Fast Sequence-Based Embedding with Diffusion Graphs (2001.07463v1)

Abstract: A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear sequences of nodes to create embeddings using a neural network. In this paper, we propose diffusion graphs as a method to rapidly generate vertex sequences for network embedding. Its computational efficiency is superior to previous methods due to simpler sequence generation, and it produces more accurate results. In experiments, we found that the performance relative to other methods improves with increasing edge density in the graph. In a community detection task, clustering nodes in the embedding space produces better results compared to other sequence-based embedding methods.

• The paper introduces Diff2Vec, a novel method that uses diffusion graphs to accelerate node sequence generation for efficient graph embeddings.
• It demonstrates superior computational efficiency, with Diff2Vec reducing preprocessing times by several orders of magnitude compared to traditional random walks.
• Empirical results show improved proximity preservation and community detection in real-world networks like BlogCatalog and PPI, highlighting its robustness.

Fast Sequence Based Embedding with Diffusion Graphs

The paper "Fast Sequence Based Embedding with Diffusion Graphs" by Benedek Rozemberczki and Rik Sarkar presents a novel approach for graph embedding utilizing diffusion graphs to accelerate sequence generation. Graph embeddings, which translate graph vertices into low-dimensional spaces while preserving node proximities and other significant properties, find applications across numerous domains, including visualization, community detection, and network routing. Traditional vertex sequence-based embedding methods, inspired by techniques such as Word2Vec, rely heavily on random walks to generate node sequences for embedding. However, the inefficiency of random walks in coverage and redundancy presents computational challenges in large graphs. Addressing these inefficiencies, this paper offers the Diff2Vec (D2V) methodology as a computationally efficient and superior alternative.

The Diff2Vec approach introduces diffusion graphs, which favorably approximate neighborhood subgraphs through a simple random sampling process. This contrast sharply with mechanisms such as Node2Vec, which implement more intricate transition probability alterations. By generating Euler tours on diffusion graphs, D2V efficiently captures neighborhood proximities and generates sequences that feed into a neural network architecture to produce embeddings. Essential findings suggest D2V's proficiency in handling graphs of increasing density, achieving superior proximity preservation accuracy, and demonstrating robustness in community detection tasks through clustering in the embedding space.

Empirical evaluations underscore D2V's advantageous performance. A stark comparative analysis against state-of-the-art Node2Vec demonstrates D2V's commendable computational efficiency, particularly in sequence generation times. For instance, experiments on various real-world networks such as BlogCatalog and the PPI network indicate a substantial reduction in pre-processing requirements when employing D2V, which reaches several orders of magnitude faster than Node2Vec. Furthermore, D2V embeddings particularly excel in approximating shortest path distances: the 128-dimensional D2V embedding maintains distortion below 20% for over 90% of node pairs—a performance unachievable by Node2Vec even in higher dimensions.

In the domain of community detection, D2V embeddings, as evidenced from modularity measures, outshine Node2Vec embeddings and other conventional clustering methods executed on graph datasets including BlogCatalog, PPI, and Wikipedia. This reinforces D2V's capability as an effective feature extractor, well-suited for subsequent machine learning tasks.

Theoretically, D2V contributes to the understanding of sequence-based graph embeddings, specifically marking a shift towards methodologies that emphasize efficiency without compromising on representation quality. Practically, the proposed high-performance parallel implementation underscores D2V's applicability in large-scale graph processing, offering significant implications for real-time data applications where rapid and reliable embeddings are crucial.

The D2V methodology, poised on diffusion processes, presents a scalable, efficient, and potent avenue for graph embeddings. Future explorations may consider extending diffusion graphs to weighted or directed contexts, potentially enhancing the versatility of D2V embeddings. Another intriguing avenue would be leveraging D2V's parallel nature within distributed computing environments, maximizing computational advantages across diverse hardware architectures. D2V's promising results suggest it as a valuable toolkit component for graph-based machine learning applications.