Prediction of Links and Weights in Networks by Reliable Routes

Examining Supervised Machine Learning Methods for Integer Link Weight Prediction Using Node Metadata

With the goal of understanding if the information contained in node metadata can help in the task of link weight prediction, we investigate herein whether incorporating it as a similarity feature (referred to as metadata similarity) between end nodes of a link improves the prediction accuracy of common supervised machine learning methods. In contrast with previous works, instead of normalizing the link weights, we treat them as count variables representing the number of interactions between end nodes, as this is a natural representation for many datasets in the literature. In this preliminary study, we find no significant evidence that metadata similarity improved the prediction accuracy of the four empirical datasets studied. To further explore the role of node metadata in weight prediction, we synthesized weights to analyze the extreme case where the weights depend solely on the metadata of the end nodes, while encoding different relationships between them using logical operators in the generation process. Under these conditions, the random forest method performed significantly better than other methods in 99.07% of cases, though the prediction accuracy was significantly degraded for the methods analyzed in comparison to the experiments with the original weights.

A Novel Multilayer Model for Link Prediction in Online Social Networks Based on Reliable Paths

Link Prediction (LP) is one of the critical problems in Online Social Networks (OSNs) analysis. LP is a technique for predicting forthcoming or missing links based on current information in the OSN. Typically, modelling an OSN platform is done in a single-layer scheme. However, this is a limitation which might lead to incorrect descriptions of some real-world details. To overcome this limitation, this paper presents a multilayer model of OSN for the LP problem by analysing Twitter and Foursquare networks. LP in multilayer networks involves performing LP on a target layer benefitting from the structural information of the other layers. Here, a novel criterion is proposed, which calculates the similarity between users by forming intralayer and interlayer links in a two-layer network (i.e. Twitter and Foursquare). Particularly, LP in the Foursquare layer is done by considering the two-layer structural information. In this paper, according to the available information from the Twitter and Foursquare OSNs, a weighted graph is created and then various topological features are extracted from it. Based on the extracted features, a database with two classes of link existence and no link has been created, and therefore the problem of LP has become a two-class classification problem that can be solved by supervised learning methods. To prove the better performance of the proposed method, Katz and FriendLink indices as well as SEM-Path algorithm have been used for comparison. Evaluations results show that the proposed method can predict new links with better precision.

Link Weight Prediction Using Weight Perturbation and Latent Factor

Link weight prediction is an important subject in network science and machine learning. Its applications to social network analysis, network modeling, and bioinformatics are ubiquitous. Although this subject has attracted considerable attention recently, the performance and interpretability of existing prediction models have not been well balanced. This article focuses on an unsupervised mixed strategy for link weight prediction. Here, the target attribute is the link weight, which represents the correlation or strength of the interaction between a pair of nodes. The input of the model is the weighted adjacency matrix without any preprocessing, as widely adopted in the existing models. Extensive observations on a large number of networks show that the new scheme is competitive to the state-of-the-art algorithms concerning both root-mean-square error and Pearson correlation coefficient metrics. Analytic and simulation results suggest that combining the weight consistency of the network and the link weight-associated latent factors of the nodes is a very effective way to solve the link weight prediction problem.

Progresses and challenges in link prediction

Link prediction is a paradigmatic problem in network science, which aims at estimating the existence likelihoods of nonobserved links, based on known topology. After a brief introduction of the standard problem and evaluation metrics of link prediction, this review will summarize representative progresses about local similarity indices, link predictability, network embedding, matrix completion, ensemble learning, and some others, mainly extracted from related publications in the last decade. Finally, this review will outline some long-standing challenges for future studies.

Path-based extensions of local link prediction methods for complex networks

Link prediction in a complex network is a problem of fundamental interest in network science and has attracted increasing attention in recent years. It aims to predict missing (or future) links between two entities in a complex system that are not already connected. Among existing methods, local similarity indices are most popular that take into account the information of common neighbours to estimate the likelihood of existence of a connection between two nodes. In this paper, we propose global and quasi-local extensions of some commonly used local similarity indices. We have performed extensive numerical simulations on publicly available datasets from diverse domains demonstrating that the proposed extensions not only give superior performance, when compared to their respective local indices, but also outperform some of the current, state-of-the-art, local and global link-prediction methods.

