Predicting missing links and identifying spurious links via likelihood analysis

Inconsistency among evaluation metrics in link prediction

Link prediction is a paradigmatic and challenging problem in network science, which aims to predict missing links, future links, and temporal links based on known topology. Along with the increasing number of link prediction algorithms, a critical yet previously ignored risk is that the evaluation metrics for algorithm performance are usually chosen at will. This paper implements extensive experiments on hundreds of real networks and 26 well-known algorithms, revealing significant inconsistency among evaluation metrics, namely different metrics probably produce remarkably different rankings of algorithms. Therefore, we conclude that any single metric cannot comprehensively or credibly evaluate algorithm performance. In terms of information content, we suggest the usage of at least two metrics: one is the area under the receiver operating characteristic curve, and the other is one of the following three candidates, say the area under the precision-recall curve, the area under the precision curve, and the normalized discounted cumulative gain. When the data are imbalanced, say the number of negative samples significantly outweighs the number of positive samples, the area under the generalized Receiver Operating Characteristic curve should also be used. In addition, as we have proved the essential equivalence of threshold-dependent metrics, if in a link prediction task, some specific thresholds are meaningful, we can consider any one threshold-dependent metric with those thresholds. This work completes a missing part in the landscape of link prediction, and provides a starting point toward a well-accepted criterion or standard to select proper evaluation metrics for link prediction.

Network-Based Methods and Their Applications in Drug Discovery

Drug discovery is time-consuming, expensive, and predominantly follows the "one drug → one target → one disease" paradigm. With the rapid development of systems biology and network pharmacology, a novel drug discovery paradigm, "multidrug → multitarget → multidisease", has emerged. This new holistic paradigm of drug discovery aligns well with the essence of networks, leading to the emergence of network-based methods in the field of drug discovery. In this Perspective, we initially introduce the concept and data sources of networks and highlight classical methodologies employed in network-based methods. Subsequently, we focus on the practical applications of network-based methods across various areas of drug discovery, such as target prediction, virtual screening, prediction of drug therapeutic effects or adverse drug events, and elucidation of molecular mechanisms. In addition, we provide representative web servers for researchers to use network-based methods in specific applications. Finally, we discuss several challenges of network-based methods and the directions for future development. In a word, network-based methods could serve as powerful tools to accelerate drug discovery.

Universality and scaling in complex networks from periods of Chinese history

Critical physical systems with large numbers of molecules can show universal and scaling behaviors. It is of interest to know whether human societies with large numbers of people can show the same behaviors. Here, we use network theory to analyze Chinese history in periods 209 BCE-23 CE and 515-618 CE) related to the Western Han-Xin Dynasty and the late Northern Wei-Sui Dynasty, respectively. Two persons are connected when they appear in the same historical event. We find that the historical networks from two periods separated about 500 years have interesting universal and scaling behaviors, and they are small-world networks; their average cluster coefficients as a function of degree are similar to the network of movie stars. In the historical networks, the persons with larger degrees prefer to connect with persons with a small degree; however, in the network of movie stars, the persons with larger degrees prefer to connect with persons with large degrees. We also find an interesting similar mechanism for the decline or collapse of historical Chinese dynasties. The collapses of the Xin dynasty (9-23 CE) and the Sui dynasty (581-618 CE) were initiated from their arrogant attitude toward neighboring states.

A Simplified Quantum Walk Model for Predicting Missing Links of Complex Networks

Prediction of missing links is an important part of many applications, such as friends' recommendations on social media, reduction of economic cost of protein functional modular mining, and implementation of accurate recommendations in the shopping platform. However, the existing algorithms for predicting missing links fall short in the accuracy and the efficiency. To ameliorate these, we propose a simplified quantum walk model whose Hilbert space dimension is only twice the number of nodes in a complex network. This property facilitates simultaneous consideration of the self-loop of each node and the common neighbour information between arbitrary pair of nodes. These effects decrease the negative effect generated by the interference effect in quantum walks while also recording the similarity between nodes and its neighbours. Consequently, the observed probability after the two-step walk is utilised to represent the score of each link as a missing link, by which extensive computations are omitted. Using the AUC index as a performance metric, the proposed model records the highest average accuracy in the prediction of missing links compared to 14 competing algorithms in nine real complex networks. Furthermore, experiments using the precision index show that our proposed model ranks in the first echelon in predicting missing links. These performances indicate the potential of our simplified quantum walk model for applications in network alignment and functional modular mining of protein-protein networks.

