# Relation Representation Learning via Signed Graph Mutual Information Maximization for Trust Prediction

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## Abstract

**:**

## 1. Introduction

- We propose a novel relation representation learning model via maximizing mutual information between the signed graph and entity relation representation, which is preferable and suitable for trust networks modeling.
- We first introduce translation principle to signed graph to explore abundant feature and semantic information of edges on the signed graph.
- We develop a trust prediction algorithm that takes the learned relation representation vector to complete the trust prediction tasks.
- Experiments with four real-world datasets show that SGMIM can obtain efficient accuracy.

## 2. Related Work

#### 2.1. Approaches Based on Social Network Analysis

#### 2.2. Approaches Based on GNNs

#### 2.3. Approaches Based on Signed Graph

## 3. Preliminaries

#### 3.1. Problem Formulation

**Definition 1**

**(Signed Trust Network).**

**Definition**

**2**

**Definition 3**

**(Trust Prediction).**

#### 3.2. Mutual Information

## 4. Proposed Method

#### 4.1. Framework

#### 4.2. Encoding Semantic Relation

#### 4.3. Learning Structure Information

#### 4.4. Model Training

Algorithm 1Traning process of SGMIM model |

Require:G: $(V,{E}^{+},E)$; A: adjacency matrix; S: sign set of edges; k: dimension of node embedding vector; m: dimension of edge embedding vector; $\beta $: hyper-parameter; epoches: iterate number. |

Ensure:U: head entity representation; V: tail entity representation; R: relation representation. |

1: Initialization U, V, R |

2: Calculate PPMI Z |

3: for iter in range(epoches) |

4: Sample positive triple (u, r, v) |

5: Generate embedding U, R, V |

6: Sample negative triple (u’, r, v’) |

7: Generate embedding U’, R, V’ |

8: ${C}_{1}={f}_{r}(U,V),{C}_{2}={f}_{r}({U}^{\prime},{V}^{\prime}))$ |

9: score = Discriminator(${C}_{1}$, ${C}_{2}$) |

10: Loss1 = BCEWithLogicLoss(score, S) |

11: Loss2 = CrossEntropyLoss(${C}_{1}$, Z) |

12: Loss = $\alpha \xb7$ Loss1+(1−$\alpha )\xb7$Loss2 |

13: Update U, R, V |

14: Loss Backforward |

15: end for |

## 5. Experiments

#### 5.1. Datasets

**Epinions**(http://www.trustlet.org/epinions.html). Epinions is an online review website where users can review any products. Users can register for free and write reviews for many different types of products such as music, software hardware. In Epinions, users can be allowed to other users to their “Web of Trust.“ Epinions datasets contain the ratings given by users to the item and the trust statements issued by users. It was collected by Paolo Massa crawl from the Epinions website in a five-week, which contains 49,290 users who rated a total of 139,738 different products at least once and writing 664,824 reviews, and 487,181 issued trust statements. The dataset consists of two data files: Ratings data and Trust data, in which trust data contains the trust statements issued by users, and every line has the following format: source-user-id, target-user-id, trust-statement-value. For example, line 10,572 11,715 −1 represents user 10,572 has expressed a negative trust statement on user 11,715. The value of the trust-statement is only 1 or −1, and 1 means positive trust, and −1 means negative ones (distrust). The detailed statistics about the Epinions dataset see Table 2.

**Slashdot**(https://www.slashdot.org). Slashdot is a technology-related news website know for its specific user community, which features editor-evaluated and user-submitted current primarily technology-oriented news. The interesting part of Slashdot is its reader comments. Generally, each news item has hundreds or even thousands of reader comments. The system will automatically randomly select moderators from active users. The selected moderator can give a score to each comment, and positive comments add 1 point and negative comments minus 1 point. Slashdot uses the SlashdotZoo feature, which allows user to tag each other as friends or foes. The User network contains friend/foe links between the users of Slashdot. Slashdot network contains nodes 82,168 and edges 948,464. See Table 2 for detailed statistics on Slashdot datasets.

**WikiElec**and

**WikiRfa**(http://snap.stanford.edu/data/wiki-Elec.html). Wikipedia is a free encyclopedia website maintained by volunteers from all over the world. To manage the administrator, Wikipedia develops a voting network (WikiElec) to decide whom to promote to the administrator via a public vote for the adminship elections, and WikiRfa is a new version of WikiElec. Both WikiElec and WikiRfa contain positive, negative, and neutral votes. According to the statistical results, we find that the average sparsity of WikiElec is larger than WikiRfa. WikiElec network contains 7194 nodes and 114,040 edges, and WikiRfa contains 10,885 nodes and 137,966 edges. See Table 2 for detailed statistics on WikiElec and WikiRfa datasets.

#### 5.2. Baselines

**Signed Spectral Clustering**[63] is a spectral clustering method based on eigenvalue decomposition. It takes the eigenvector of the k smallest eigenvalues obtained by the signed spectral decomposition as the node’s representation vector. The spectral method’s performance in real tasks would be affected by the dimension of the eigenvector, and it is more suitable for undirected graphs.

**SiNE**[64]: SiNE incorporates the structural balance theory into deep learning model for learning the node embedding on the signed graph. It assumes the signed graph is an undirected graph.

**SNE**[23]: SNE is a signed graph representation learning method based on random walk. It extracts many short node paths by random walk along with the graph, and then further adopts the log-bilinear model to learn the node representation.

