Signed Network Embedding Research Articles

Trustworthiness-Driven Graph Convolutional Networks for Signed Network Embedding

The problem of representing nodes in a signed network as low-dimensional vectors, known as signed network embedding (SNE), has garnered considerable attention in recent years. While several SNE methods based on graph convolutional networks (GCNs) have been proposed for this problem, we point out that they significantly rely on the assumption that the decades-old balance theory always holds in the real-world. To address this limitation, we propose a novel GCN-based SNE approach, named as TrustSGCN, which corrects for incorrect embedding propagation in GCN by utilizing the trustworthiness on edge signs for high-order relationships inferred by the balance theory. The proposed approach consists of three modules: (M1) generation of each node’s extended ego-network; (M2) measurement of trustworthiness on edge signs; and (M3) trustworthiness-aware propagation of embeddings. Specifically, TrustSGCN leverages topological information to measure trustworthiness on edge sign for high-order relationships inferred by balance theory. It then considers structural properties inherent to an input network, such as the ratio of triads, to correct for incorrect embedding propagation. Furthermore, TrustSGCN learns the node embeddings by leveraging two well-known social theories, i.e., balance and status, to jointly preserve the edge sign and direction between nodes connected by existing edges in the embedding space. The experiments on six real-world signed network datasets demonstrate that TrustSGCN consistently outperforms six state-of-the-art GCN-based SNE methods. The code is available at https://github.com/kmj0792/TrustSGCN .

Learning Embedding for Signed Network in Social Media With Global Information

Signed networks contain nodes connected by positive and negative signed links. Signed network representation learning concentrates on learning the low-dimensional representations of these nodes, which facilitates downstream tasks such as link prediction using general data mining framework. However, most signed network embedding (SiNE) approaches neglect global information in the networks, limiting the capacity to learn genuine signed graph topology. To overcome this limitation, a deep graph neural network (GNN) framework SiG to learn SiNE with global information is proposed. To be more explicit, a hierarchical pooling mechanism is developed to encode the high-level features of the networks. Moreover, a graph convolution layer is introduced to aggregate both positive and negative information from neighbor nodes, and the concatenation of two parts generates the final embedding of nodes. Extensive experiments on four large real-world signed network datasets demonstrate the effectiveness and excellence of the proposed method.

DynamiSE: dynamic signed network embedding for link prediction

DynamiSE: dynamic signed network embedding for link prediction

SHEEP, a Signed Hamiltonian Eigenvector Embedding for Proximity

Signed network embedding methods allow for a low-dimensional representation of nodes and primarily focus on partitioning the graph into clusters, hence losing information on continuous node attributes. Here, we introduce a spectral embedding algorithm for understanding proximal relationships between nodes in signed graphs, where edges can take either positive or negative weights. Inspired by a physical model, we construct our embedding as the minimum energy configuration of a Hamiltonian dependent on the distance between nodes and locate the optimal embedding dimension. We show through a series of experiments on synthetic and empirical networks, that our method (SHEEP) can recover continuous node attributes showcasing its main advantages: re-configurability into a computationally efficient eigenvector problem, retrieval of ground state energy which can be used as a statistical test for the presence of strong balance, and measure of node extremism, computed as the distance to the origin in the optimal embedding.

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.

Enhanced Signed Graph Neural Network with Node Polarity.

Signed graph neural networks learn low-dimensional representations for nodes in signed networks with positive and negative links, which helps with many downstream tasks like link prediction. However, most existing signed graph neural networks ignore individual characteristics of nodes and thus limit the ability to learn the underlying structure of real signed graphs. To address this limitation, a deep graph neural network framework SiNP to learn Signed network embedding with Node Polarity is proposed. To be more explicit, a node-signed property metric mechanism is developed to encode the individual characteristics of the nodes. In addition, a graph convolution layer is added so that both positive and negative information from neighboring nodes can be combined. The final embedding of nodes is produced by concatenating the outcomes of these two portions. Finally, extensive experiments have been conducted on four significant real-world signed network datasets to demonstrate the efficiency and superiority of the proposed method in comparison to the state-of-the-art.

MUSE: Multi-faceted attention for signed network embedding

Signed network embedding is an approach to learning low-dimensional representations of nodes in signed networks with both positive and negative links, which facilitates downstream tasks such as link prediction with general data mining frameworks. Due to the distinct properties and significant added value of negative links, existing signed network embedding methods usually design dedicated methods based on social theories such as balance theory and status theory. However, existing signed network embedding methods ignore the characteristics of multiple facets of each node and mix them up in one single representation, which limits the ability to capture the fine-grained attentions between node pairs. In this paper, we propose MUSE, a MUlti-faceted attention-based Signed network Embedding framework to tackle this problem. Specifically, a joint intra- and inter-facet attention mechanism is introduced to aggregate fine-grained information from neighbor nodes. Moreover, balance theory is also utilized to guide information aggregation from multi-order balanced and unbalanced neighbors. Experimental results on four real-world signed network datasets demonstrate the effectiveness of our proposed framework.