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.

TLP-CCC: Temporal Link Prediction Based on Collective Community and Centrality Feature Fusion

In the domain of network science, the future link between nodes is a significant problem in social network analysis. Recently, temporal network link prediction has attracted many researchers due to its valuable real-world applications. However, the methods based on network structure similarity are generally limited to static networks, and the methods based on deep neural networks often have high computational costs. This paper fully mines the network structure information and time-domain attenuation information, and proposes a novel temporal link prediction method. Firstly, the network collective influence (CI) method is used to calculate the weights of nodes and edges. Then, the graph is divided into several community subgraphs by removing the weak link. Moreover, the biased random walk method is proposed, and the embedded representation vector is obtained by the modified Skip-gram model. Finally, this paper proposes a novel temporal link prediction method named TLP-CCC, which integrates collective influence, the community walk features, and the centrality features. Experimental results on nine real dynamic network data sets show that the proposed method performs better for area under curve (AUC) evaluation compared with the classical link prediction methods.

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.

Missing link prediction and spurious link detection based on attractive force and community

With the rapid development of Internet and information technology, networks have become an important media of information diffusion in the global. In view of the increasing scale of network data, how to ensure the completeness and accuracy of the obtainable links from networks has been an urgent problem that needs to be solved. Different from most traditional link prediction methods only focus on the missing links, a novel link prediction approach is proposed in this paper to handle both the missing links and the spurious links in networks. At first, we define the attractive force for any pair of nodes to denote the strength of the relation between them. Then, all the nodes can be divided into some communities according to their degrees and the attractive force on them. Next, we define the connection probability for each pair of unconnected nodes to measure the possibility if they are connected, the missing links can be predicted by calculating and comparing the connection probabilities of all the pairs of unconnected nodes. Moreover, we define the break probability for each pair of connected nodes to measure the possibility if they are broken, the spurious links can also be detected by calculating and comparing the break probabilities of all the pairs of connected nodes. To verify the validity of the proposed approach, we conduct experiments on some real-world networks. The results show the proposed approach can achieve higher prediction accuracy and more stable performance compared with some existing methods.

Towards effective link prediction: A hybrid similarity model

Link prediction is an important research direction in complex network analysis and has drawn increasing attention from researchers in various fields. So far, a plethora of structural similarity-based methods have been proposed to solve the link prediction problem. To achieve stable performance on different networks, this paper proposes a hybrid similarity model to conduct link prediction. In the proposed model, the Grey Relation Analysis (GRA) approach is employed to integrate four carefully selected similarity indexes, which are designed according to different structural features. In addition, to adaptively estimate the weight for each index based on the observed network structures, a new weight calculation method is presented by considering the distribution of similarity scores. Due to taking separate similarity indexes into account, the proposed method is applicable to multiple different types of network. Experimental results show that the proposed method outperforms other prediction methods in terms of accuracy and stableness on 10 benchmark networks.

Similarity-based link prediction in social networks using latent relationships between the users

Social network analysis has recently attracted lots of attention among researchers due to its wide applicability in capturing social interactions. Link prediction, related to the likelihood of having a link between two nodes of the network that are not connected, is a key problem in social network analysis. Many methods have been proposed to solve the problem. Among these methods, similarity-based methods exhibit good efficiency by considering the network structure and using as a fundamental criterion the number of common neighbours between two nodes to establish structural similarity. High structural similarity may suggest that a link between two nodes is likely to appear. However, as shown in the paper, the number of common neighbours may not be always sufficient to provide comprehensive information about structural similarity between a pair of nodes. To address this, a neighbourhood vector is first specified for each node. Then, a novel measure is proposed to determine the similarity of each pair of nodes based on the number of common neighbours and correlation between the neighbourhood vectors of the nodes Experimental results, on a range of different real-world networks, suggest that the proposed method results in higher accuracy than other state-of-the-art similarity-based methods for link prediction.

