Layer Information Similarity Concerned Network Embedding

Great achievements have been made in network embedding based on single-layer networks. However, there are a variety of scenarios and systems that can be presented as multiplex networks, which can reveal more interesting patterns hidden in the data compared to single-layer networks. In the field of network embedding, in order to project the multiplex network into the latent space, it is necessary to consider richer structural information among network layers. However, current methods for multiplex network embedding mostly focus on the similarity of nodes in each layer of the network, while ignoring the similarity between different layers. In this paper, for multiplex network embedding, we propose a Layer Information Similarity Concerned Network Embedding (LISCNE) model considering the similarities between layers. Firstly, we introduce the common vector for each node shared by all layers and layer vectors for each layer where common vectors obtain the overall structure of the multiplex network and layer vectors learn semantics for each layer. We get the node embeddings in each layer by concatenating the common vectors and layer vectors with the consideration that the node embedding is related not only to the surrounding neighbors but also to the overall semantics. Furthermore, we define an index to formalize the similarity between different layers and the cross-network association. Constrained by layer similarity, the layer vectors with greater similarity are closer to each other and the aligned node embedding in these layers is also closer. To evaluate our proposed model, we conduct node classification and link prediction tasks to verify the effectiveness of our model, and the results show that LISCNE can achieve better or comparable performance compared to existing baseline methods.

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MultiVERSE: a multiplex and multiplex-heterogeneous network embedding approach

Scientific Reports ◽

10.1038/s41598-021-87987-1 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Léo Pio-Lopez ◽

Alberto Valdeolivas ◽

Laurent Tichit ◽

Élisabeth Remy ◽

Anaïs Baudot

Keyword(s):

Heterogeneous Networks ◽

Heterogeneous Network ◽

Link Prediction ◽

Network Embedding ◽

Multiplex Networks ◽

Multiplex Network ◽

Gene Associations ◽

Different Types ◽

Embedding Methods ◽

Node Embeddings

AbstractNetwork embedding approaches are gaining momentum to analyse a large variety of networks. Indeed, these approaches have demonstrated their effectiveness in tasks such as community detection, node classification, and link prediction. However, very few network embedding methods have been specifically designed to handle multiplex networks, i.e. networks composed of different layers sharing the same set of nodes but having different types of edges. Moreover, to our knowledge, existing approaches cannot embed multiple nodes from multiplex-heterogeneous networks, i.e. networks composed of several multiplex networks containing both different types of nodes and edges. In this study, we propose MultiVERSE, an extension of the VERSE framework using Random Walks with Restart on Multiplex (RWR-M) and Multiplex-Heterogeneous (RWR-MH) networks. MultiVERSE is a fast and scalable method to learn node embeddings from multiplex and multiplex-heterogeneous networks. We evaluate MultiVERSE on several biological and social networks and demonstrate its performance. MultiVERSE indeed outperforms most of the other methods in the tasks of link prediction and network reconstruction for multiplex network embedding, and is also efficient in link prediction for multiplex-heterogeneous network embedding. Finally, we apply MultiVERSE to study rare disease-gene associations using link prediction and clustering. MultiVERSE is freely available on github at https://github.com/Lpiol/MultiVERSE.

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Link prediction via layer relevance of multiplex networks

International Journal of Modern Physics C ◽

10.1142/s0129183117501017 ◽

2017 ◽

Vol 28 (08) ◽

pp. 1750101 ◽

Cited By ~ 7

Author(s):

Yabing Yao ◽

Ruisheng Zhang ◽

Fan Yang ◽

Yongna Yuan ◽

Qingshuang Sun ◽

...

Keyword(s):

Structural Properties ◽

Link Prediction ◽

Structural Information ◽

Similarity Index ◽

Single Layer ◽

Structural Features ◽

Prediction Performance ◽

Multiplex Networks ◽

Multiplex Network ◽

Node Similarity

In complex networks, the existing link prediction methods primarily focus on the internal structural information derived from single-layer networks. However, the role of interlayer information is hardly recognized in multiplex networks, which provide more diverse structural features than single-layer networks. Actually, the structural properties and functions of one layer can affect that of other layers in multiplex networks. In this paper, the effect of interlayer structural properties on the link prediction performance is investigated in multiplex networks. By utilizing the intralayer and interlayer information, we propose a novel “Node Similarity Index” based on “Layer Relevance” (NSILR) of multiplex network for link prediction. The performance of NSILR index is validated on each layer of seven multiplex networks in real-world systems. Experimental results show that the NSILR index can significantly improve the prediction performance compared with the traditional methods, which only consider the intralayer information. Furthermore, the more relevant the layers are, the higher the performance is enhanced.