The application of degree related clustering coefficient in estimating the link predictability and predicting missing links of networks

Though a lot of valuable algorithms of link prediction have been created, it is still difficult to improve the accuracy of link prediction for some networks. Such difficulties may be due to the intrinsic topological features of these networks. To reveal the correlation between the network topology and the link predictability, we generate a group of artificial networks by keeping some structural features of an initial seed network. Based on these artificial networks and some real networks, we find that five topological measures including clustering coefficient, structural consistency, random walk entropy, network diameter, and average path length significantly show their impact on the link predictability. Then, we define a topological score that combines these important topological features. Specifically, it is an integration of structural consistency with degree-related clustering coefficient defined in this work. This topological score exhibits high correlation with the link predictability. Finally, we propose an algorithm for link prediction based on this topological score. Our experiment on eight real networks verifies good performance of this algorithm in link prediction, which supports the reasonability of the new topological score. This work could be insightful for the study of the link predictability.

A Pólya urn approach to information filtering in complex networks

The increasing availability of data demands for techniques to filter information in large complex networks of interactions. A number of approaches have been proposed to extract network backbones by assessing the statistical significance of links against null hypotheses of random interaction. Yet, it is well known that the growth of most real-world networks is non-random, as past interactions between nodes typically increase the likelihood of further interaction. Here, we propose a filtering methodology inspired by the Pólya urn, a combinatorial model driven by a self-reinforcement mechanism, which relies on a family of null hypotheses that can be calibrated to assess which links are statistically significant with respect to a given network's own heterogeneity. We provide a full characterization of the filter, and show that it selects links based on a non-trivial interplay between their local importance and the importance of the nodes they belong to.

Link Prediction based on Quantum-Inspired Ant Colony Optimization

Incomplete or partial observations of network structures pose a serious challenge to theoretical and engineering studies of real networks. To remedy the missing links in real datasets, topology-based link prediction is introduced into the studies of various networks. Due to the complexity of network structures, the accuracy and robustness of most link prediction algorithms are not satisfying enough. In this paper, we propose a quantum-inspired ant colony optimization algorithm that integrates ant colony optimization and quantum computing to predict links in networks. Extensive experiments on both synthetic and real networks show that the accuracy and robustness of the new algorithm is competitive in respect to most of the state of the art algorithms. This result suggests that the application of intelligent optimization to link prediction is promising for boosting its accuracy and robustness.

On Graph Mining With Deep Learning: Introducing Model R for Link Weight Prediction

Deep learning has been successful in various domains including image recognition, speech recognition and natural language processing. However, the research on its application in graph mining is still in an early stage. Here we present Model R, a neural network model created to provide a deep learning approach to the link weight prediction problem. This model uses a node embedding technique that extracts node embeddings (knowledge of nodes) from the known links’ weights (relations between nodes) and uses this knowledge to predict the unknown links’ weights. We demonstrate the power of Model R through experiments and compare it with the stochastic block model and its derivatives. Model R shows that deep learning can be successfully applied to link weight prediction and it outperforms stochastic block model and its derivatives by up to 73% in terms of prediction accuracy. We analyze the node embeddings to confirm that closeness in embedding space correlates with stronger relationships as measured by the link weight. We anticipate this new approach will provide effective solutions to more graph mining tasks.

Quantifying the Effects of Topology and Weight for Link Prediction in Weighted Complex Networks

In weighted networks, both link weight and topological structure are significant characteristics for link prediction. In this study, a general framework combining null models is proposed to quantify the impact of the topology, weight correlation and statistics on link prediction in weighted networks. Three null models for topology and weight distribution of weighted networks are presented. All the links of the original network can be divided into strong and weak ties. We can use null models to verify the strong effect of weak or strong ties. For two important statistics, we construct two null models to measure their impacts on link prediction. In our experiments, the proposed method is applied to seven empirical networks, which demonstrates that this model is universal and the impact of the topology and weight distribution of these networks in link prediction can be quantified by it. We find that in the USAir, the Celegans, the Gemo, the Lesmis and the CatCortex, the strong ties are easier to predict, but there are a few networks whose weak edges can be predicted more easily, such as the Netscience and the CScientists. It is also found that the weak ties contribute more to link prediction in the USAir, the NetScience and the CScientists, that is, the strong effect of weak ties exists in these networks. The framework we proposed is versatile, which is not only used to link prediction but also applicable to other directions in complex networks.