EPMDA: Edge Perturbation Based Method for miRNA-Disease Association Prediction

In the recent few years, plenty of research has shown that microRNA (miRNA) is likely to be involved in the formation of many human diseases. So effectively predicting potential associations between miRNAs and diseases helps to understand the development and treatment of diseases. In this study, an edge perturbation based method is proposed for predicting potential miRNA-disease association (EPMDA). Different from the previous studies, we design an feature vector to describe each edge of a graph by structural Hamiltonian information. Moreover, the extracted features are used to train a multi-layer perception model to predict the candidate disease-miRNA associations. The experimental results on the HMDD dataset show that EPMDA achieves the AUC value of 0.9818 through 5-fold cross-validation, which improves the AUC values by approximately 3.5 percent compared to the latest method DeepMDA. For the leave-one-disease-out cross-validation, EPMDA achieves the AUC value of 0.9371, which improves the AUC values by approximately 7.4 percent compared to DeepMDA. In the case study, we verify the prediction performance of EPMDA on three human diseases. As a result, there are 42, 46, and 41 of the top 50 predicted miRNAs for these three diseases which are confirmed by the published experimental discoveries, respectively.

Link Prediction through Deep Generative Model

Inferring missing links based on the currently observed network is known as link prediction, which has tremendous real-world applications in biomedicine, e-commerce, social media, and criminal intelligence. Numerous methods have been proposed to solve the link prediction problem. Yet, many of these methods are designed for undirected networks only and based on domain-specific heuristics. Here we developed a new link prediction method based on deep generative models, which does not rely on any domain-specific heuristic and works for general undirected or directed complex networks. Our key idea is to represent the adjacency matrix of a network as an image and then learn hierarchical feature representations of the image by training a deep generative model. Those features correspond to structural patterns in the network at different scales, from small subgraphs to mesoscopic communities. When applied to various real-world networks from different domains, our method shows overall superior performance against existing methods.

•

A novel link prediction method based on deep generative models is developed

•

This method works for general undirected or directed complex networks

•

Leveraging structural patterns at different scales, this method outperforms others

The sensitivity of network statistics to incomplete electrode sampling on intracranial EEG

Network neuroscience applied to epilepsy holds promise to map pathological networks, localize seizure generators, and inform targeted interventions to control seizures. However, incomplete sampling of the epileptic brain because of sparse placement of intracranial electrodes may affect model results. In this study, we evaluate the sensitivity of several published network measures to incomplete spatial sampling and propose an algorithm using network subsampling to determine confidence in model results. We retrospectively evaluated intracranial EEG data from 28 patients implanted with grid, strip, and depth electrodes during evaluation for epilepsy surgery. We recalculated global and local network metrics after randomly and systematically removing subsets of intracranial EEG electrode contacts. We found that sensitivity to incomplete sampling varied significantly across network metrics. This sensitivity was largely independent of whether seizure onset zone contacts were targeted or spared from removal. We present an algorithm using random subsampling to compute patient-specific confidence intervals for network localizations. Our findings highlight the difference in robustness between commonly used network metrics and provide tools to assess confidence in intracranial network localization. We present these techniques as an important step toward translating personalized network models of seizures into rigorous, quantitative approaches to invasive therapy.

Missing Link Prediction using Common Neighbor and Centrality based Parameterized Algorithm

Real world complex networks are indirect representation of complex systems. They grow over time. These networks are fragmented and raucous in practice. An important concern about complex network is link prediction. Link prediction aims to determine the possibility of probable edges. The link prediction demand is often spotted in social networks for recommending new friends, and, in recommender systems for recommending new items (movies, gadgets etc) based on earlier shopping history. In this work, we propose a new link prediction algorithm namely “Common Neighbor and Centrality based Parameterized Algorithm” (CCPA) to suggest the formation of new links in complex networks. Using AUC (Area Under the receiver operating characteristic Curve) as evaluation criterion, we perform an extensive experimental evaluation of our proposed algorithm on eight real world data sets, and against eight benchmark algorithms. The results validate the improved performance of our proposed algorithm.

