test edges can have a significant distribution shift in some datasets due to graph incompleteness.
Applying the traditional Common Neighbor (CN) heuristic on the incomplete graph can lead to a large performance degradation compared to the complete graph.

Quotes

"Incompleteness of input graph is ubiquitous for link prediction, as the task itself is to predict unobserved edges which do not exist in the input graph."
"We empirically find that incompleteness leads to distribution shift between the training and test set and loss of common neighbor information."

Key Insights Distilled From

Neural Common Neighbor with Completion for Link Prediction

by Xiyuan Wang,... at arxiv.org 05-06-2024

https://arxiv.org/pdf/2302.00890.pdf

Deeper Inquiries

How can the proposed intervention methods (CNC and TLR) be generalized to other types of graph data beyond link prediction, such as node classification or graph classification tasks?

The CNC (Common Neighbor Completion) and TLR (Target Link Removal) methods can be generalized to other types of graph data tasks by adapting them to suit the specific requirements of node classification or graph classification.
For node classification tasks, CNC can be modified to focus on completing the neighborhood information of nodes rather than links. By predicting the existence of edges between nodes based on their shared neighbors, CNC can help in completing the graph structure for nodes, which can then be used for node classification. TLR, on the other hand, can be applied to remove specific target nodes or edges from the graph to create a more balanced and unbiased dataset for node classification.
In the case of graph classification tasks, CNC can be extended to predict the presence of specific subgraphs or patterns within the graph that are indicative of certain classes or labels. By completing the graph with missing subgraphs or patterns, CNC can enhance the graph representation for classification. TLR can be utilized to remove certain subgraphs or components from the graph to study the impact of different graph structures on the classification task.
Overall, by adapting CNC and TLR to focus on completing or modifying graph structures relevant to node or graph classification, these intervention methods can be effectively generalized to a variety of graph data tasks beyond link prediction.

What are the potential limitations or drawbacks of the CNC and TLR methods, and how can they be further improved or extended?

While CNC and TLR are effective intervention methods for addressing graph incompleteness in link prediction tasks, they do have some limitations and potential drawbacks that should be considered:

Computational Complexity: CNC and TLR may introduce additional computational overhead, especially when applied iteratively or on large graphs. This can impact the scalability of the methods.

Data Leakage: TLR, if not carefully implemented, can lead to data leakage by removing target links from the training set. This can result in biased model performance.

Generalization: CNC and TLR may not generalize well to all types of graph data or may require fine-tuning for different datasets and tasks.

To improve and extend CNC and TLR, the following strategies can be considered:

Efficient Algorithms: Develop more efficient algorithms for completing graph structures and removing target links to reduce computational complexity.

Regularization Techniques: Implement regularization techniques to prevent data leakage in TLR and ensure that the model learns from the incomplete graph structure effectively.

Adaptive Strategies: Develop adaptive strategies for CNC and TLR that can adjust to different graph characteristics and data distributions for improved generalization.

By addressing these limitations and incorporating these improvements, CNC and TLR can be further enhanced and extended for a wider range of graph data tasks.

Given the importance of common neighbor information for link prediction, are there other structural properties of the graph that could be leveraged to further boost the performance of link prediction models?

In addition to common neighbor information, several other structural properties of the graph can be leveraged to enhance the performance of link prediction models:

Node Degree: The degree of nodes in the graph can provide valuable information about their connectivity and importance. Models can incorporate node degree information to prioritize certain nodes or edges in the prediction process.

Graph Density: The overall density of the graph, i.e., the ratio of actual edges to possible edges, can influence link prediction. Models can consider the density of different subgraphs or neighborhoods to make more accurate predictions.

Community Structure: Identifying communities or clusters within the graph can help in understanding the relationships between nodes. Models can leverage community detection algorithms to capture the community structure and improve link prediction.

Centrality Measures: Centrality measures such as betweenness centrality or closeness centrality can highlight important nodes or paths in the graph. Link prediction models can use these measures to prioritize certain links for prediction.

Graph Motifs: Identifying recurring patterns or motifs in the graph can provide insights into the underlying graph structure. Models can analyze graph motifs to extract meaningful features for link prediction.

By incorporating these additional structural properties of the graph into link prediction models, it is possible to enhance the predictive performance and gain a deeper understanding of the relationships within the graph.