**nSNE**[65]: nSNE is a neural network signed network embedding method. It learns both node embedding and edge embedding by modeling first-order proximity and second-order between the nodes on the signed graph with negative link.

#### 5.3. Evaluation Metric

#### 5.4. Experimental Results

#### 5.5. Parameter Sensitivity

#### 5.5.1. Dimension

#### 5.5.2. Hyper-Parameters

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Performance (Macro-F, AUC) comparison w.r.t different size of dimension on Epinions, Slashdot and WikiRra datasets.

Notation | Description |
---|---|

G | signed trust network |

V | set of vertexes |

${E}^{+}$ | set of positive edges |

${E}^{-}$ | set of negative edges |

${D}^{+}$ | out degree of node |

${D}^{-}$ | in degree of node |

${k}_{1}$ | dimensions of node representation |

${k}_{2}$ | dimensions of relation representation |

n | size of vertex |

Statistics | Epinions | Slashdot | WikiElec | WikiRfa |
---|---|---|---|---|

nodes num | 131,828 | 82,140 | 7194 | 10,885 |

edges num | 841,372 | 549,202 | 114,040 | 137,966 |

positive num | 717,690 | 425,083 | 90,890 | 109,269 |

negative num | 123,682 | 124,119 | 23,150 | 28,697 |

average sparsity | 22.4 | 14.7 | 25.5 | 31.3 |

Dataset | Epinions | Slashdot | WikiElec | WikiRfa | |||||
---|---|---|---|---|---|---|---|---|---|

Dimension | Algorithm | F1 | AUC | F1 | AUC | F1 | AUC | F1 | AUC |

SC | 0.729 | 0.801 | 0.687 | 0.761 | 0.708 | 0.724 | 0.719 | 0.783 | |

SNE | 0.748 | 0.854 | 0.712 | 0.830 | 0.734 | 0.827 | 0.740 | 0.852 | |

K = 20 | SiNE | 0.756 | 0.879 | 0.726 | 0.849 | 0.749 | 0.845 | 0.754 | 0.866 |

nSNE | 0.739 | 0.847 | 0.720 | 0.827 | 0.743 | 0.869 | 0.731 | 0.830 | |

SGMIM | 0.780 | 0.872 | 0.734 | 0.853 | 0.750 | 0.863 | 0.756 | 0.857 | |

SC | 0.754 | 0.813 | 0.694 | 0.787 | 0.702 | 0.815 | 0.713 | 0.781 | |

SNE | 0.785 | 0.856 | 0.739 | 0.859 | 0.724 | 0.841 | 0.760 | 0.843 | |

K = 50 | SiNE | 0.790 | 0.883 | 0.742 | 0.822 | 0.731 | 0.866 | 0.754 | 0.853 |

nSNE | 0.809 | 0.802 | 0.737 | 0.748 | 0.757 | 0.870 | 0.741 | 0.862 | |

SGMIM | 0.818 | 0.896 | 0.761 | 0.871 | 0.763 | 0.887 | 0.772 | 0.886 | |

SC | 0.764 | 0.789 | 0.705 | 0.773 | 0.697 | 0.822 | 0.704 | 0.813 | |

SNE | 0.783 | 0.863 | 0.748 | 0.859 | 0.738 | 0.840 | 0.780 | 0.846 | |

K = 80 | SiNE | 0.787 | 0.891 | 0.763 | 0.886 | 0.745 | 0.868 | 0.795 | 0.881 |

nSNE | 0.812 | 0.882 | 0.766 | 0.842 | 0.726 | 0.865 | 0.782 | 0.858 | |

SGMIM | 0.833 | 0.901 | 0.778 | 0.892 | 0.781 | 0.899 | 0.805 | 0.902 | |

SC | 0.769 | 0.789 | 0.711 | 0.764 | 0.720 | 0.812 | 0.713 | 0.813 | |

SNE | 0.803 | 0.873 | 0.759 | 0.859 | 0.767 | 0.880 | 0.781 | 0.882 | |

K = 100 | SiNE | 0.816 | 0.901 | 0.776 | 0.892 | 0.805 | 0.908 | 0.809 | 0.894 |

nSNE | 0.832 | 0.912 | 0.750 | 0.841 | 0.782 | 0.879 | 0.773 | 0.886 | |

SGMIM | 0.857 | 0.921 | 0.794 | 0.905 | 0.814 | 0.919 | 0.814 | 0.914 |

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## Share and Cite

**MDPI and ACS Style**

Jing, Y.; Wang, H.; Shao, K.; Huo, X.
Relation Representation Learning via Signed Graph Mutual Information Maximization for Trust Prediction. *Symmetry* **2021**, *13*, 115.
https://doi.org/10.3390/sym13010115

**AMA Style**

Jing Y, Wang H, Shao K, Huo X.
Relation Representation Learning via Signed Graph Mutual Information Maximization for Trust Prediction. *Symmetry*. 2021; 13(1):115.
https://doi.org/10.3390/sym13010115

**Chicago/Turabian Style**

Jing, Yongjun, Hao Wang, Kun Shao, and Xing Huo.
2021. "Relation Representation Learning via Signed Graph Mutual Information Maximization for Trust Prediction" *Symmetry* 13, no. 1: 115.
https://doi.org/10.3390/sym13010115