Relative-path-based algorithm for link prediction on complex networks using a basic similarity factor

Complex networks have found many applications in various fields. An important problem in theories of complex networks is to find factors that aid link prediction, which is needed for network reconstruction and to study network evolution mechanisms. Though current similarity-based algorithms study factors of common neighbors and local paths connecting a target node pair, they ignore factor information on paths between a node and its neighbors. Therefore, this paper first supposes that paths between nodes and neighbors provide basic similarity features. Accordingly, we propose a so-called relative-path-based method. This method utilizes factor information on paths between nodes and neighbors, besides paths between node pairs, in similarity calculation for link prediction. Furthermore, we solve the problem of determining the parameters in our algorithm as well as in other algorithms after a series of discoveries and validations. Experimental results on six disparate real networks demonstrate that the relative-path-based method can obtain greater prediction accuracy than other methods, as well as performance robustness.

Application of hyperbolic geometry in link prediction of multiplex networks

Recently multilayer networks are introduced to model real systems. In these models the individuals make connection in multiple layers. Transportation networks, biological systems and social networks are some examples of multilayer networks. There are various link prediction algorithms for single-layer networks and some of them have been recently extended to multilayer networks. In this manuscript, we propose a new link prediction algorithm for multiplex networks using two novel similarity metrics based on the hyperbolic distance of node pairs. We use the proposed methods to predict spurious and missing links in multiplex networks. Missing links are those links that may appear in the future evolution of the network, while spurious links are the existing connections that are unlikely to appear if the network is evolving normally. One may interpret spurious links as abnormal links in the network. We apply the proposed algorithm on real-world multiplex networks and the numerical simulations reveal its superiority than the state-of-the-art algorithms.

Pioneering topological methods for network-based drug-target prediction by exploiting a brain-network self-organization theory

The bipartite network representation of the drug–target interactions (DTIs) in a biosystem enhances understanding of the drugs’ multifaceted action modes, suggests therapeutic switching for approved drugs and unveils possible side effects. As experimental testing of DTIs is costly and time-consuming, computational predictors are of great aid. Here, for the first time, state-of-the-art DTI supervised predictors custom-made in network biology were compared—using standard and innovative validation frameworks—with unsupervised pure topological-based models designed for general-purpose link prediction in bipartite networks. Surprisingly, our results show that the bipartite topology alone, if adequately exploited by means of the recently proposed local-community-paradigm (LCP) theory—initially detected in brain-network topological self-organization and afterwards generalized to any complex network—is able to suggest highly reliable predictions, with comparable performance with the state-of-the-art-supervised methods that exploit additional (non-topological, for instance biochemical) DTI knowledge. Furthermore, a detailed analysis of the novel predictions revealed that each class of methods prioritizes distinct true interactions; hence, combining methodologies based on diverse principles represents a promising strategy to improve drug–target discovery. To conclude, this study promotes the power of bio-inspired computing, demonstrating that simple unsupervised rules inspired by principles of topological self-organization and adaptiveness arising during learning in living intelligent systems (like the brain) can efficiently equal perform complicated algorithms based on advanced, supervised and knowledge-based engineering.

Analysis of correlation-based biomolecular networks from different omics data by fitting stochastic block models

Background: Biological entities such as genes, promoters, mRNA, metabolites or proteins do not act alone, but in concert in their network context. Modules, i.e., groups of nodes with similar topological properties in these networks characterize important biological functions of the underlying biomolecular system. Edges in such molecular networks represent regulatory and physical interactions, and comparing them between conditions provides valuable information on differential molecular mechanisms. However, biological data is inherently noisy and network reduction techniques can propagate errors particularly to the level of edges. We aim to improve the analysis of networks of biological molecules by deriving modules together with edge relevance estimations that are based on global network characteristics. Methods: The key challenge we address here is investigating the capability of stochastic block models (SBMs) for representing and analyzing different types of biomolecular networks. Fitting them to SBMs both delivers modules of the networks and enables the derivation of edge confidence scores, and it has not yet been investigated for analyzing biomolecular networks. We apply SBM-based analysis independently to three correlation-based networks of breast cancer data originating from high-throughput measurements of different molecular layers: either transcriptomics, proteomics, or metabolomics. The networks were reduced by thresholding for correlation significance or by requirements on scale-freeness.  Results and discussion: We find that the networks are best represented by the hierarchical version of the SBM, and many of the predicted blocks have a biologically and phenotypically relevant functional annotation. The edge confidence scores are overall in concordance with the biological evidence given by the measurements. We conclude that biomolecular networks can be appropriately represented and analyzed by fitting SBMs. As the SBM-derived edge confidence scores are based on global network connectivity characteristics and potential hierarchies within the biomolecular networks are considered, they could be used as additional, integrated features in network-based data comparisons.