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Scalable Multiplex Network Embedding

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/428 ◽

2018 ◽

Cited By ~ 22

Author(s):

Hongming Zhang ◽

Liwei Qiu ◽

Lingling Yi ◽

Yangqiu Song

Keyword(s):

Link Prediction ◽

State Of The Art ◽

High Dimensional ◽

Network Embedding ◽

Current State ◽

Multiplex Network ◽

Different Types ◽

Comparable Performance ◽

Combine Information ◽

Real World Problems

Network embedding has been proven to be helpful for many real-world problems. In this paper, we present a scalable multiplex network embedding model to represent information of multi-type relations into a unified embedding space. To combine information of different types of relations while maintaining their distinctive properties, for each node, we propose one high-dimensional common embedding and a lower-dimensional additional embedding for each type of relation. Then multiple relations can be learned jointly based on a unified network embedding model. We conduct experiments on two tasks: link prediction and node classification using six different multiplex networks. On both tasks, our model achieved better or comparable performance compared to current state-of-the-art models with less memory use.

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Unsupervised Attributed Multiplex Network Embedding

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i04.5985 ◽

2020 ◽

Vol 34 (04) ◽

pp. 5371-5378

Author(s):

Chanyoung Park ◽

Donghyun Kim ◽

Jiawei Han ◽

Hwanjo Yu

Keyword(s):

Single Type ◽

Network Embedding ◽

Global Properties ◽

Multiplex Network ◽

Relation Type ◽

Global Representation ◽

Node Attributes ◽

Node Labels ◽

Embedding Methods ◽

Node Embeddings

Nodes in a multiplex network are connected by multiple types of relations. However, most existing network embedding methods assume that only a single type of relation exists between nodes. Even for those that consider the multiplexity of a network, they overlook node attributes, resort to node labels for training, and fail to model the global properties of a graph. We present a simple yet effective unsupervised network embedding method for attributed multiplex network called DMGI, inspired by Deep Graph Infomax (DGI) that maximizes the mutual information between local patches of a graph, and the global representation of the entire graph. We devise a systematic way to jointly integrate the node embeddings from multiple graphs by introducing 1) the consensus regularization framework that minimizes the disagreements among the relation-type specific node embeddings, and 2) the universal discriminator that discriminates true samples regardless of the relation types. We also show that the attention mechanism infers the importance of each relation type, and thus can be useful for filtering unnecessary relation types as a preprocessing step. Extensive experiments on various downstream tasks demonstrate that DMGI outperforms the state-of-the-art methods, even though DMGI is fully unsupervised.

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Nonlinear Structural Fusion for Multiplex Network

Complexity ◽

10.1155/2020/7041564 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Nianwen Ning ◽

Feiyu Long ◽

Chunchun Wang ◽

Youjie Zhang ◽

Yilin Yang ◽

...

Keyword(s):

Network Analysis ◽

Real World ◽

Structural Information ◽

Single Layer ◽

Multiplex Networks ◽

Multiplex Network ◽

Low Weight ◽

Fusion Methods ◽

Low Dimensional ◽

Single Layer Network

Many real-world complex systems have multiple types of relations between their components, and they are popularly modeled as multiplex networks with each type of relation as one layer. Since the fusion analysis of multiplex networks can provide a comprehensive insight, the structural information fusion of multiplex networks has become a crucial issue. However, most of these existing data fusion methods are inappropriate for researchers to apply to complex network analysis directly. The feature-based fusion methods ignore the sharing and complementarity of interlayer structural information. To tackle this problem, we propose a multiplex network structural fusion (MNSF) model, which can construct a network with comprehensive information. It is composed of two modules: the network feature extraction (NFE) module and the network structural fusion (NSF) module. (1) In NFE, MNSF first extracts a low-dimensional vector representation of a node from each layer. Then, we construct a node similarity network based on embedding matrices and K-D tree algorithm. (2) In NSF, we present a nonlinear enhanced iterative fusion (EIF) strategy. EIF can strengthen high-weight edges presented in one (i.e., complementary information) or more (i.e., shared information) networks and weaken low-weight edges (i.e., redundant information). The retention of low-weight edges shared by all layers depends on the tightness of connections of their K-order proximity. The usage of higher-order proximity in EIF alleviates the dependence on the quality of node embedding. Besides, the fused network can be easily exploited by traditional single-layer network analysis methods. Experiments on real-world networks demonstrate that MNSF outperforms the state-of-the-art methods in tasks link prediction and shared community detection.

