scholarly journals Multiplex Network Embedding Model with High-Order Node Dependence

Complexity ◽  
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.

scholarly journals Nonlinear Structural Fusion for Multiplex Network

Complexity ◽  
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.

scholarly journals Principled approach to the selection of the embedding dimension of networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Weiwei Gu ◽  
Aditya Tandon ◽  
Yong-Yeol Ahn ◽  
Filippo Radicchi
Keyword(s):  
Real World ◽  
Structural Information ◽  
General Purpose ◽  
Embedding Dimension ◽  
Network Embedding ◽  
Machine Learning Technique ◽  
Learning Technique ◽  
Low Dimensional ◽  
Large Corpus ◽  
Selection Of

AbstractNetwork embedding is a general-purpose machine learning technique that encodes network structure in vector spaces with tunable dimension. Choosing an appropriate embedding dimension – small enough to be efficient and large enough to be effective – is challenging but necessary to generate embeddings applicable to a multitude of tasks. Existing strategies for the selection of the embedding dimension rely on performance maximization in downstream tasks. Here, we propose a principled method such that all structural information of a network is parsimoniously encoded. The method is validated on various embedding algorithms and a large corpus of real-world networks. The embedding dimension selected by our method in real-world networks suggest that efficient encoding in low-dimensional spaces is usually possible.

scholarly journals MultiVERSE: a multiplex and multiplex-heterogeneous network embedding approach

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.

Link prediction via layer relevance of multiplex networks

2017 ◽  
Vol 28 (08) ◽  
pp. 1750101 ◽  
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.

scholarly journals Crawling the Community Structure of Multiplex Networks

2019 ◽  
Vol 33 ◽  
pp. 168-175 ◽  
Author(s):  
Ricky Laishram ◽  
Jeremy D. Wendt ◽  
Sucheta Soundarajan
Keyword(s):  
Community Structure ◽  
Real World ◽  
Multiplex Networks ◽  
Data Collector ◽  
Multiplex Network ◽  
Multiple Levels ◽  
Novel Algorithm ◽  
Collection Costs

We examine the problem of crawling the community structure of a multiplex network containing multiple layers of edge relationships. While there has been a great deal of work examining community structure in general, and some work on the problem of sampling a network to preserve its community structure, to the best of our knowledge, this is the first work to consider this problem on multiplex networks. We consider the specific case in which the layers of a multiplex network have different query (collection) costs and reliabilities; and a data collector is interested in identifying the community structure of the most expensive layer. We propose MultiComSample (MCS), a novel algorithm for crawling a multiplex network. MCS uses multiple levels of multi-armed bandits to determine the best layers, communities and node roles for selecting nodes to query. We test MCS against six baseline algorithms on real-world multiplex networks, and achieved large gains in performance. For example, after consuming a budget equivalent to sampling 20% of the nodes in the expensive layer, we observe that MCS outperforms the best baseline by up to 49%.

scholarly journals Layer Information Similarity Concerned Network Embedding

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ruili Lu ◽  
Pengfei Jiao ◽  
Yinghui Wang ◽  
Huaming Wu ◽  
Xue Chen
Keyword(s):  
Structural Information ◽  
Single Layer ◽  
Network Embedding ◽  
Network Layers ◽  
Multiplex Network ◽  
Proposed Model ◽  
Latent Space ◽  
Comparable Performance ◽  
The Common ◽  
Node Embeddings

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.

scholarly journals Learning embeddings for multiplex networks using triplet loss

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Seyedsaeed Hajiseyedjavadi ◽  
Yu-Ru Lin ◽  
Konstantinos Pelechrinis
Keyword(s):  
Real World ◽  
Online Social Network ◽  
Single Layer ◽  
Interaction Network ◽  
Machine Learning Techniques ◽  
Collaboration Network ◽  
Multiplex Networks ◽  
Multiplex Network ◽  
Triplet Loss ◽  
Low Dimensional

AbstractLearning low-dimensional representations of graphs has facilitated the use of traditional machine learning techniques to solving classic network analysis tasks such as link prediction, node classification, community detection, etc. However, to date, the vast majority of these learning tasks are focused on traditional single-layer/unimodal networks and largely ignore the case of multiplex networks. A multiplex network is a suitable structure to model multi-dimensional real-world complex systems. It consists of multiple layers where each layer represents a different relationship among the network nodes. In this work, we propose MUNEM, a novel approach for learning a low-dimensional representation of a multiplex network using a triplet loss objective function. In our approach, we preserve the global structure of each layer, while at the same time fusing knowledge among different layers during the learning process. We evaluate the effectiveness of our proposed method by testing and comparing on real-world multiplex networks from different domains, such as collaboration network, protein-protein interaction network, online social network. Finally, in order to deliberately examine the effect of our model’s parameters we conduct extensive experiments on synthetic multiplex networks.

