Adversarial Robustness of Probabilistic Network Embedding for Link Prediction

Network embedding aims to learn distributed vector representations of nodes in a network. The problem of network embedding is fundamentally important. It plays crucial roles in many applications, such as node classification, link prediction, and so on. As the real-world networks are often sparse with few observed links, many recent works have utilized the local and global network structure proximity with shallow models for better network embedding. In reality, each node is usually associated with rich attributes. Some attributed network embedding models leveraged the node attributes in these shallow network embedding models to alleviate the data sparsity issue. Nevertheless, the underlying structure of the network is complex. What is more, the connection between the network structure and node attributes is also hidden. Thus, these previous shallow models fail to capture the nonlinear deep information embedded in the attributed network, resulting in the suboptimal embedding results. In this paper, we propose a deep attributed network embedding framework to capture the complex structure and attribute information. Specifically, we first adopt a personalized random walk-based model to capture the interaction between network structure and node attributes from various degrees of proximity. After that, we construct an enhanced matrix representation of the attributed network by summarizing the various degrees of proximity. Then, we design a deep neural network to exploit the nonlinear complex information in the enhanced matrix for network embedding. Thus, the proposed framework could capture the complex attributed network structure by preserving both the various degrees of network structure and node attributes in a unified framework. Finally, empirical experiments show the effectiveness of our proposed framework on a variety of network embedding-based tasks.

Interactomes such as Protein interaction networks have many undiscovered links between entities. Experimental verification of every link in these networks is prohibitively expensive, and therefore computational methods to direct the search for possible links are of great value. The problem of finding undiscovered links in a network is also referred to as the link prediction problem. A popular approach for link prediction has been to formulate it as a binary classification problem in which class labels indicate the existence or absence of a link (we refer to these as positive links or negative links respectively) between a pair of nodes in the network. Researchers have successfully applied such supervised classification techniques to determine the presence of links in protein interaction networks. However, it is quite common for protein-protein interaction (PPI) networks to have a large proportion of undiscovered links. Thus, a link prediction approach could incorrectly treat undiscovered positive links as negative links, thereby introducing a bias in the learning. In this paper, we propose to denoise the class of negative links in the training data via a Gaussian process anomaly detector. We show that this significantly reduces the noise due to mislabelled negative links and improves the resulting link prediction accuracy. We evaluate the approach by introducing synthetic noise into the PPI networks and measuring how accurately we can reconstruct the original PPI networks using classifiers trained on both noisy and denoised data. Experiments were performed with five different PPI network datasets and the results indicate a significant reduction in bias due to label noise, and more importantly, a significant improvement in the accuracy of detecting missing links via classification.

Link prediction aims to find the missing link in current networks or estimate the likelihood the link will appear in the future. In many real-world scenarios, networks can be massive and drastically evolving. Many recent works concentrated on how to solve the procession of massive data, which cares less about the effects of the temporal information. In some dynamic networks, the edge that appears a long time ago will have fewer effects on the appearance of edges in the future. The accuracy of link prediction in dynamic networks can be further improved by adding temporal information in prediction measures. In this paper, we mainly explore the effects of the link temporal information in the graph stream link prediction. We design a graph stream-based framework to solve link prediction problems in dynamic networks which can provide a convenient platform to implement different link prediction methods for dynamic networks, and evaluate these methods on a fair basis. Then, we proposed the Time Decay-based Link Prediction (TDLP) method to improve the efficient of link prediction problem in the dynamic networks. TDLP extends the neighborhood-based measure with time decay functions in graph stream scenarios which can handle temporal information and massive data. Experiment results demonstrate that the accuracy of link prediction for dynamic networks can be efficiently improved in our TDLP method.

