Nonlinear Structural Fusion for Multiplex 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.

Download Full-text

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.

Download Full-text

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.

Download Full-text

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.

Download Full-text

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.

Download Full-text

Principled approach to the selection of the embedding dimension of networks

Nature Communications ◽

10.1038/s41467-021-23795-5 ◽

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.

Download Full-text

Crawling the Community Structure of Multiplex Networks

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.3301168 ◽

2019 ◽

Vol 33 ◽

pp. 168-175 ◽

Cited By ~ 3

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%.

Download Full-text

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.

Download Full-text

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.

Download Full-text

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.

Download Full-text