Multi-Net: A Scalable Multiplex Network Embedding Framework

Meta-path-based random walk strategy has attracted tremendous attention in heterogeneous network representation, which can capture network semantics with heterogeneous neighborhoods of nodes. Despite the success of meta-path-based random walk strategy in plain heterogeneous networks which contain no attributes, it remains unexplored how meta-path-based random walk strategy could be utilized on attributed heterogeneous networks to simultaneously capture structural heterogeneity and attribute proximity. Moreover, the importance of node attributes and structural relations generally varies across data sets, thus requiring careful considerations when they are incorporated into representations. To tackle these problems, we propose a novel method, Attributed Heterogeneous Network embedding based on Aggregate-path (AHNA), which generates aggregate-path-based random walks on attributed heterogeneous networks and adaptively fuses topological structures and node attributes based on the learned importance. Specifically, AHNA first converts node attributes to additional links in the network to deal with the heterogeneity of structures and attributes, which is followed by an adaptive random walk strategy to strike the importance balance between node attributes and topological structures, thereby generating high-quality representations. Extensive experiments are conducted on three real-world data sets, where AHNA outperforms state-of-the-art approaches by up to 22.7%, 2.6%, and 2.3% on link prediction, community detection, and node classification, respectively. Moreover, our qualitative analysis indicates that AHNA can capture different balances of topological structures and node attributes on various data sets and thus boost the quality of node representations.

Link prediction in multilayer networks using weighted reliable local random walk algorithm

Learning 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.

Link prediction methods can help to reconstruct systems from incomplete datasets, to understand the structure dynamic complex networks, and to predict future interactions in evolving networks. Link prediction in multiplex networks is the problem of finding missing links between users based on information from other layers. Although the link prediction problem has been widely studied in multiplex networks, most methods do not consider both interlayer and intralayer features at the same time. Similarity metrics are one of the most common approaches to solving the link prediction problem. However, the development of similarity metrics over multiple layers with the definition of multiplex networks has become an important challenge that has caught the attention of many researchers. In this article, a novel similarity metric is introduced by considering reliable paths between users for link prediction in multiplex networks. The proposed method maps the network to a weighted network by extracting different interlayer and intralayer features from multiplex networks. Finally, the proposed similarity metric develops the FriendLink metric by considering the weight of links and reliable paths. The proposed method is evaluated in comparison with classical similarity metrics and equivalence algorithms such as SEM-Path, LPIS, and SOIDP. Two real datasets based on multiplex networks including Twitter–Foursquare and Twitter–Instagram have been used to evaluate. Experiments prove the superiority of link prediction in the proposed method over other algorithms.

Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on network structure. However, in practice we often have auxiliary information about the nodes and/or their interactions, e.g., content of scientific papers in co-authorship networks, or topics of communication in Twitter mention networks. Here we propose a novel embedding method that uses both network structure and edge attributes to learn better network representations. Our method jointly minimizes the reconstruction error for higher-order node neighborhood, social roles and edge attributes using a deep architecture that can adequately capture highly non-linear interactions. We demonstrate the efficacy of our model over existing state-of-the-art methods on a variety of real-world networks including collaboration networks, and social networks. We also observe that using edge attributes to inform network embedding yields better performance in downstream tasks such as link prediction and node classification.

The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multilayer networks, i.e., networks where each layer stands for a different type of interaction between the same set of nodes. There is today a growing interest in understanding when and why a description in terms of a multiplex network is necessary and more informative than a single-layer projection. Here we contribute to this debate by presenting a comprehensive study of correlations in multiplex networks. Correlations in node properties, especially degree-degree correlations, have been thoroughly studied in single-layer networks. Here we extend this idea to investigate and characterize correlations between the different layers of a multiplex network. Such correlations are intrinsically multiplex, and we first study them empirically by constructing and analyzing several multiplex networks from the real world. In particular, we introduce various measures to characterize correlations in the activity of the nodes and in their degree at the different layers and between activities and degrees. We show that real-world networks exhibit indeed nontrivial multiplex correlations. For instance, we find cases where two layers of the same multiplex network are positively correlated in terms of node degrees, while other two layers are negatively correlated. We then focus on constructing synthetic multiplex networks, proposing a series of models to reproduce the correlations observed empirically and/or to assess their relevance.

Efficient sampling of complex network with modified random walk strategies

This chapter presents the existing modelling frameworks for multiplex and multilayer networks. Multiplex network models are divided into growing multiplex network models and null models of multiplex networks. Growing multiplex networks are here shown to explain the main dynamical rules responsible to the emergent properties of multiplex networks, including the scale-free degree distribution, interlayer degree correlations and multilayer communities. Null models of multiplex networks are described in the context of maximum-entropy multiplex network ensembles. Randomization algorithms to test the relevant of network properties against null models are here described. Moreover, Multi-slice temporal networks Models capturing main properties of real temporal network data are presented. Finally, null models of general multilayer networks and networks of networks are characterized.

