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Cleora: A Simple, Strong and Scalable Graph Embedding Scheme (2102.02302v1)

Published 3 Feb 2021 in cs.LG and cs.AI

Abstract: The area of graph embeddings is currently dominated by contrastive learning methods, which demand formulation of an explicit objective function and sampling of positive and negative examples. This creates a conceptual and computational overhead. Simple, classic unsupervised approaches like Multidimensional Scaling (MSD) or the Laplacian eigenmap skip the necessity of tedious objective optimization, directly exploiting data geometry. Unfortunately, their reliance on very costly operations such as matrix eigendecomposition make them unable to scale to large graphs that are common in today's digital world. In this paper we present Cleora: an algorithm which gets the best of two worlds, being both unsupervised and highly scalable. We show that high quality embeddings can be produced without the popular step-wise learning framework with example sampling. An intuitive learning objective of our algorithm is that a node should be similar to its neighbors, without explicitly pushing disconnected nodes apart. The objective is achieved by iterative weighted averaging of node neigbors' embeddings, followed by normalization across dimensions. Thanks to the averaging operation the algorithm makes rapid strides across the embedding space and usually reaches optimal embeddings in just a few iterations. Cleora runs faster than other state-of-the-art CPU algorithms and produces embeddings of competitive quality as measured on downstream tasks: link prediction and node classification. We show that Cleora learns a data abstraction that is similar to contrastive methods, yet at much lower computational cost. We open-source Cleora under the MIT license allowing commercial use under https://github.com/Synerise/cleora.

Citations (17)

Summary

  • The paper presents Cleora, an unsupervised graph embedding algorithm that iteratively averages neighbor embeddings to bypass the complexity of contrastive methods.
  • The method converges rapidly using iterative weighted averaging and supports diverse graph types, including hypergraphs via Clique and Star expansions.
  • Cleora’s additive and inductive properties enable efficient merging of embeddings and fast updates, making it practical for large-scale, dynamic graph applications.

Cleora: A Simple, Strong and Scalable Graph Embedding Scheme

In this paper, the authors present Cleora, an algorithm for graph embeddings that addresses the limitations of contemporary approaches dominated by contrastive learning methods. Cleora aims to reduce the computational and conceptual overhead often associated with explicit objective function formulation and example sampling in contrastive methods. It combines unsupervised learning principles with scalability to handle real-world large graphs efficiently.

Methodology

Cleora avoids the complex, step-wise optimization characteristic of many contrastive methods. Instead, it utilizes a learning objective whereby a node should be similar to its neighbors. This is achieved through iterative weighted averaging of a node's neighbors' embeddings, followed by normalization across dimensions. This approach enables Cleora to make significant changes across embedding space rapidly, often converging to optimal embeddings in just a few iterations.

The algorithm supports various graph types, including undirected, directed, and weighted edges, and can scale efficiently to embed massive graphs. Cleora employs two hypergraph expansion strategies—Clique and Star—that facilitate the transformation of hyperedges into pairwise edges. This flexibility ensures that Cleora can handle diverse graph structures optimally.

Results

The paper reports that Cleora is faster than other state-of-the-art CPU-based algorithms, making it a practical choice for embedding large graphs. It produces embeddings of competitive quality for tasks like link prediction and node classification across various datasets, demonstrating a balance between performance and computational efficiency.

Crucially, Cleora's unsupervised nature with only two configurable parameters—iteration number and embedding dimensionality—offers a straightforward configuration process compared to methods like PBG, which require tuning numerous parameters. The embeddings generated by Cleora are versatile, not being explicitly optimized for a single downstream task, thus enhancing usability across different applications.

Practical Implications

Cleora exhibits two noteworthy properties: additivity and inductivity. These properties allow embeddings from partitioned graphs to be merged seamlessly and enable efficient embedding of new nodes post hoc, attributes that are particularly beneficial for dynamic and large-scale graph environments typically found in industrial applications. In practice, Cleora has demonstrated the capability to embed e-commerce graphs, consisting of millions of nodes and billions of edges, within feasible timeframes using standard computational resources.

Theoretical and Future Considerations

The algorithm's emphasis on leveraging neighborhood similarity rather than detailed structural equivalence suggests potential applications in scenarios where such similarities are paramount, like recommendation systems. The inherent scalability of Cleora opens paths for future research into even larger, perhaps streaming, graph embeddings, where incremental updates could become more crucial.

By releasing Cleora as open-source software, the authors facilitate further exploration and adaptation in diverse contexts, potentially stimulating additional advancements in graph-based machine learning applications.

Overall, Cleora establishes itself as a competitive, efficient alternative in the landscape of graph embedding methods, offering a substantial compromise between simplicity and performance. Its design principles might inspire future developments towards more scalable and easily adaptable algorithms in the broader AI and machine learning domains.