REGAL: Representation Learning-based Graph Alignment (1802.06257v3)

Abstract: Problems involving multiple networks are prevalent in many scientific and other domains. In particular, network alignment, or the task of identifying corresponding nodes in different networks, has applications across the social and natural sciences. Motivated by recent advancements in node representation learning for single-graph tasks, we propose REGAL (REpresentation learning-based Graph ALignment), a framework that leverages the power of automatically-learned node representations to match nodes across different graphs. Within REGAL we devise xNetMF, an elegant and principled node embedding formulation that uniquely generalizes to multi-network problems. Our results demonstrate the utility and promise of unsupervised representation learning-based network alignment in terms of both speed and accuracy. REGAL runs up to 30x faster in the representation learning stage than comparable methods, outperforms existing network alignment methods by 20 to 30% accuracy on average, and scales to networks with millions of nodes each.

• The paper presents REGAL, which uses unsupervised node representation learning via xNetMF to align networks across diverse domains.
• It employs efficient low-rank matrix approximation and greedy alignment, achieving up to 30x speed-up and 20-30% accuracy improvement over traditional methods.
• The framework robustly handles both attributed and unattributed networks, paving the way for advanced applications in multi-network analysis.

Overview of REGAL: Representation Learning-based Graph Alignment

The paper "REGAL: Representation Learning-based Graph Alignment" by Heimann et al., proposes a novel framework, REGAL, for network alignment leveraging representation learning. Network alignment, which involves identifying corresponding nodes across different networks, is a key operation in multiple scientific fields, including social sciences and bioinformatics. The presented work stands out by offering a framework that utilizes automatically-learned node representations to facilitate network alignment, proposing the Cross-Network Matrix Factorization (xNetMF) as a core component.

Methodology

REGAL aims to improve upon existing network alignment methods by adopting a representation learning approach that generalizes well to multi-network scenarios. The framework is centered around xNetMF, an unsupervised representation learning technique specifically designed to capture node identities in a way that supports cross-network applicability.

The key steps of the REGAL framework include:

1. Node Identity Extraction: This step involves computing structural and attribute-related information for each node. xNetMF, in particular, captures a node's identity by extracting information about the degrees of its neighboring nodes up to K hops away. This approach is adaptable and does not rely on node-to-node proximity, allowing it to generalize across disjoint networks.
2. Efficient Similarity-based Representation: To avoid the computational burden of full pairwise similarity calculations, REGAL employs a low-rank approximation technique through the Nyström method. This method uses a subset of nodes (landmarks) to approximate the similarity matrix, reducing the factorization problem to a more manageable size without sacrificing accuracy significantly.
3. Fast Node Representation Alignment: Once nodes are embedded, alignment is achieved by matching embeddings in a greedy manner while ensuring computational efficiency through the use of data structures like k-d trees.

Results and Discussion

The evaluation of REGAL shows that it is both fast and accurate. The framework outperforms traditional network alignment methods by 20-30% in terms of accuracy and offers a speed-up of up to 30x during the representation learning phase. These results highlight the efficacy of REGAL in handling large-scale networks, up to millions of nodes, with a noteworthy improvement in runtime over other approaches.

The authors conducted extensive experiments to demonstrate REGAL's robustness against structural and attribute noise, showing superior or competitive accuracy compared to baseline methods. Moreover, REGAL's flexibility is demonstrated by its applicability to both attributed and unattributed graphs, a capability not inherent in some of the compared methods.

Implications and Future Work

The introduction of a representation learning-based approach to network alignment opens up several avenues for future research. Notably, the capability to handle various types of networks, including attributed ones, sets the stage for more sophisticated applications and broader cross-network analyses. The implicit method of matrix factorization incorporated by REGAL could serve as a foundation for further exploration into more complex network types, such as those with weighted edges or those incorporating temporal dynamics.

The paper suggests potential theoretical and practical implications for extending these methods to support other applications such as multi-network clustering or anomaly detection. As the field of graph mining and network analysis advances, frameworks like REGAL that leverage the power of representation learning could redefine how complex, interconnected data is processed and analyzed, paving the way for future developments in artificial intelligence and data science.