Link prediction via layer relevance of multiplex networks

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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Link prediction in real-world multiplex networks via layer reconstruction method

Royal Society Open Science ◽

10.1098/rsos.191928 ◽

2020 ◽

Vol 7 (7) ◽

pp. 191928

Author(s):

Amir Mahdi Abdolhosseini-Qomi ◽

Seyed Hossein Jafari ◽

Amirheckmat Taghizadeh ◽

Naser Yazdani ◽

Masoud Asadpour ◽

...

Keyword(s):

Real World ◽

Link Prediction ◽

Large Body ◽

Single Layer ◽

Structural Features ◽

Prediction Performance ◽

Reconstruction Method ◽

Multiplex Networks ◽

Technological Complex ◽

Different Types

Networks are invaluable tools to study real biological, social and technological complex systems in which connected elements form a purposeful phenomenon. A higher resolution image of these systems shows that the connection types do not confine to one but to a variety of types. Multiplex networks encode this complexity with a set of nodes which are connected in different layers via different types of links. A large body of research on link prediction problem is devoted to finding missing links in single-layer (simplex) networks. In recent years, the problem of link prediction in multiplex networks has gained the attention of researchers from different scientific communities. Although most of these studies suggest that prediction performance can be enhanced by using the information contained in different layers of the network, the exact source of this enhancement remains obscure. Here, it is shown that similarity w.r.t. structural features (eigenvectors) is a major source of enhancements for link prediction task in multiplex networks using the proposed layer reconstruction method and experiments on real-world multiplex networks from different disciplines. Moreover, we characterize how low values of similarity w.r.t. structural features result in cases where improving prediction performance is substantially hard.

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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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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 based on local weighted paths for complex networks

International Journal of Modern Physics C ◽

10.1142/s012918311750053x ◽

2017 ◽

Vol 28 (04) ◽

pp. 1750053

Author(s):

Yabing Yao ◽

Ruisheng Zhang ◽

Fan Yang ◽

Yongna Yuan ◽

Rongjing Hu ◽

...

Keyword(s):

Complex Networks ◽

Real World ◽

Link Prediction ◽

Structural Similarity ◽

Prediction Performance ◽

Topological Feature ◽

Topological Features ◽

Node Similarity ◽

Weighted Paths ◽

Path Dependent

As a significant problem in complex networks, link prediction aims to find the missing and future links between two unconnected nodes by estimating the existence likelihood of potential links. It plays an important role in understanding the evolution mechanism of networks and has broad applications in practice. In order to improve prediction performance, a variety of structural similarity-based methods that rely on different topological features have been put forward. As one topological feature, the path information between node pairs is utilized to calculate the node similarity. However, many path-dependent methods neglect the different contributions of paths for a pair of nodes. In this paper, a local weighted path (LWP) index is proposed to differentiate the contributions between paths. The LWP index considers the effect of the link degrees of intermediate links and the connectivity influence of intermediate nodes on paths to quantify the path weight in the prediction procedure. The experimental results on 12 real-world networks show that the LWP index outperforms other seven prediction baselines.

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The Multiplex Dependency Structure of Financial Markets

Complexity ◽

10.1155/2017/9586064 ◽

2017 ◽

Vol 2017 ◽

pp. 1-13 ◽

Cited By ~ 26

Author(s):

Nicolò Musmeci ◽

Vincenzo Nicosia ◽

Tomaso Aste ◽

Tiziana Di Matteo ◽

Vito Latora

Keyword(s):

Financial Markets ◽

Financial Time Series ◽

Single Layer ◽

Separate Analysis ◽

Dependency Structure ◽

Multiplex Networks ◽

Multiplex Network ◽

Different Types ◽

Partial Correlations ◽

Filtering Procedure

We propose here a multiplex network approach to investigate simultaneously different types of dependency in complex datasets. In particular, we consider multiplex networks made of four layers corresponding, respectively, to linear, nonlinear, tail, and partial correlations among a set of financial time series. We construct the sparse graph on each layer using a standard network filtering procedure, and we then analyse the structural properties of the obtained multiplex networks. The study of the time evolution of the multiplex constructed from financial data uncovers important changes in intrinsically multiplex properties of the network, and such changes are associated with periods of financial stress. We observe that some features are unique to the multiplex structure and would not be visible otherwise by the separate analysis of the single-layer networks corresponding to each dependency measure.