Learning Embedding for Signed Network in Social Media with Hierarchical Graph Pooling

Signed network embedding concentrates on learning fixed-length representations for nodes in signed networks with positive and negative links, which contributes to many downstream tasks in social media, such as link prediction. However, most signed network embedding approaches neglect hierarchical graph pooling in the networks, limiting the capacity to learn genuine signed graph topology. To overcome this limitation, this paper presents a unique deep learning-based Signed network embedding model with Hierarchical Graph Pooling (SHGP). To be more explicit, a hierarchical pooling mechanism has been developed to encode the high-level features of the networks. Moreover, a graph convolution layer is introduced to aggregate both positive and negative information from neighbor nodes, and the concatenation of two parts generates the final embedding of the nodes. Extensive experiments on three large real-world signed network datasets demonstrate the effectiveness and excellence of the proposed method.

Two-stream signed directed graph convolutional network for link prediction

Using graph neural networks(GNNs) to transfer and enhance the richness of node information has played an important role in link prediction. However, most traditional GNNs only consider undirected graphs or unsigned graphs, which is limited for information extraction. In order to obtain a richer node representation, we propose a Two-Stream Signed Directed Graph Convolution Network(2S-SDGCN). We consider both the sign and direction when aggregating, which can characterize the topological structure information of the graph. To combine the information together, we conduct a new two-stream network, one for extracting latent factor and transfer pattern features, and the other for obtaining directional positive and negative features. We use five real social networks as datasets to verify the effectiveness of our model. These datasets are usually used as benchmarks to verify the effectiveness of signed network embedding. Experiments show that our model outperforms the existing methods.

Structure information learning for neutral links in signed network embedding

Nowadays, signed network has become an important research topic because it can reflect more complex relationships in reality than traditional network, especially in social networks. However, most signed network methods that achieve excellent performance through structure information learning always neglect neutral links, which have unique information in social networks. At the same time, previous approach for neutral links cannot utilize the graph structure information, which has been proved to be useful in node embedding field. Thus, in this paper, we proposed the Signed Graph Convolutional Network with Neutral Links (NL-SGCN) to address the structure information learning problem of neutral links in signed network, which shed new insight on signed network embedding. In NL-SGCN, we learn two representations for each node in each layer from both inner character and outward attitude aspects and propagate their information by balance theory. Among these three types of links, information of neutral links will be limited propagated by the learned coefficient matrix. To verify the performance of the proposed model, we choose several classical datasets in this field to perform empirical experiment. The experimental result shows that NL-SGCN significantly outperforms the existing state-of-the-art baseline methods for link prediction in signed network with neutral links, which supports the efficacy of structure information learning in neutral links.

Signed Network Node Embedding via Dual Attention Mechanism

In signed networks, GNNs are used to get node embedding by aggregating node neighbor information. Most of the existing methods aggregate neighbor information from the node level, and the different paths between nodes and neighbors will also affect node embedding. The target node and its neighbors have different link positive,negative signs and link directions, which together constitute different paths.These different paths have different contributions to the target node.Based on the structural balance theory and status theory, this paper divides the different paths between nodes and their neighbors into 20 kinds of motifs, which are using to capture the different effects of paths on target nodes. Comprehensive consideration at the node level and path level, SNEDA (Signed Network Embedding via dual attention Mechanism) is proposed based on the graph attention Network. The model has two attention mechanisms: node-level attention captures different influences between nodes at the node level; path-level attention captures the different influences between motifs at the path level. The final vector representation of nodes is obtained by aggregating neighbor information selectively based on important motifs, and the vector representation is applied to link prediction. Experiments on four real social network data sets show that the network representation obtained by the model can improve the accuracy of link prediction. Experimental results demonstrate the effectiveness of the proposed framework through a signed link prediction task on four real-world signed network datasets.

WSHE: User feedback-based weighted signed heterogeneous information network embedding

Heterogeneous information networks (HINs), which have rich semantic relations, can flexibly model multisource heterogeneous data in recommendation systems. Learning more comprehensive features of users based on HINs is a way to improve recommendation performance. User feedback can truly reflect user preferences. Most meta-path-based HIN embedding methods measure the similarity among users by counting the number of meta-paths and cannot fully learn the polar similarity of user preferences. In this work, we proposed a user feedback-based weighted signed HIN embedding method to learn more comprehensive embeddings of users and items. First, we defined a similarity measure using the weighted meta-path to measure the polar similarities of users. Second, we designed a weighted signed network embedding method based on the weighted sampling random walk. The embeddings of different meta-paths were deeply fused guided by an attention mechanism. The fused embeddings were further fused with attribute information using a pooling operation to capture their interactions. Finally, we utilized the rating prediction task to optimize the model and obtain the final embeddings of users and items. Extensive experiments performed on four datasets demonstrated the effectiveness of the model. In addition, we analyzed the importance of the different semantic meta-paths in the rating prediction task based on the interpretability of the attention mechanism.