Analysis of correlation-based biomolecular networks from different omics data by fitting stochastic block models

Background: Biological entities such as genes, promoters, mRNA, metabolites or proteins do not act alone, but in concert in their network context. Modules, i.e., groups of nodes with similar topological properties in these networks characterize important biological functions of the underlying biomolecular system. Edges in such molecular networks represent regulatory and physical interactions, and comparing them between conditions provides valuable information on differential molecular mechanisms. However, biological data is inherently noisy and network reduction techniques can propagate errors particularly to the level of edges. We aim to improve the analysis of networks of biological molecules by deriving modules together with edge relevance estimations that are based on global network characteristics.  Methods: We propose to fit the networks to stochastic block models (SBM), a method that has not yet been investigated for the analysis of biomolecular networks. This procedure both delivers modules of the networks and enables the derivation of edge confidence scores. We apply it to correlation-based networks of breast cancer data originating from high-throughput measurements of diverse molecular layers such as transcriptomics, proteomics, and metabolomics. The networks were reduced by thresholding for correlation significance or by requirements on scale-freeness.  Results and discussion: We find that the networks are best represented by the hierarchical version of the SBM, and many of the predicted blocks have a biological meaning according to functional annotation. The edge confidence scores are overall in concordance with the biological evidence given by the measurements. As they are based on global network connectivity characteristics and potential hierarchies within the biomolecular networks are taken into account, they could be used as additional, integrated features in network-based data comparisons. Their tight relationship to edge existence probabilities can be exploited to predict missing or spurious edges in order to improve the network representation of the underlying biological system.

Brain Network Modeling Based on Mutual Information and Graph Theory for Predicting the Connection Mechanism in the Progression of Alzheimer's Disease

Alzheimer's disease (AD) is a progressive disease that causes problems of cognitive and memory functions decline. Patients with AD usually lose their ability to manage their daily life. Exploring the progression of the brain from normal controls (NC) to AD is an essential part of human research. Although connection changes have been found in the progression, the connection mechanism that drives these changes remains incompletely understood. The purpose of this study is to explore the connection changes in brain networks in the process from NC to AD, and uncovers the underlying connection mechanism that shapes the topologies of AD brain networks. In particular, we propose a mutual information brain network model (MINM) from the perspective of graph theory to achieve our aim. MINM concerns the question of estimating the connection probability between two cortical regions with the consideration of both the mutual information of their observed network topologies and their Euclidean distance in anatomical space. In addition, MINM considers establishing and deleting connections, simultaneously, during the networks modeling from the stage of NC to AD. Experiments show that MINM is sufficient to capture an impressive range of topological properties of real brain networks such as characteristic path length, network efficiency, and transitivity, and it also provides an excellent fit to the real brain networks in degree distribution compared to experiential models. Thus, we anticipate that MINM may explain the connection mechanism for the formation of the brain network organization in AD patients.

A unified framework for link prediction based on non-negative matrix factorization with coupling multivariate information

Many link prediction methods have been developed to infer unobserved links or predict missing links based on the observed network structure that is always incomplete and subject to interfering noise. Thus, the performance of existing methods is usually limited in that their computation depends only on input graph structures, and they do not consider external information. The effects of social influence and homophily suggest that both network structure and node attribute information should help to resolve the task of link prediction. This work proposes SASNMF, a link prediction unified framework based on non-negative matrix factorization that considers not only graph structure but also the internal and external auxiliary information, which refers to both the node attributes and the structural latent feature information extracted from the network. Furthermore, three different combinations of internal and external information are proposed and input into the framework to solve the link prediction problem. Extensive experimental results on thirteen real networks, five node attribute networks and eight non-attribute networks show that the proposed framework has competitive performance compared with benchmark methods and state-of-the-art methods, indicating the superiority of the presented algorithm.