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Layer Information Similarity Concerned Network Embedding

Complexity ◽

10.1155/2021/2260488 ◽

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.

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Discovering spurious links in multiplex networks based on interlayer relevance

Journal of Complex Networks ◽

10.1093/comnet/cnz007 ◽

2019 ◽

Vol 7 (5) ◽

pp. 641-658 ◽

Cited By ~ 2

Author(s):

Zeynab Samei ◽

Mahdi Jalili

Keyword(s):

Social Networks ◽

Social Networking ◽

Link Prediction ◽

Large Scale ◽

Transportation Networks ◽

Similarity Index ◽

Similarity Measures ◽

Computation Complexity ◽

Multiplex Networks ◽

Large Scale Networks

Abstract Many real-world complex systems can be better modelled as multiplex networks, where the same individuals develop connections in multiple layers. Examples include social networks between individuals on multiple social networking platforms, and transportation networks between cities based on air, rail and road networks. Accurately predicting spurious links in multiplex networks is a challenging issue. In this article, we show that one can effectively use interlayer information to build an algorithm for spurious link prediction. We propose a similarity index that combines intralayer similarity with interlayer relevance for the link prediction purpose. The proposed similarity index is used to rank the node pairs, and identify those that are likely to be spurious. Our experimental results show that the proposed metric is much more accurate than intralayer similarity measures in correctly predicting the spurious links. The proposed method is an unsupervised method and has low computation complexity, and thus can be effectively applied for spurious link prediction in large-scale networks.

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Learning embeddings for multiplex networks using triplet loss

Applied Network Science ◽

10.1007/s41109-019-0242-0 ◽

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.

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Deep Learning Roles based Approach to Link Prediction in Networks

10.5121/csit.2020.101416 ◽

2020 ◽

Author(s):

Aman Gupta ◽

Yadul Raghav

Keyword(s):

Deep Learning ◽

Link Prediction ◽

Information Science ◽

Structural Information ◽

Structural Features ◽

Similarity Score ◽

Node Attribute ◽

Depth Analysis ◽

Real World Datasets ◽

Better Than

The problem of predicting links has gained much attention in recent years due to its vast application in various domains such as sociology, network analysis, information science, etc. Many methods have been proposed for link prediction such as RA, AA, CCLP, etc. These methods required hand-crafted structural features to calculate the similarity scores between a pair of nodes in a network. Some methods use local structural information while others use global information of a graph. These methods do not tell which properties are better than others. With an in-depth analysis of these methods, we understand that one way to overcome this problem is to consider network structure and node attribute information to capture the discriminative features for link prediction tasks. We proposed a deep learning Autoencoder based Link Prediction (ALP) architecture for the latent representation of a graph, unified with non-negative matrix factorization to automatically determine the underlying roles in a network, after that assigning a mixed-membership of these roles to each node in the network. The idea is to transfer these roles as a feature vector for the link prediction task in the network. Further, cosine similarity is applied after getting the required features to compute the pairwise similarity score between the nodes. We present the performance of the algorithm on the real-world datasets, where it gives the competitive result compared to other algorithms.

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Multiplex Networks of the Guarantee Market: Evidence from China

Complexity ◽

10.1155/2017/9781890 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7 ◽

Cited By ~ 4

Author(s):

Shouwei Li ◽

Shihang Wen

Keyword(s):

Betweenness Centrality ◽

Single Layer ◽

Eigenvector Centrality ◽

Scale Free ◽

Multiplex Networks ◽

Multiplex Network ◽

Different Types ◽

Single Layer Network

We investigate a multiplex network of the guarantee market with three layers corresponding to different types of guarantee relationships in China. We find that three single-layer networks all have the scale-free property and are of disassortative nature. A single-layer network is not quite representative of another single-layer network. The result of the betweenness centrality shows that central companies in one layer are not necessarily central in another layer. And the eigenvector centrality has the same result of the betweenness centrality except the top central company.

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