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Multiplex Network Embedding Model with High-Order Node Dependence

Complexity ◽

10.1155/2021/6644111 ◽

2021 ◽

Vol 2021 ◽

pp. 1-18

Author(s):

Nianwen Ning ◽

Qiuyue Li ◽

Kai Zhao ◽

Bin Wu

Keyword(s):

Real World ◽

Information Diffusion ◽

Structural Information ◽

High Order ◽

Network Embedding ◽

Multiplex Networks ◽

Cross Domain ◽

Multiplex Network ◽

Node Attributes ◽

Two Phases

Multiplex networks have been widely used in information diffusion, social networks, transport, and biology multiomics. They contain multiple types of relations between nodes, in which each type of the relation is intuitively modeled as one layer. In the real world, the formation of a type of relations may only depend on some attribute elements of nodes. Most existing multiplex network embedding methods only focus on intralayer and interlayer structural information while neglecting this dependence between node attributes and the topology of each layer. Attributes that are irrelevant to the network structure could affect the embedding quality of multiplex networks. To address this problem, we propose a novel multiplex network embedding model with high-order node dependence, called HMNE. HMNE simultaneously considers three properties: (1) intralayer high-order proximity of nodes, (2) interlayer dependence in respect of nodes, and (3) the dependence between node attributes and the topology of each layer. In the intralayer embedding phase, we present a symmetric graph convolution-deconvolution model to embed high-order proximity information as the intralayer embedding of nodes in an unsupervised manner. In the interlayer embedding phase, we estimate the local structural complementarity of nodes as an embedding constraint of interlayer dependence. Through these two phases, we can achieve the disentangled representation of node attributes, which can be treated as fined-grained semantic dependence on the topology of each layer. In the restructure phase of node attributes, we perform a linear fusion of attribute disentangled representations for each node as a reconstruction of original attributes. Extensive experiments have been conducted on six real-world networks. The experimental results demonstrate that the proposed model outperforms the state-of-the-art methods in cross-domain link prediction and shared community detection tasks.

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W-MMP2Vec: Topic-driven network embedding model for link prediction in content-based heterogeneous information network

Intelligent Data Analysis ◽

10.3233/ida-205168 ◽

2021 ◽

Vol 25 (3) ◽

pp. 711-738

Author(s):

Phu Pham ◽

Phuc Do

Keyword(s):

Link Prediction ◽

Representation Learning ◽

Information Network ◽

Network Embedding ◽

Heterogeneous Information Network ◽

Heterogeneous Information ◽

Learning Framework ◽

Novel Approach ◽

Proposed Model ◽

Meta Path

Link prediction on heterogeneous information network (HIN) is considered as a challenge problem due to the complexity and diversity in types of nodes and links. Currently, there are remained challenges of meta-path-based link prediction in HIN. Previous works of link prediction in HIN via network embedding approach are mainly focused on exploiting features of node rather than existing relations in forms of meta-paths between nodes. In fact, predicting the existence of new links between non-linked nodes is absolutely inconvincible. Moreover, recent HIN-based embedding models also lack of thorough evaluations on the topic similarity between text-based nodes along given meta-paths. To tackle these challenges, in this paper, we proposed a novel approach of topic-driven multiple meta-path-based HIN representation learning framework, namely W-MMP2Vec. Our model leverages the quality of node representations by combining multiple meta-paths as well as calculating the topic similarity weight for each meta-path during the processes of network embedding learning in content-based HINs. To validate our approach, we apply W-TMP2Vec model in solving several link prediction tasks in both content-based and non-content-based HINs (DBLP, IMDB and BlogCatalog). The experimental outputs demonstrate the effectiveness of proposed model which outperforms recent state-of-the-art HIN representation learning models.