Modelling Self-Organization in Complex Networks Via a Brain-Inspired Network Automata Theory Improves Link Reliability in Protein Interactomes

Protein interactomes are epitomes of incomplete and noisy networks. Methods for assessing link-reliability using exclusively topology are valuable in network biology, and their investigation facilitates the general understanding of topological mechanisms and models to draw and correct complex network connectivity. Here, I revise and extend the local-community-paradigm (LCP). Initially detected in brain-network topological self-organization and afterward generalized to any complex network, the LCP is a theory to model local-topology-dependent link-growth in complex networks using network automata. Four novel LCP-models are compared versus baseline local-topology-models. It emerges that the reliability of an interaction between two proteins is higher: (i) if their common neighbours are isolated in a complex (local-community) that has low tendency to interact with other external proteins; (ii) if they have a low propensity to link with other proteins external to the local-community. These two rules are mathematically combined in C1*: a proposed mechanistic model that, in fact, outperforms the others. This theoretical study elucidates basic topological rules behind self-organization principia of protein interactomes and offers the conceptual basis to extend this theory to any class of complex networks. The link-reliability improvement, based on the mere topology, can impact many applied domains such as systems biology and network medicine.

Network-Based Methods for Prediction of Drug-Target Interactions

Drug-target interaction (DTI) is the basis of drug discovery. However, it is time-consuming and costly to determine DTIs experimentally. Over the past decade, various computational methods were proposed to predict potential DTIs with high efficiency and low costs. These methods can be roughly divided into several categories, such as molecular docking-based, pharmacophore-based, similarity-based, machine learning-based, and network-based methods. Among them, network-based methods, which do not rely on three-dimensional structures of targets and negative samples, have shown great advantages over the others. In this article, we focused on network-based methods for DTI prediction, in particular our network-based inference (NBI) methods that were derived from recommendation algorithms. We first introduced the methodologies and evaluation of network-based methods, and then the emphasis was put on their applications in a wide range of fields, including target prediction and elucidation of molecular mechanisms of therapeutic effects or safety problems. Finally, limitations and perspectives of network-based methods were discussed. In a word, network-based methods provide alternative tools for studies in drug repurposing, new drug discovery, systems pharmacology and systems toxicology.

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.

Validation of a smartphone app to map social networks of proximity

Social network analysis is a prominent approach to investigate interpersonal relationships. Most studies use self-report data to quantify the connections between participants and construct social networks. In recent years smartphones have been used as an alternative to map networks by assessing the proximity between participants based on Bluetooth and GPS data. While most studies have handed out specially programmed smartphones to study participants, we developed an application for iOS and Android to collect Bluetooth data from participants’ own smartphones. In this study, we compared the networks estimated with the smartphone app to those obtained from sociometric badges and self-report data. Participants (n = 21) installed the app on their phone and wore a sociometric badge during office hours. Proximity data was collected for 4 weeks. A contingency table revealed a significant association between proximity data (ϕ = 0.17, p<0.0001), but the marginal odds were higher for the app (8.6%) than for the badges (1.3%), indicating that dyads were more often detected by the app. We then compared the networks that were estimated using the proximity and self-report data. All three networks were significantly correlated, although the correlation with self-reported data was lower for the app (ρ = 0.25) than for badges (ρ = 0.67). The scanning rates of the app varied considerably between devices and was lower on iOS than on Android. The association between the app and the badges increased when the network was estimated between participants whose app recorded more regularly. These findings suggest that the accuracy of proximity networks can be further improved by reducing missing data and restricting the interpersonal distance at which interactions are detected.

