Link Sign Prediction Research Articles

A Signed Subgraph Encoding Approach via Linear Optimization for Link Sign Prediction.

In this article, we consider the problem of inferring the sign of a link based on known sign data in signed networks. Regarding this link sign prediction problem, signed directed graph neural networks (SDGNNs) provides the best prediction performance currently to the best of our knowledge. In this article, we propose a different link sign prediction architecture called subgraph encoding via linear optimization (SELO), which obtains overall leading prediction performances compared to the state-of-the-art algorithm SDGNN. The proposed model utilizes a subgraph encoding approach to learn edge embeddings for signed directed networks. In particular, a signed subgraph encoding approach is introduced to embed each subgraph into a likelihood matrix instead of the adjacency matrix through a linear optimization (LO) method. Comprehensive experiments are conducted on five real-world signed networks with area under curve (AUC), F1, micro-F1, and macro-F1 as the evaluation metrics. The experiment results show that the proposed SELO model outperforms existing baseline feature-based methods and embedding-based methods on all the five real-world networks and in all the four evaluation metrics.

SDEGNN: Signed graph neural network for link sign prediction enhanced by signed distance encoding

SDEGNN: Signed graph neural network for link sign prediction enhanced by signed distance encoding

Status-Aware Signed Heterogeneous Network Embedding With Graph Neural Networks.

Many real-world applications are inherently modeled as signed heterogeneous networks or graphs with positive and negative links. Signed graph embedding embeds rich structural and semantic information of a signed graph into low-dimensional node representations. Existing methods usually exploit social structural balance theory to capture the semantics of the complex structure in a signed graph. These methods either omit the node features or may discard the direction information of the links. To address these issues, we propose a new framework, called a status-aware graph neural network (S-GNN), to boost the representation learning performance. S-GNN is equipped with a loss function designed based on status theory, a social-psychological theory specifically developed for directed signed graphs. Extensive experimental results on benchmarking datasets verified that S-GNN can distill comprehensive information ingrained in a signed graph in the embedding space. Specifically, S-GNN achieves state-of-the-art accuracy, robustness, and scalability: it speeds up the processing time of link sign prediction by up to 6.5 × and increases accuracy by up to 18.8% as compared with the alternatives. We also show that S-GNN can obtain effective status scores of nodes for link sign prediction and node ranking tasks, both of which yield state-of-the-art performance.

Implicit Negative Link Prediction With a Network Topology Perspective

Sign prediction in signed social networks is a new research direction in the field of social relation mining, which reveals underlying links between users. Traditional sign prediction research focuses on the prediction of positive signs and neglects the mining of potential implicit links, and there is little research on negative sign prediction. To address these problems, we propose a two-stage model that uses implicit link detection and link sign prediction. First, we use the preference attachment closeness degree (PACD) to predict possible implicit links by adding a measure of relationship closeness to the traditional link prediction algorithm (PA). Next, we propose a negative link sign prediction (Ne-LP) method to predict relation types through multidimensional negative sign-related features, including those of nodes, user similarity, and structural balance, and merge them by a logistic regression model. Finally, we evaluate PACD and Ne-LP through extensive experiments on three real-world social network datasets, whose results demonstrate that the method can effectively mine implicit relations and accurately predict negative links.

Learning Weight Signed Network Embedding with Graph Neural Networks

Network embedding aims to map nodes in a network to low-dimensional vector representations. Graph neural networks (GNNs) have received much attention and have achieved state-of-the-art performance in learning node representation. Using fundamental sociological theories (status theory and balance theory) to model signed networks, basing GNN on learning node embedding has become a hot topic in signed network embedding. However, most GNNs fail to use edge weight information in signed networks, and most models cannot be directly used in weighted signed networks. We propose a novel signed directed graph neural networks model named WSNN to learn node embedding for Weighted signed networks. The proposed model reconstructs link signs, link directions, and signed directed triangles simultaneously. Based on the network representations learned by the proposed model, we conduct link sign prediction in signed networks. Extensive experimental results in real-world datasets demonstrate the superiority of the proposed model over the state-of-the-art network embedding algorithms for graph representation learning in signed networks.

Signed random walk diffusion for effective representation learning in signed graphs.

How can we model node representations to accurately infer the signs of missing edges in a signed social graph? Signed social graphs have attracted considerable attention to model trust relationships between people. Various representation learning methods such as network embedding and graph convolutional network (GCN) have been proposed to analyze signed graphs. However, existing network embedding models are not end-to-end for a specific task, and GCN-based models exhibit a performance degradation issue when their depth increases. In this paper, we propose Signed Diffusion Network (SidNet), a novel graph neural network that achieves end-to-end node representation learning for link sign prediction in signed social graphs. We propose a new random walk based feature aggregation, which is specially designed for signed graphs, so that SidNet effectively diffuses hidden node features and uses more information from neighboring nodes. Through extensive experiments, we show that SidNet significantly outperforms state-of-the-art models in terms of link sign prediction accuracy.