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RLC-GNN: An Improved Deep Architecture for Spatial-Based Graph Neural Network with Application to Fraud Detection

Applied Sciences ◽

10.3390/app11125656 ◽

2021 ◽

Vol 11 (12) ◽

pp. 5656

Author(s):

Yufan Zeng ◽

Jiashan Tang

Keyword(s):

Numerical Experiments ◽

State Of The Art ◽

Single Layer ◽

Fraud Detection ◽

Layer By Layer ◽

Residual Structure ◽

Detection Algorithms ◽

Deep Architecture ◽

Graph Neural Networks ◽

Node Embeddings

Graph neural networks (GNNs) have been very successful at solving fraud detection tasks. The GNN-based detection algorithms learn node embeddings by aggregating neighboring information. Recently, CAmouflage-REsistant GNN (CARE-GNN) is proposed, and this algorithm achieves state-of-the-art results on fraud detection tasks by dealing with relation camouflages and feature camouflages. However, stacking multiple layers in a traditional way defined by hop leads to a rapid performance drop. As the single-layer CARE-GNN cannot extract more information to fix the potential mistakes, the performance heavily relies on the only one layer. In order to avoid the case of single-layer learning, in this paper, we consider a multi-layer architecture which can form a complementary relationship with residual structure. We propose an improved algorithm named Residual Layered CARE-GNN (RLC-GNN). The new algorithm learns layer by layer progressively and corrects mistakes continuously. We choose three metrics—recall, AUC, and F1-score—to evaluate proposed algorithm. Numerical experiments are conducted. We obtain up to 5.66%, 7.72%, and 9.09% improvements in recall, AUC, and F1-score, respectively, on Yelp dataset. Moreover, we also obtain up to 3.66%, 4.27%, and 3.25% improvements in the same three metrics on the Amazon dataset.

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Network Embedding on Hierarchical Community Structure Network

ACM Transactions on Knowledge Discovery from Data ◽

10.1145/3434747 ◽

2021 ◽

Vol 15 (4) ◽

pp. 1-23

Author(s):

Guojie Song ◽

Yun Wang ◽

Lun Du ◽

Yi Li ◽

Junshan Wang

Keyword(s):

Community Structure ◽

Structural Information ◽

Spherical Surface ◽

Network Embedding ◽

The Galaxy ◽

Community Information ◽

The Hierarchical Structure ◽

Network Properties ◽

Multi Class Classification ◽

Low Dimensional

Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low-dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification, network visualization, and link prediction. The source code of GNE is available online.

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Interpretable Variational Graph Autoencoder with Noninformative Prior

Future Internet ◽

10.3390/fi13020051 ◽

2021 ◽

Vol 13 (2) ◽

pp. 51

Author(s):

Lili Sun ◽

Xueyan Liu ◽

Min Zhao ◽

Bo Yang

Keyword(s):

Latent Variables ◽

Latent Variable ◽

Expert Knowledge ◽

Structural Information ◽

Standard Normal Distribution ◽

Noninformative Prior ◽

Latent Space ◽

Distribution Parameters ◽

Standard Normal ◽

Low Dimensional

Variational graph autoencoder, which can encode structural information and attribute information in the graph into low-dimensional representations, has become a powerful method for studying graph-structured data. However, most existing methods based on variational (graph) autoencoder assume that the prior of latent variables obeys the standard normal distribution which encourages all nodes to gather around 0. That leads to the inability to fully utilize the latent space. Therefore, it becomes a challenge on how to choose a suitable prior without incorporating additional expert knowledge. Given this, we propose a novel noninformative prior-based interpretable variational graph autoencoder (NPIVGAE). Specifically, we exploit the noninformative prior as the prior distribution of latent variables. This prior enables the posterior distribution parameters to be almost learned from the sample data. Furthermore, we regard each dimension of a latent variable as the probability that the node belongs to each block, thereby improving the interpretability of the model. The correlation within and between blocks is described by a block–block correlation matrix. We compare our model with state-of-the-art methods on three real datasets, verifying its effectiveness and superiority.

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