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Whole-Graph Representation Learning For the Classification of Signed Networks

Noé Cecillon, Vincent Labatut, Richard Dufour, Nejat Arınık

TL;DR

This article proposes two approaches to learning whole-graph representations of general signed graphs that rely on a modification of the Weisfeiler-Lehman relabelling procedure and assesses their methods on a benchmark.

Abstract

Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of attention in recent years. The overwhelming majority of existing methods handle unsigned graphs. However, signed graphs appear in an increasing number of application domains to model systems involving two types of opposed relationships. Several authors took an interest in signed graphs and proposed methods for providing vertex-level representations, but only one exists for whole-graph representations, and it can handle only fully connected graphs. In this article, we tackle this issue by proposing two approaches to learning whole-graph representations of general signed graphs. The first is a SG2V, a signed generalization of the whole-graph embedding method Graph2vec that relies on a modification of the Weisfeiler--Lehman relabelling procedure. The second one is WSGCN, a whole-graph generalization of the signed vertex embedding method SGCN that relies on the introduction of master nodes into the GCN. We propose several variants of both these approaches. A bottleneck in the development of whole-graph-oriented methods is the lack of data. We constitute a benchmark composed of three collections of signed graphs with corresponding ground truths. We assess our methods on this benchmark, and our results show that the signed whole-graph methods learn better representations for this task. Overall, the baseline obtains an F-measure score of 58.57, when SG2V and WSGCN reach 73.01 and 81.20, respectively. Our source code and benchmark dataset are both publicly available online.

Whole-Graph Representation Learning For the Classification of Signed Networks

TL;DR

This article proposes two approaches to learning whole-graph representations of general signed graphs that rely on a modification of the Weisfeiler-Lehman relabelling procedure and assesses their methods on a benchmark.

Abstract

Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of attention in recent years. The overwhelming majority of existing methods handle unsigned graphs. However, signed graphs appear in an increasing number of application domains to model systems involving two types of opposed relationships. Several authors took an interest in signed graphs and proposed methods for providing vertex-level representations, but only one exists for whole-graph representations, and it can handle only fully connected graphs. In this article, we tackle this issue by proposing two approaches to learning whole-graph representations of general signed graphs. The first is a SG2V, a signed generalization of the whole-graph embedding method Graph2vec that relies on a modification of the Weisfeiler--Lehman relabelling procedure. The second one is WSGCN, a whole-graph generalization of the signed vertex embedding method SGCN that relies on the introduction of master nodes into the GCN. We propose several variants of both these approaches. A bottleneck in the development of whole-graph-oriented methods is the lack of data. We constitute a benchmark composed of three collections of signed graphs with corresponding ground truths. We assess our methods on this benchmark, and our results show that the signed whole-graph methods learn better representations for this task. Overall, the baseline obtains an F-measure score of 58.57, when SG2V and WSGCN reach 73.01 and 81.20, respectively. Our source code and benchmark dataset are both publicly available online.
Paper Structure (28 sections, 4 equations, 5 figures, 10 tables)

This paper contains 28 sections, 4 equations, 5 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Signed Graphs
  4. Graph Representation Learning
  5. Whole Graphs
  6. Signed Graphs
  7. Signed Graph Datasets
  8. SpaceOrigin Conversations
  9. Correlation Clustering Instances
  10. European Parliament Roll-Calls
  11. Brief Comparison
  12. Representation Methods
  13. Aggregated Signed Network Embedding
  14. Signed Graph2vec
  15. Whole-graph Signed GCN
  16. ...and 13 more sections

Figures (5)

  • Figure 1: Examples of perfectly balanced graphs according to a) Structural Balance; and b) Generalized Balance ($k=3$).
  • Figure 2: Triads used in SiNE, as inputs of the dual neural network. Mixed triplets (a) are used directly, positive ones (b) require a transformation, and negative ones (not represented) are not used.
  • Figure 3: Unsigned (a) and signed (b) graphs used to illustrate the relabelling rules of G2V and SG2V (cf. text). The numeric values are the vertex degrees.
  • Figure 4: Update rules of SGCN, applied to an example graph. Only the edges belonging to a shortest path between the vertex of interest $v_1$ and some other vertex are shown.
  • Figure 5: Examples of the 5 proposed interconnection schemes: WSGCN+ (a), WSGCN- (b), WSGCN± (c), WSGCNsb (d) and WSGCNgb (e). MN stands for Master Node. Green and red edges represent positive and negative connections, respectively. Each colored ellipse is a cluster.