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

Trust prediction is essential to enhancing reliability and reducing risk from the unreliable node, especially for online applications in open network environments. An essential fact in trust prediction is to measure the relation of both the interacting entities accurately. However, most of the existing methods infer the trust relation between interacting entities usually rely on modeling the similarity between nodes on a graph and ignore semantic relation and the influence of negative links (e.g., distrust relation). In this paper, we proposed a relation representation learning via signed graph mutual information maximization (called SGMIM). In SGMIM, we incorporate a translation model and positive point-wise mutual information to enhance the relation representations and adopt Mutual Information Maximization to align the entity and relation semantic spaces. Moreover, we further develop a sign prediction model for making accurate trust predictions. We conduct link sign prediction in trust networks based on learned the relation representation. Extensive experimental results in four real-world datasets on trust prediction task show that SGMIM significantly outperforms state-of-the-art baseline methods.

Predicting the Signs of the Links in a Network

It is hard to deny the importance of graph analysis techniques, particularly the problem of link and link-sign prediction, in many real-world applications. Predicting future sign of connections in a network is an important task for online systems such as social networks, e-commerce, scientific research, and others. Several research studies have been presented since the early days of this century to predict either the existence of a link in the future or the property of the link. In this study we present a novel approach that combine both families by using machine learning techniques. Instead of focusing on the established links, we follow a new research approach that focusing on no-link relationship. We aim to understand the move between two states of no-link and link. We evaluate our methods in popular real-world signed networks datasets. We believe that the new approach by understanding the no-link relation has a lot of potential improvement in the future.

Decoupled Variational Embedding for Signed Directed Networks

Node representation learning for signed directed networks has received considerable attention in many real-world applications such as link sign prediction, node classification, and node recommendation. The challenge lies in how to adequately encode the complex topological information of the networks. Recent studies mainly focus on preserving the first-order network topology that indicates the closeness relationships of nodes. However, these methods generally fail to capture the high-order topology that indicates the local structures of nodes and serves as an essential characteristic of the network topology. In addition, for the first-order topology, the additional value of non-existent links is largely ignored. In this article, we propose to learn more representative node embeddings by simultaneously capturing the first-order and high-order topology in signed directed networks. In particular, we reformulate the representation learning problem on signed directed networks from a variational auto-encoding perspective and further develop a decoupled variational embedding (DVE) method. DVE leverages a specially designed auto-encoder structure to capture both the first-order and high-order topology of signed directed networks, and thus learns more representative node embeddings. Extensive experiments are conducted on three widely used real-world datasets. Comprehensive results on both link sign prediction and node recommendation task demonstrate the effectiveness of DVE. Qualitative results and analysis are also given to provide a better understanding of DVE.

Semi-Supervised Gated Spectral Convolution on a Directed Signed Network

A complex network is a powerful tool that enables a complex system in the real world to be represented as a network structure. Due to the heterogeneous edges and nodes implying rich semantic information, network representation has received considerable attention in both research and industrial domain. Over the recent years, the graph convolutional network (GCN) has provided a novel approach for learning network embeddings. However, this primarily supports undirected unsigned networks; that is, it cannot be directly applied to directed signed networks because it is challenging to effectively depict the direction and signs of edges in such models. In this paper, we therefore propose a method for semi-supervised gated spectral convolution in directed signed networks. We first extend the concept of the GCN to directed signed networks, which not only preserves the advantages of the traditional GCN but also properly describes the significance of the directions and signs of the edges. We then innovatively define sign (label) propagation rules in directed signed networks, rendering the networks semi-supervised. Furthermore, we enhance the balance theory to constrain the process of sign propagation to obtain network embedding with better interpretability. To satisfy the needs of large-scale complex networks, we propose a gating mechanism to adaptively forget sign information, which significantly reduces the time-space complexity of the sign propagation process. Finally, we compare the proposed method with state-of-the-art baselines using four real-world data sets for the classical link sign prediction task. Experimental results demonstrate that the proposed method is competitive.

Deep Network Embedding for Graph Representation Learning in Signed Networks.

Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a given network. The vast majority of existing network embedding algorithms, however, are only designed for unsigned networks, and the signed networks containing both positive and negative links, have pretty distinct properties from the unsigned counterpart. In this paper, we propose a deep network embedding model to learn the low-dimensional node vector representations with structural balance preservation for the signed networks. The model employs a semisupervised stacked auto-encoder to reconstruct the adjacency connections of a given signed network. As the adjacency connections are overwhelmingly positive in the real-world signed networks, we impose a larger penalty to make the auto-encoder focus more on reconstructing the scarce negative links than the abundant positive links. In addition, to preserve the structural balance property of signed networks, we design the pairwise constraints to make the positively connected nodes much closer than the negatively connected nodes in the embedding space. Based on the network representations learned by the proposed model, we conduct link sign prediction and community detection in signed networks. Extensive experimental results in real-world datasets demonstrate the superiority of the proposed model over the state-of-the-art network embedding algorithms for graph representation learning in signed networks.