The link prediction problem is a time-evolving model in network science that has simultaneously abetted myriad applications and experienced extensive methodological improvement. Inferring the possibility of emerging links in dynamic social networks, also known as the dynamic link prediction task, is complex and challenging. In contrast to the link prediction in cross-sectional networks, dynamic link prediction methods need to cater to the actor-level temporal changes and associated evolutionary information regarding their micro- (i.e., link formation/deletion) and mesoscale (i.e., community formation) network structure. With the advent of abundant community detection algorithms, the research community has examined community-aware link prediction strategies in static networks. However, the same task in dynamic networks where, apart from the actors and links among them, their community pattern is also dynamic, is yet to be explored. Evolutionary community-aware information, including the associated link structure and temporal neighborhood changes, can effectively be mined to build dynamic similarity metrics for dynamic link prediction. This study aims to develop and integrate such dynamic features with machine learning algorithms for link prediction tasks in dynamic social networks. It also compares the performances of these features against well-known similarity metrics (i.e., ResourceAllocation) for static networks and a time series-based link prediction strategy in dynamic networks. These proposed features achieved high-performance scores, representing them as prospective candidates for both dynamic link prediction tasks and modeling the network growth.

Community preserving adaptive graph convolutional networks for link prediction in attributed networks

Real-world graphs are dynamic, constantly evolving with new interactions, such as financial transactions in financial networks. Temporal Graph Neural Networks (TGNNs) have been developed to effectively capture the evolving patterns in dynamic graphs. While these models have demonstrated their superiority, being widely adopted in various important fields, their vulnerabilities against adversarial attacks remain largely unexplored. In this paper, we propose T-SPEAR, a simple and effective adversarial attack method for link prediction on continuous-time dynamic graphs, focusing on investigating the vulnerabilities of TGNNs. Specifically, before the training procedure of a victim model, which is a TGNN for link prediction, we inject edge perturbations to the data that are unnoticeable in terms of the four constraints we propose, and yet effective enough to cause malfunction of the victim model. Moreover, we propose a robust training approach T-SHIELD to mitigate the impact of adversarial attacks. By using edge filtering and enforcing temporal smoothness to node embeddings, we enhance the robustness of the victim model. Our experimental study shows that T-SPEAR significantly degrades the victim model's performance on link prediction tasks, and even more, our attacks are transferable to other TGNNs, which differ from the victim model assumed by the attacker. Moreover, we demonstrate that T-SHIELD effectively filters out adversarial edges and exhibits robustness against adversarial attacks, surpassing the link prediction performance of the naive TGNN by up to 11.2% under T-SPEAR. The code and datasets are available at https://github.com/wooner49/T-spear-shield

Networks have been widely used as the data structure for abstracting real-world systems as well as organizing the relations among entities. Network embedding models are powerful tools in mapping nodes in a network into continuous vector-space representations in order to facilitate subsequent tasks such as classification and link prediction. Existing network embedding models comprehensively integrate all information of each node, such as links and attributes, towards a single embedding vector to represent the node's general role in the network. However, a real-world entity could be multifaceted, where it connects to different neighborhoods due to different motives or self-characteristics that are not necessarily correlated. For example, in a movie recommender system, a user may love comedies or horror movies simultaneously, but it is not likely that these two types of movies are mutually close in the embedding space, nor the user embedding vector could be sufficiently close to them at the same time. In this paper, we propose a polysemous embedding approach for modeling multiple facets of nodes, as motivated by the phenomenon of word polysemy in language modeling. Each facet of a node is mapped as an embedding vector, while we also maintain association degree between each pair of node and facet. The proposed method is adaptive to various existing embedding models, without significantly complicating the optimization process. We also discuss how to engage embedding vectors of different facets for inference tasks including classification and link prediction. Experiments on real-world datasets help comprehensively evaluate the performance of the proposed method.