Similarity-based Regularized Latent Feature Model for Link Prediction in Bipartite Networks

Link prediction is an attractive research topic in the field of data mining and has significant applications in improving performance of recommendation system and exploring evolving mechanisms of the complex networks. A variety of complex systems in real world should be abstractly represented as bipartite networks, in which there are two types of nodes and no links connect nodes of the same type. In this paper, we propose a framework for link prediction in bipartite networks by combining the similarity based structure and the latent feature model from a new perspective. The framework is called Similarity Regularized Nonnegative Matrix Factorization (SRNMF), which explicitly takes the local characteristics into consideration and encodes the geometrical information of the networks by constructing a similarity based matrix. We also develop an iterative scheme to solve the objective function based on gradient descent. Extensive experiments on a variety of real world bipartite networks show that the proposed framework of link prediction has a more competitive, preferable and stable performance in comparison with the state-of-art methods.

Link prediction based on non-negative matrix factorization

With the rapid expansion of internet, the complex networks has become high-dimensional, sparse and redundant. Besides, the problem of link prediction in such networks has also obatined increasingly attention from different types of domains like information science, anthropology, sociology and computer sciences. It makes requirements for effective link prediction techniques to extract the most essential and relevant information for online users in internet. Therefore, this paper attempts to put forward a link prediction algorithm based on non-negative matrix factorization. In the algorithm, we reconstruct the correlation between different types of matrix through the projection of high-dimensional vector space to a low-dimensional one, and then use the similarity between the column vectors of the weight matrix as the scoring matrix. The experiment results demonstrate that the algorithm not only reduces data storage space but also effectively makes the improvements of the prediction performance during the process of sustaining a low time complexity.

Link predication based on matrix factorization by fusion of multi class organizations of the network

Link predication aims at forecasting the latent or unobserved edges in the complex networks and has a wide range of applications in reality. Almost existing methods and models only take advantage of one class organization of the networks, which always lose important information hidden in other organizations of the network. In this paper, we propose a link predication framework which makes the best of the structure of networks in different level of organizations based on nonnegative matrix factorization, which is called NMF ³ here. We first map the observed network into another space by kernel functions, which could get the different order organizations. Then we combine the adjacency matrix of the network with one of other organizations, which makes us obtain the objective function of our framework for link predication based on the nonnegative matrix factorization. Third, we derive an iterative algorithm to optimize the objective function, which converges to a local optimum, and we propose a fast optimization strategy for large networks. Lastly, we test the proposed framework based on two kernel functions on a series of real world networks under different sizes of training set, and the experimental results show the feasibility, effectiveness, and competitiveness of the proposed framework.

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.

Can local-community-paradigm and epitopological learning enhance our understanding of how local brain connectivity is able to process, learn and memorize chronic pain?

The mystery behind the origin of the pain and the difficulty to propose methodologies for its quantitative characterization fascinated philosophers (and then scientists) from the dawn of our modern society. Nowadays, studying patterns of information flow in mesoscale activity of brain networks is a valuable strategy to offer answers in computational neuroscience. In this paper, complex network analysis was performed on the time-varying brain functional connectomes of a rat model of persistent peripheral neuropathic pain, obtained by means of local field potential and spike train analysis. A wide range of topological network measures (14 in total, the code is publicly released at: https://github.com/biomedical-cybernetics/topological_measures_wide_analysis) was employed to quantitatively investigate the rewiring mechanisms of the brain regions responsible for development and upkeep of pain along time, from three hours to 16 days after nerve injury. The time trend (across the days) of each network measure was correlated with a behavioural test for rat pain, and surprisingly we found that the rewiring mechanisms associated with two local topological measure, the local-community-paradigm and the power-lawness, showed very high statistical correlations (higher than 0.9, being the maximum value 1) with the behavioural test. We also disclosed clear functional connectivity patterns that emerged in association with chronic pain in the primary somatosensory cortex (S1) and ventral posterolateral (VPL) nuclei of thalamus. This study represents a pioneering attempt to exploit network science models in order to elucidate the mechanisms of brain region re-wiring and engram formations that are associated with chronic pain in mammalians. We conclude that the local-community-paradigm is a model of complex network organization that triggers a local learning rule, which seems associated to processing, learning and memorization of chronic pain in the brain functional connectivity. This rule is based exclusively on the network topology, hence was named epitopological learning.

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.