A Gram classification of principal Cox-regular edge-bipartite graphs via inflation algorithm

The paper is devoted to a Gram classification of an important class of signed graphs with loops playing an important role in many branches of mathematics, physics and computer science including game theory, crystallography, Diophantine geometry, Lie theory, spectral graph theory, a graph coloring technique, algebraic methods in graph theory. They have many deep applications in spectral machine learning methods, electrical networks, to link sign prediction in signed unipartite and bipartite networks, and community partition in social networks.We continue the study of finite connected edge-bipartite graphs Δ (bigraphs, for short), with m≥2 vertices (a class of signed graphs), started in Simson (2013) and developed in Simson (2016) by means of the non-symmetric Gram matrix GˇΔ∈Mm(Z) defining Δ, its symmetric Gram matrix GΔ:=12[GˇΔ+GˇΔtr]∈Mm(12Z), and the Gram quadratic form qΔ:Zm→Z. In the present paper, given n≥1, we mainly study connected principal Cox-regular edge-bipartite graphs Δ with loops and n+1≥2 vertices, in the sense that the symmetric Gram matrix GΔ∈Mn+1(Z) of Δ is positive semi-definite of rank n≥1. Our aim is to classify such edge-bipartite graphs by means of an inflation algorithm, up to the weak Gram Z-congruence Δ∼ZΔ′, where Δ∼ZΔ′ means that GΔ′=Btr⋅GΔ⋅B, for some B∈Mn+1(Z) with detB=±1. Our main result of the paper asserts that, given a principal Cox-regular connected edge-bipartite graph Δ with n+1≥2 vertices, there exists an edge-bipartite Euclidean graph Dn+1 of Tables A and B, and a suitably chosen sequence t•− of the inflation operators, each of one of the forms Δ′↦ta−Δ′ or Δ′↦tab−Δ′, such that the composite operator Δ↦t•−Δ reduces Δ to the bigraph Dn+1 such that: (i) Δ∼ZDn+1 and (ii) the bigraphs Δ, and Dn+1 have the same number of loops. The algorithm does not change loops and computes a matrix B∈Mn+1(Z), with detB=±1, defining the weak Gram Z-congruence Δ∼ZDn+1, that is, satisfying the equation GDn+1=Btr⋅GΔ⋅B.

Link sign prediction by Variational Bayesian Probabilistic Matrix Factorization with Student-t Prior

In signed social networks, link sign prediction refers to using the observed link signs to infer the signs of the remaining links, which is important for mining and analyzing the evolution of social networks. The widely used matrix factorization-based approach – Bayesian Probabilistic Matrix Factorization (BMF), assumes that the noise between the real and predicted entry is Gaussian noise, and the prior of latent features is multivariate Gaussian distribution. However, Gaussian noise model is sensitive to outliers and is not robust. Gaussian prior model neglects the differences between latent features, that is, it does not distinguish between important and non-important features. Thus, Gaussian assumption based models perform poorly on real-world (sparse) datasets. To address these issues, a novel Variational Bayesian Probabilistic Matrix Factorization with Student-t prior model (TBMF) is proposed in this paper. A univariate Student-t distribution is used to fit the prediction noise, and a multivariate Student-t distribution is adopted for the prior of latent features. Due to the high kurtosis of Student-t distribution, TBMF can select informative latent features automatically, characterize long-tail cases and obtain reasonable representations on many real-world datasets. Experimental results show that TBMF improves the prediction performance significantly compared with the state-of-the-art algorithms, especially when the observed links are few.

Link sign prediction and ranking in signed directed social networks

Signed directed social networks, in which the relationships between users can be either positive (indicating relations such as trust) or negative (indicating relations such as distrust), are increasingly common. Thus the interplay between positive and negative relationships in such networks has become an important research topic. Most recent investigations focus upon edge sign inference using structural balance theory or social status theory. Neither of these two theories, however, can explain an observed edge sign well when the two nodes connected by this edge do not share a common neighbor (e.g., common friend). In this paper, we develop a novel approach to handle this situation by applying a new model for node types and use the proposed model to perform link sign prediction and link ranking. Initially, we analyze the local node structure in a fully observed signed directed network, inferring underlying node types. The sign of an edge between two nodes must be consistent with their types; this explains edge signs well even when there are no common neighbors. We show, moreover, that our approach can be extended to incorporate directed triads, when they exist, just as in models based upon structural balance or social status theory. We compute Bayesian node types within empirical studies based upon partially observed Wikipedia, Slashdot, and Epinions networks in which the largest network (Epinions) has 119K nodes and 841K edges. Based upon the proposed features, we present the link sign prediction and link ranking models subsequently. We show that our approaches yield better performance than state-of-the-art approaches for these two tasks based upon three signed directed networks.

A Parallel Approach to Link Sign Prediction in Large-Scale Online Social Networks

A Parallel Approach to Link Sign Prediction in Large-Scale Online Social Networks