Predicting potential drug-drug interactions on topological and semantic similarity features using statistical learning

Drug-drug interaction (DDI) is a change in the effect of a drug when patient takes another drug. Characterizing DDIs is extremely important to avoid potential adverse drug reactions. We represent DDIs as a complex network in which nodes refer to drugs and links refer to their potential interactions. Recently, the problem of link prediction has attracted much consideration in scientific community. We represent the process of link prediction as a binary classification task on networks of potential DDIs. We use link prediction techniques for predicting unknown interactions between drugs in five arbitrary chosen large-scale DDI databases, namely DrugBank, KEGG, NDF-RT, SemMedDB, and Twosides. We estimated the performance of link prediction using a series of experiments on DDI networks. We performed link prediction using unsupervised and supervised approach including classification tree, k-nearest neighbors, support vector machine, random forest, and gradient boosting machine classifiers based on topological and semantic similarity features. Supervised approach clearly outperforms unsupervised approach. The Twosides network gained the best prediction performance regarding the area under the precision-recall curve (0.93 for both random forests and gradient boosting machine). The applied methodology can be used as a tool to help researchers to identify potential DDIs. The supervised link prediction approach proved to be promising for potential DDIs prediction and may facilitate the identification of potential DDIs in clinical research.

Refine gene functional similarity network based on interaction networks

BACKGROUND

In recent years, biological interaction networks have become the basis of some essential study and achieved success in many applications. Some typical networks such as protein-protein interaction networks have already been investigated systematically. However, little work has been available for the construction of gene functional similarity networks so far. In this research, we will try to build a high reliable gene functional similarity network to promote its further application.

RESULTS

Here, we propose a novel method to construct and refine the gene functional similarity network. It mainly contains three steps. First, we establish an integrated gene functional similarity networks based on different functional similarity calculation methods. Then, we construct a referenced gene-gene association network based on the protein-protein interaction networks. At last, we refine the spurious edges in the integrated gene functional similarity network with the help of the referenced gene-gene association network. Experiment results indicate that the refined gene functional similarity network (RGFSN) exhibits a scale-free, small world and modular architecture, with its degrees fit best to power law distribution. In addition, we conduct protein complex prediction experiment for human based on RGFSN and achieve an outstanding result, which implies it has high reliability and wide application significance.

CONCLUSIONS

Our efforts are insightful for constructing and refining gene functional similarity networks, which can be applied to build other high quality biological networks.

Link prediction on Twitter

With over 300 million active users, Twitter is among the largest online news and social networking services in existence today. Open access to information on Twitter makes it a valuable source of data for research on social interactions, sentiment analysis, content diffusion, link prediction, and the dynamics behind human collective behaviour in general. Here we use Twitter data to construct co-occurrence language networks based on hashtags and based on all the words in tweets, and we use these networks to study link prediction by means of different methods and evaluation metrics. In addition to using five known methods, we propose two effective weighted similarity measures, and we compare the obtained outcomes in dependence on the selected semantic context of topics on Twitter. We find that hashtag networks yield to a large degree equal results as all-word networks, thus supporting the claim that hashtags alone robustly capture the semantic context of tweets, and as such are useful and suitable for studying the content and categorization. We also introduce ranking diagrams as an efficient tool for the comparison of the performance of different link prediction algorithms across multiple datasets. Our research indicates that successful link prediction algorithms work well in correctly foretelling highly probable links even if the information about a network structure is incomplete, and they do so even if the semantic context is rationalized to hashtags.

Temporally Factorized Network Modeling for Evolutionary Network Analysis

The problem of evolutionary network analysis has gained increasing attention in recent years, because of an increasing number of networks, which are encountered in temporal settings. For example, social networks, communication networks, and information networks continuously evolve over time, and it is desirable to learn interesting trends about how the network structure evolves over time, and in terms of other interesting trends. One challenging aspect of networks is that they are inherently resistant to parametric modeling, which allows us to truly express the edges in the network as functions of time. This is because, unlike multidimensional data, the edges in the network reflect interactions among nodes, and it is difficult to independently model the edge as a function of time, without taking into account its correlations and interactions with neighboring edges. Fortunately, we show that it is indeed possible to achieve this goal with the use of a matrix factorization, in which the entries are parameterized by time. This approach allows us to represent the edge structure of the network purely as a function of time, and predict the evolution of the network over time. This opens the possibility of using the approach for a wide variety of temporal network analysis problems, such as predicting future trends in structures, predicting links, and node-centric anomaly/event detection. This flexibility is because of the general way in which the approach allows us to express the structure of the network as a function of time. We present a number of experimental results on a number of temporal data sets showing the effectiveness of the approach.