With the rapid deployment of graph neural networks (GNNs) based techniques in a wide range of applications such as link prediction, community detection, and node classification, the explainability of GNNs become an indispensable component for predictive and trustworthy decision making. To achieve this goal, some recent works focus on designing explainable GNN models such as GNNExplainer, PGExplainer, and Gem. These GNN explainers have shown remarkable performance in explaining the predictive results from GNNs. Despite their success, the robustness of these explainers is less explored in terms of vulnerabilities of GNN explainers. Graph perturbations such as adversarial attacks can lead to inaccurate explanations and consequently cause catastrophes. Thus, in this paper, we take the first step and strive to explore the robustness of GNN explainers. To be specific, we first define two adversarial attack scenarios—aggressive adversary and conservative adversary to contaminate graph structures. We then investigate the impacts of the poisoned graphs on the explainability of three prevalent GNN explainers with three standard evaluation metrics: \(Fidelity^+\), \(Fidelity^-\), and Sparsity. We conduct experiments on synthetic and real-world datasets and focus on two popular graph mining tasks: node classification and graph classification. Our empirical results suggest that GNN explainers are generally not robust to the adversarial attacks caused by graph structural noises.KeywordsGraph neural networksGNN explainersAdversarial attacksRobustness

Info2vec: An aggregative representation method in multi-layer and heterogeneous networks

The establishment of new collaborations among scientists fertilizes the scientific environment, fostering novel discoveries. Understanding the dynamics driving the development of scientific collaborations is thus crucial to characterize the structure and evolution of science. In this work, we leverage the information included in publication records and reconstruct a categorical multiplex networks to improve the prediction of new scientific collaborations. Specifically, we merge different bibliographic sources to quantify the prediction potential of scientific credit, represented by citations, and common interests, measured by the usage of common keywords. We compare several link prediction algorithms based on different dyadic and triadic interactions among scientists, including a recently proposed metric that fully exploits the multiplex representation of scientific networks. Our work paves the way for a deeper understanding of the dynamics driving scientific collaborations, and validates a new algorithm that can be readily applied to link prediction in systems represented as multiplex networks.

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamic determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions Lévy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions.In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like Lévy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks.

This chapter presents the problem of link prediction in complex networks. It provides general description, formal definition of the problem and applications. It gives a state-of-art of various existing link prediction approaches concentrating more on topological approaches. It presents the main challenges of link prediction task in real networks. There is description of our new link prediction approach based on supervised rank aggregation and our attempts to deal with two of the challenges to improve the prediction results. One approach is to extend the set of attributes describing an example (pair of nodes) calculated in a multiplex network that includes the target network. Multiplex networks have a layered structure, each layer having different kinds of links between same sets of nodes. The second way is to use community information for sampling of examples to deal with the problem of class imbalance. All experiments have been conducted on real networks extracted from well-known DBLP bibliographic database.

Recent researches on multiview learning have received widespread attention due to the increasing generalization of multiview data. As an effective probabilistic model, random walk has also shown encouraging performance in various fields. To further exploit the potential of utilizing random walk schemes to address multiview learning problems, this article proposes a simple yet efficient multigraph random walk scheme for both multiview clustering and semisupervised classification tasks. The proposed model integrates random walk with multiview learning, and recursively learns a globally stable probability distribution matrix from multiple views, on the basis of which the label indicator is obtained in the scene of clustering or semisupervised classification. Furthermore, an adaptive weight vector is learned to incorporate the diversity and complementarity of multiview data. Besides, the relationships between the proposed scheme and spectral clustering, neighborhood embedding and manifold embedding are analyzed theoretically. Finally, comprehensive comparative experiments are conducted with several state-of-the-art multiview clustering and semisupervised classification methods on eight real-world datasets. The experimental results demonstrate the superiority of the proposed method in terms of both clustering and classification performance.

Network Representation Learning (NRL), which aims to embed nodes into a latent, low-dimensional vector space while preserving some network properties, facilitates the network analysis tasks. The goal of most NRL methods is to make similar nodes represented similarly in the embedding space. Many methods adopt the skip-gram model to achieve such goal by maximizing the predictive probability among the context nodes for each center node. The context nodes are usually determined based on the concept of \textit{proximity} which is defined based on some explicit network features. However, these proximities may result in a loss of training samples and have limited discriminative power. We propose a general and unified generative adversarial learning framework to address the problems. The proposed framework can handle almost all kinds of networks in a unified way, including homogeneous plain networks, attribute augmented networks and heterogeneous networks. It can improve the performances of the most of the state-of-the-art skip-gram based NRL methods. Moreover, another unified and general NRL method is extended from the framework. It can learn the network representation independently. Extensive experiments on proximity preserving evaluation and two network analysis tasks, i.e., link prediction and node classifications, demonstrate the superiority and versatility of our framework.