Improving embedding-based link prediction performance using clustering

Link prediction is one of hot research topics in social network analysis. Link prediction problem is to find a small set of node pairs in the networks that are not directly connected, but will be very likely to be connected in the future. To improve the prediction accuracy, many works have attempted to consider the community information, if available, in the social network structure. One common strategy of the prior community-aware link prediction algorithms is that they devised a sort of unified link prediction formulation that simply includes a premium term to express whether a link is structurally in the same community or not. However, since the formulation of the premium term relies on the structural formation of communities only, it cannot take into account the fact that the communities in different social networks, though they form almost identical community structures, can make different levels of influence on the link prediction. To cope with this limitation, we propose an adaptive approach, in which we use two separate link predictions depending on inter or intra links in community, and then balance the links based on the degree of community influence on link prediction. In the meantime, we provide a set of experimental results to show how much the proposed approach is effective.

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

The rapid development of heterogeneous networks has proposed new challenges to the long-standing link prediction problem. Existing models trained on the verified edge samples from different types usually learn type-specific knowledge, and their type-specific predictions may be contradictory for unverified edge samples with uncertain types. This challenge is termed edge-type disturbance in link prediction in heterogeneous networks. To address this challenge, we develop a disturbance-resilient prediction method ( DRPM ) comprising a structural characterizer, a type differentiator, and a resilient predictor. The structural characterizer is responsible for learning edge representations for link prediction. Concurrently, the type differentiator distinguishes type-specific edge representations to generate diverse type experts while maximizing their link prediction performances on specific types. Furthermore, the resilient predictor evaluates the reliability weights of different type experts to develop a resilient prediction mechanism to aggregate discriminable predictions. Extensive experiments conducted on various real-world datasets demonstrate the importance of the explainable introduction of the edge-type disturbance and the superiority of DRPM over state-of-the-art methods.

Network embedding which aims to embed a given network into a low-dimensional vector space has been proved effective in various network analysis and mining tasks such as node classification, link prediction and network visualization. The emerging network embedding methods have shifted of emphasis in utilizing mature deep learning models. The neural-network based network embedding has become a mainstream solution because of its high efficiency and capability of preserving the nonlinear characteristics of the network. In this paper, we propose Adversarial Network Embedding using Structural Similarity (ANESS), a novel, versatile, low-complexity GAN-based network embedding model which utilizes the inherent vertex-to-vertex structural similarity attribute of the network. ANESS learns robustness and effective vertex embeddings via a adversarial training procedure. Specifically, our method aims to exploit the strengths of generative adversarial networks in generating high-quality samples and utilize the structural similarity identity of vertexes to learn the latent representations of a network. Meanwhile, ANESS can dynamically update the strategy of generating samples during each training iteration. The extensive experiments have been conducted on the several benchmark network datasets, and empirical results demonstrate that ANESS significantly outperforms other state-of-the-art network embedding methods.

We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. With the advances of deep learning, current link prediction methods commonly compute features from subgraphs centered at two neighboring nodes and use the features to predict the label of the link between these two nodes. In this formalism, a link prediction problem is converted to a graph classification task. In order to extract fixed-size features for classification, graph pooling layers are necessary in the deep learning model, thereby incurring information loss. To overcome this key limitation, we propose to seek a radically different and novel path by making use of the line graphs in graph theory. In particular, each node in a line graph corresponds to a unique edge in the original graph. Therefore, link prediction problems in the original graph can be equivalently solved as a node classification problem in its corresponding line graph, instead of a graph classification task. Experimental results on fourteen datasets from different applications demonstrate that our proposed method consistently outperforms the state-of-the-art methods, while it has fewer parameters and high training efficiency.

Link prediction problem in social networks has received significant interest in the recent past from the researchers in diverse fields. Understanding and analyzing the present links in the social network or any complex networks either to understand their evolution or to predict the future possible links from the existing network (or links) forms the interesting link prediction problem. Link prediction based on Firefly optimization algorithm is proposed in this paper for social networks. The proposed algorithm is executed on a logical graph similar to social network and tested over real networks taking the benchmark data sets. Experimental values are compared with the other methods existing in the literature. From the comparison we can see that the proposed method performs better in terms of precision over the other methods.

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.