A new two-stage method for revealing missing parts of edges in protein-protein interaction networks

With the increasing availability of high-throughput data, various computational methods have recently been developed for understanding the cell through protein-protein interaction (PPI) networks at a systems level. However, due to the incompleteness of the original PPI networks those efforts have been significantly hindered. In this paper, we propose a two stage method to predict underlying links between two originally unlinked protein pairs. First, we measure gene expression and gene functional similarly between unlinked protein pairs on Saccharomyces cerevisiae benchmark network and obtain new constructed networks. Then, we select the significant part of the new predicted links by analyzing the difference between essential proteins that have been identified based on the new constructed networks and the original network. Furthermore, we validate the performance of the new method by using the reliable and comprehensive PPI dataset obtained from the STRING database and compare the new proposed method with four other random walk-based methods. Comparing the results indicates that the new proposed strategy performs well in predicting underlying links. This study provides a general paradigm for predicting new interactions between protein pairs and offers new insights into identifying essential proteins.

Mutual information model for link prediction in heterogeneous complex networks

Recently, a number of meta-path based similarity indices like PathSim, HeteSim, and random walk have been proposed for link prediction in heterogeneous complex networks. However, these indices suffer from two major drawbacks. Firstly, they are primarily dependent on the connectivity degrees of node pairs without considering the further information provided by the given meta-path. Secondly, most of them are required to use a single and usually symmetric meta-path in advance. Hence, employing a set of different meta-paths is not straightforward. To tackle with these problems, we propose a mutual information model for link prediction in heterogeneous complex networks. The proposed model, called as Meta-path based Mutual Information Index (MMI), introduces meta-path based link entropy to estimate the link likelihood and could be carried on a set of available meta-paths. This estimation measures the amount of information through the paths instead of measuring the amount of connectivity between the node pairs. The experimental results on a Bibliography network show that the MMI obtains high prediction accuracy compared with other popular similarity indices.

The integration of weighted human gene association networks based on link prediction

Background

Physical and functional interplays between genes or proteins have important biological meaning for cellular functions. Some efforts have been made to construct weighted gene association meta-networks by integrating multiple biological resources, where the weight indicates the confidence of the interaction. However, it is found that these existing human gene association networks share only quite limited overlapped interactions, suggesting their incompleteness and noise.

Results

Here we proposed a workflow to construct a weighted human gene association network using information of six existing networks, including two weighted specific PPI networks and four gene association meta-networks. We applied link prediction algorithm to predict possible missing links of the networks, cross-validation approach to refine each network and finally integrated the refined networks to get the final integrated network.

Conclusions

The common information among the refined networks increases notably, suggesting their higher reliability. Our final integrated network owns much more links than most of the original networks, meanwhile its links still keep high functional relevance. Being used as background network in a case study of disease gene prediction, the final integrated network presents good performance, implying its reliability and application significance. Our workflow could be insightful for integrating and refining existing gene association data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0398-0) contains supplementary material, which is available to authorized users.

The geometric nature of weights in real complex networks

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.

Complex networks have been conjectured to be hidden in metric spaces, which offer geometric interpretation of networks' topologies. Here the authors extend this concept to weighted networks, providing empirical evidence on the metric natures of weights, which are shown to be reproducible by a gravity model.

Weight prediction in complex networks based on neighbor set

Link weights are essential to network functionality, so weight prediction is important for understanding weighted networks given incomplete real-world data. In this work, we develop a novel method for weight prediction based on the local network structure, namely, the set of neighbors of each node. The performance of this method is validated in two cases. In the first case, some links are missing altogether along with their weights, while in the second case all links are known and weight information is missing for some links. Empirical experiments on real-world networks indicate that our method can provide accurate predictions of link weights in both cases.

Predicting missing links in complex networks based on common neighbors and distance

The algorithms based on common neighbors metric to predict missing links in complex networks are very popular, but most of these algorithms do not account for missing links between nodes with no common neighbors. It is not accurate enough to reconstruct networks by using these methods in some cases especially when between nodes have less common neighbors. We proposed in this paper a new algorithm based on common neighbors and distance to improve accuracy of link prediction. Our proposed algorithm makes remarkable effect in predicting the missing links between nodes with no common neighbors and performs better than most existing currently used methods for a variety of real-world networks without increasing complexity.