Sampling Graphlets of Multiplex Networks: A Restricted Random Walk Approach

2021 ◽  
Vol 15 (4) ◽  
pp. 1-31
Author(s):  
Simiao Jiao ◽  
Zihui Xue ◽  
Xiaowei Chen ◽  
Yuedong Xu
Keyword(s):  
Random Walk ◽  
Real World ◽  
High Efficiency ◽  
Large Network ◽  
Induced Subgraph ◽  
Multiplex Networks ◽  
Multiplex Network ◽  
Random Node ◽  
Edge Sampling ◽  
And Function

Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of effort has been devoted to calculating graphlet statistics where random walk-based approaches are commonly used to access restricted graphs through the available application programming interfaces (APIs). However, most of them merely consider individual networks while overlooking the strong coupling between different networks. In this article, we estimate the graphlet concentration in multiplex networks with real-world applications. An inter-layer edge connects two nodes in different layers if they actually belong to the same node. The access to a multiplex network is restrictive in the sense that the upper layer allows random walk sampling, whereas the nodes of lower layers can be accessed only through the inter-layer edges and only support random node or edge sampling. To cope with this new challenge, we define a suit of two-layer graphlets and propose novel random walk sampling algorithms to estimate the proportion of all the three-node graphlets. An analytical bound on the sampling steps is proved to guarantee the convergence of our unbiased estimator. We further generalize our algorithm to explore the tradeoff between the estimated accuracy of different graphlets when the sample budget is split into different layers. Experimental evaluation on real-world and synthetic multiplex networks demonstrates the accuracy and high efficiency of our unbiased estimators.

scholarly journals DGE: Deep Generative Network Embedding Based on Commonality and Individuality

2020 ◽  
Vol 34 (04) ◽  
pp. 6949-6956
Author(s):  
Sheng Zhou ◽  
Xin Wang ◽  
Jiajun Bu ◽  
Martin Ester ◽  
Pinggang Yu ◽  
...  
Keyword(s):  
Network Topology ◽  
Real World ◽  
Information Source ◽  
Model Parameters ◽  
Network Embedding ◽  
Generative Process ◽  
Attributed Network ◽  
Node Attributes ◽  
Real World Datasets ◽  
The One

Network embedding plays a crucial role in network analysis to provide effective representations for a variety of learning tasks. Existing attributed network embedding methods mainly focus on preserving the observed node attributes and network topology in the latent embedding space, with the assumption that nodes connected through edges will share similar attributes. However, our empirical analysis of real-world datasets shows that there exist both commonality and individuality between node attributes and network topology. On the one hand, similar nodes are expected to share similar attributes and have edges connecting them (commonality). On the other hand, each information source may maintain individual differences as well (individuality). Simultaneously capturing commonality and individuality is very challenging due to their exclusive nature and existing work fail to do so. In this paper, we propose a deep generative embedding (DGE) framework which simultaneously captures commonality and individuality between network topology and node attributes in a generative process. Stochastic gradient variational Bayesian (SGVB) optimization is employed to infer model parameters as well as the node embeddings. Extensive experiments on four real-world datasets show the superiority of our proposed DGE framework in various tasks including node classification and link prediction.

scholarly journals Heterogeneous Attributed Network Embedding with Graph Convolutional Networks

2019 ◽  
Vol 33 ◽  
pp. 10061-10062 ◽  
Author(s):  
Yueyang Wang ◽  
Ziheng Duan ◽  
Binbing Liao ◽  
Fei Wu ◽  
Yueting Zhuang
Keyword(s):  
Real World ◽  
Network Embedding ◽  
High Quality ◽  
Embedding Method ◽  
The Real ◽  
Convolutional Networks ◽  
Attributed Network ◽  
Node Attributes ◽  
Attributed Networks

Network embedding which assigns nodes in networks to lowdimensional representations has received increasing attention in recent years. However, most existing approaches, especially the spectral-based methods, only consider the attributes in homogeneous networks. They are weak for heterogeneous attributed networks that involve different node types as well as rich node attributes and are common in real-world scenarios. In this paper, we propose HANE, a novel network embedding method based on Graph Convolutional Networks, that leverages both the heterogeneity and the node attributes to generate high-quality embeddings. The experiments on the real-world dataset show the effectiveness of our method.

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