SNEGAN: Signed Network Embedding by Using Generative Adversarial Nets

Network embedding (NE) aims to learn low-dimensional node representations of networks while preserving essential node structures and properties. Existing NE methods mainly preserve simple link structures in unsigned networks, neglecting conflicting relationships that widely exist in social media and Internet of things. In this paper, we propose a novel generative adversarial nets learning framework (called SNEGAN) for signed network embedding, which tries to preserve link structures signed by positive or negative labels. SNEGAN combines a generator with a signed random walker technique and a graph softmax function to generate fake links that are used to deceive discriminator. Moreover, it combines a discriminator with a tanh function to discriminate truths and signs of links sampled from the generator and real network structures. The generator and discriminator play a two-player minimax game, and they will eventually generate low-dimensional node representations of signed networks. Extensive experiments on both LFR benchmark and real-world signed networks show the superiority of SNEGAN over the state-of-the-art NE methods in tackling both link (sign) prediction and reconstruction tasks.

Hyperbolic node embedding for signed networks

Signed network embedding methods aim to learn vector representations of nodes in signed networks. However, existing algorithms only managed to embed networks into low-dimensional Euclidean spaces whereas many intrinsic features of signed networks are reported more suitable for non-Euclidean spaces. For instance, previous works did not consider the hierarchical structures of networks, which is widely witnessed in real-world networks. In this work, we answer an open question that whether the hyperbolic space is a good choice to accommodate signed networks and learn embeddings that can preserve the corresponding special characteristics. We also propose a non-Euclidean signed network embedding method based on structural balance theory and Riemannian optimization, which embeds signed networks into a Poincaré ball in a hyperbolic space. This space enables our approach to capture underlying hierarchy of nodes in signed networks because it can be seen as a continuous tree. We empirically compare our method against six Euclidean-based baselines in three tasks on seven real-world datasets, and the results show the effectiveness of our method.

Learning Signed Network Embedding via Graph Attention

Learning the low-dimensional representations of graphs (i.e., network embedding) plays a critical role in network analysis and facilitates many downstream tasks. Recently graph convolutional networks (GCNs) have revolutionized the field of network embedding, and led to state-of-the-art performance in network analysis tasks such as link prediction and node classification. Nevertheless, most of the existing GCN-based network embedding methods are proposed for unsigned networks. However, in the real world, some of the networks are signed, where the links are annotated with different polarities, e.g., positive vs. negative. Since negative links may have different properties from the positive ones and can also significantly affect the quality of network embedding. Thus in this paper, we propose a novel network embedding framework SNEA to learn Signed Network Embedding via graph Attention. In particular, we propose a masked self-attentional layer, which leverages self-attention mechanism to estimate the importance coefficient for pair of nodes connected by different type of links during the embedding aggregation process. Then SNEA utilizes the masked self-attentional layers to aggregate more important information from neighboring nodes to generate the node embeddings based on balance theory. Experimental results demonstrate the effectiveness of the proposed framework through signed link prediction task on several real-world signed network datasets.

Attending Over Triads for Learning Signed Network Embedding.

Network embedding, which aims at learning distributed representations for nodes in networks, is a critical task with wide downstream applications. Most existing studies focus on networks with a single type of edges, whereas in many cases, the edges of networks can be derived from two opposite relationships, yielding signed networks. This paper studies network embedding for the signed network, and a novel approach called TEA is proposed. Similar to existing methods, TEA (Triad+Edge+Attention) learns node representations by predicting the sign of each edge in the network. However, many existing methods only consider the local structural information (i.e., the representations of nodes in an edge) for prediction, which can be biased especially for sparse networks. By contrast, TEA seeks to leverage the high-order structures by drawing inspirations from the Structural Balance Theory. More specifically, for an edge linking two nodes, TEA predicts the edge sign by considering the triangles connecting the two nodes as features. Meanwhile, an attention mechanism is proposed, which assigns different weights to the different triangles before aggregating their predictions for more precise results. We conduct experiments on several real-world signed networks, and the results prove the effectiveness of TEA over many strong baseline approaches.

Learning node and edge embeddings for signed networks

Abstract Machine learning tasks for edges and nodes in networks heavily rely on feature engineering which requires expert knowledge and careful effort. Recent years, people become interested in the low dimensional vector representation of nodes and edges. However, existing methods on signed networks only aim to learn the node vectors, resulting in omitting edge information and extra effort to design edge vectors. In this work, we develop a framework for learning both nodes and edge vectors for signed networks. Thus, we can directly use edge vectors to represent the properties of the edges, and thereby improving the performance of link-oriented tasks. Our framework for learning network features is as below. We assume that there is a global mapping between the node and edge vector spaces. This assumption allows us to transform the problem into learning the mapping function and the node vectors. We propose node proximity for signed networks, a definition that is generalized from the second-order node proximity for unsigned networks. It provides a unified objective function that can preserve both the node and edge pattern of the network. Based on this definition, we propose two signed network representation methods. The first method is neural network signed network embedding (nSNE). It learns the node vectors and the mapping function via neural networks approach, which can uses the power of deep learning to fit with the data. The second method is light signed network embedding (lSNE). It specifies the mapping function as simply and linear function. It has fewer parameters to estimate and is equal to factorize both similarity and sign matrixes. We compare our methods with three state-of-the-art methods on four datasets. The results show that our methods are competitive.

Cultures of the Central Highlands, New Guinea

Cultures of the Central Highlands, New Guinea