Playing the role of weak clique property in link prediction: A friend recommendation model

An important fact in studying link prediction is that the structural properties of networks have significant impacts on the performance of algorithms. Therefore, how to improve the performance of link prediction with the aid of structural properties of networks is an essential problem. By analyzing many real networks, we find a typical structural property: nodes are preferentially linked to the nodes with the weak clique structure (abbreviated as PWCS to simplify descriptions). Based on this PWCS phenomenon, we propose a local friend recommendation (FR) index to facilitate link prediction. Our experiments show that the performance of FR index is better than some famous local similarity indices, such as Common Neighbor (CN) index, Adamic-Adar (AA) index and Resource Allocation (RA) index. We then explain why PWCS can give rise to the better performance of FR index in link prediction. Finally, a mixed friend recommendation index (labelled MFR) is proposed by utilizing the PWCS phenomenon, which further improves the accuracy of link prediction.

Link Prediction in Criminal Networks: A Tool for Criminal Intelligence Analysis

The problem of link prediction has recently received increasing attention from scholars in network science. In social network analysis, one of its aims is to recover missing links, namely connections among actors which are likely to exist but have not been reported because data are incomplete or subject to various types of uncertainty. In the field of criminal investigations, problems of incomplete information are encountered almost by definition, given the obvious anti-detection strategies set up by criminals and the limited investigative resources. In this paper, we work on a specific dataset obtained from a real investigation, and we propose a strategy to identify missing links in a criminal network on the basis of the topological analysis of the links classified as marginal, i.e. removed during the investigation procedure. The main assumption is that missing links should have opposite features with respect to marginal ones. Measures of node similarity turn out to provide the best characterization in this sense. The inspection of the judicial source documents confirms that the predicted links, in most instances, do relate actors with large likelihood of co-participation in illicit activities.

Link Prediction in Weighted Networks: A Weighted Mutual Information Model

The link-prediction problem is an open issue in data mining and knowledge discovery, which attracts researchers from disparate scientific communities. A wealth of methods have been proposed to deal with this problem. Among these approaches, most are applied in unweighted networks, with only a few taking the weights of links into consideration. In this paper, we present a weighted model for undirected and weighted networks based on the mutual information of local network structures, where link weights are applied to further enhance the distinguishable extent of candidate links. Empirical experiments are conducted on four weighted networks, and results show that the proposed method can provide more accurate predictions than not only traditional unweighted indices but also typical weighted indices. Furthermore, some in-depth discussions on the effects of weak ties in link prediction as well as the potential to predict link weights are also given. This work may shed light on the design of algorithms for link prediction in weighted networks.

A Noise-Filtering Method for Link Prediction in Complex Networks

Link prediction plays an important role in both finding missing links in networked systems and complementing our understanding of the evolution of networks. Much attention from the network science community are paid to figure out how to efficiently predict the missing/future links based on the observed topology. Real-world information always contain noise, which is also the case in an observed network. This problem is rarely considered in existing methods. In this paper, we treat the existence of observed links as known information. By filtering out noises in this information, the underlying regularity of the connection information is retrieved and then used to predict missing or future links. Experiments on various empirical networks show that our method performs noticeably better than baseline algorithms.

An efficient method for link prediction in weighted multiplex networks

Background

A great variety of artificial and natural systems can be abstracted into a set of entities interacting with each other. Such abstractions can very well represent the underlying dynamics of the system when modeled as the network of vertices coupled by edges. Prediction of dynamics in these structures based on topological attribute or dependency relations is an important task. Link Prediction in such complex networks is regarded useful in almost all types of networks as it can be used to extract missing information, identify spurious interactions, and evaluate network evolving mechanisms. Various similarity and likelihood-based indices have been employed to infer different topological and relation-based information to form a link prediction algorithm. These algorithms, however, are too specific to the domain and do not encapsulate the generic nature of the real-world information. In most natural and engineered systems, the entities are linked with multiple types of associations and relations which play a factor in the dynamics of the network. It forms multiple subsystems or multiple layers of networked information. These networks are regarded as Multiplex Networks.

Methods

This work presents an approach for link prediction in Multiplex networks where the associations are learned from the multiple layers of networks for link prediction purposes. Most of the real-world networks are represented as weighted networks. Weight prediction coupled with Link Prediction can be of great use. Link scores are received using various similarity measures and used to predict weights. This work further proposes and testifies a strategy for weight prediction.

Results and Conclusions

This work successfully proposes an algorithm for Weight Prediction using Link similarity measures on multiplex networks. The predicted weights show very less deviation from their actual weights. In comparison to other indices, the proposed method has a far low error rate and outperforms them concerning the metric performance NRMSE.