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Embedding Learning on Multiplex Networks for Link Prediction

Orell Trautmann, Olaf Wolkenhauer, Clémence Réda

TL;DR

This paper surveys embedding learning for link prediction on multiplex networks, emphasizing the need to integrate cross-layer information while preserving layer-specific structure. It introduces a representation taxonomy (unique, enriched, and multiple embeddings) and a two-level method taxonomy (aggregation, matrix factorization, random walks, optimization, and neural networks) to classify existing approaches. Additionally, it addresses reproducibility and fairness in evaluation, proposing a novel testing procedure for directed multiplex networks and outlining guidelines for robust assessment. The work highlights practical challenges and offers a structured framework to advance tractable, high-performing multiplex embeddings for link prediction across diverse applications.

Abstract

Over the past years, embedding learning on networks has shown tremendous results in link prediction tasks for complex systems, with a wide range of real-life applications. Learning a representation for each node in a knowledge graph allows us to capture topological and semantic information, which can be processed in downstream analyses later. In the link prediction task, high-dimensional network information is encoded into low-dimensional vectors, which are then fed to a predictor to infer new connections between nodes in the network. As the network complexity (that is, the numbers of connections and types of interactions) grows, embedding learning turns out increasingly challenging. This review covers published models on embedding learning on multiplex networks for link prediction. First, we propose refined taxonomies to classify and compare models, depending on the type of embeddings and embedding techniques. Second, we review and address the problem of reproducible and fair evaluation of embedding learning on multiplex networks for the link prediction task. Finally, we tackle evaluation on directed multiplex networks by proposing a novel and fair testing procedure. This review constitutes a crucial step towards the development of more performant and tractable embedding learning approaches for multiplex networks and their fair evaluation for the link prediction task. We also suggest guidelines on the evaluation of models, and provide an informed perspective on the challenges and tools currently available to address downstream analyses applied to multiplex networks.

Embedding Learning on Multiplex Networks for Link Prediction

TL;DR

This paper surveys embedding learning for link prediction on multiplex networks, emphasizing the need to integrate cross-layer information while preserving layer-specific structure. It introduces a representation taxonomy (unique, enriched, and multiple embeddings) and a two-level method taxonomy (aggregation, matrix factorization, random walks, optimization, and neural networks) to classify existing approaches. Additionally, it addresses reproducibility and fairness in evaluation, proposing a novel testing procedure for directed multiplex networks and outlining guidelines for robust assessment. The work highlights practical challenges and offers a structured framework to advance tractable, high-performing multiplex embeddings for link prediction across diverse applications.

Abstract

Over the past years, embedding learning on networks has shown tremendous results in link prediction tasks for complex systems, with a wide range of real-life applications. Learning a representation for each node in a knowledge graph allows us to capture topological and semantic information, which can be processed in downstream analyses later. In the link prediction task, high-dimensional network information is encoded into low-dimensional vectors, which are then fed to a predictor to infer new connections between nodes in the network. As the network complexity (that is, the numbers of connections and types of interactions) grows, embedding learning turns out increasingly challenging. This review covers published models on embedding learning on multiplex networks for link prediction. First, we propose refined taxonomies to classify and compare models, depending on the type of embeddings and embedding techniques. Second, we review and address the problem of reproducible and fair evaluation of embedding learning on multiplex networks for the link prediction task. Finally, we tackle evaluation on directed multiplex networks by proposing a novel and fair testing procedure. This review constitutes a crucial step towards the development of more performant and tractable embedding learning approaches for multiplex networks and their fair evaluation for the link prediction task. We also suggest guidelines on the evaluation of models, and provide an informed perspective on the challenges and tools currently available to address downstream analyses applied to multiplex networks.
Paper Structure (21 sections, 23 equations, 7 figures, 3 tables)

This paper contains 21 sections, 23 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Definitions and Preliminaries on Networks
  3. Representation and Method Taxonomies
  4. Representation Taxonomy
  5. Method Taxonomy
  6. Aggregation Methods
  7. Matrix Factorization
  8. Random Walk-Based Methods
  9. Random walk process.
  10. Similarity function.
  11. Embedding algorithm.
  12. Optimization Methods
  13. Neural Network-Based Methods
  14. Graph Convolution Neural Networks.
  15. Adversarial Networks
  16. ...and 6 more sections

Figures (7)

  • Figure 1: Examples of multiplex networks. Each layer corresponds to a specific relation, or view, in the network. The dashed lines represent interlayer connections between replica nodes (same entity represented on different layers), which are the only allowed type of interlayer edges in multiplex networks, whereas solid lines match intralayer connections. Figures \ref{['fig:multiplex3layers']} and \ref{['fig:multiplex3layersOther']} both show the same network using two different styles: with an edge to every replica node or simply edges to connect the layers from the top layer to the bottom layer.
  • Figure 2: Single-layer embeddings, enriched embeddings, and unique embeddings fall onto the same spectrum of preservation and collaboration MVN2Vec.
  • Figure 3: Difference between network-level and embedding-level aggregations. The aggregation step is depicted by the braces.
  • Figure 4: Figure \ref{['fig:multiplexForRW']} shows the original multiplex network. Figure \ref{['fig:transitionProbabilities']} displays the transition probabilities for the random walk: the thicker the line, the higher the probability of walking this edge. Figure \ref{['fig:BiasedRW']} depicts a random walk using the most likely node transitions, where the green node is the seed of the random walk, and the red arrows the path taken. Figure \ref{['fig:RWR']} illustrates a random walk with restart on a multiplex network, where the dashed red arrow indicates the teleportation back to the seed node.
  • Figure 5: Optimization models mainly aim at preserving first-order and second-order proximity information, here on a monoplex network. This figure was inspired by Figure 2 in zooGuide.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Definition 1: Multiplex Network