Networks extracted from social media platforms frequently include multiple types of links that dynamically change over time; these links can be used to represent dyadic interactions such as economic transactions, communications, and shared activities. Organizing this data into a dynamic multiplex network, where each layer is composed of a single edge type linking the same underlying vertices, can reveal interesting cross-layer interaction patterns. In coevolving networks, links in one layer result in an increased probability of other types of links forming between the same node pair. Hence we believe that a holistic approach in which all the layers are simultaneously considered can outperform a factored approach in which link prediction is performed separately in each layer. This paper introduces a comprehensive framework, MLP (Multilayer Link Prediction), in which link existence likelihoods for the target layer are learned from the other network layers. These likelihoods are used to reweight the output of a single layer link prediction method that uses rank aggregation to combine a set of topological metrics. Our experiments show that our reweighting procedure outperforms other methods for fusing information across network layers.
A variety of computational approaches have been employed for predicting links in single layer networks, including supervised classifiers, statistical relational learning, matrix factorization, metric learning, and probabilistic graphical models (see surveys by @cite_3 @cite_25 @cite_16 for a more comprehensive description). Regardless of the computational framework, topological network measures are commonly used as features to describe node pairs and can be combined in a supervised or unsupervised fashion to do link prediction. @cite_1 . In this paper, we aggregate several of these metrics (listed in the next section), but our framework can be easily generalized to include other types of features.
@cite_16 @cite_1 @cite_25 @cite_3
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Many important real-world systems, modeled naturally as complex networks, have heterogeneous interactions and complicated dependency structures. Link prediction in such networks must model the influences between heterogenous relationships and distinguish the formation mechanisms of each link type, a task which is beyond the simple topological features commonly used to score potential links. In this paper, we introduce a novel probabilistically weighted extension of the Adamic Adar measure for heterogenous information networks, which we use to demonstrate the potential benefits of diverse evidence, particularly in cases where homogeneous relationships are very sparse. However, we also expose some fundamental flaws of traditional unsupervised link prediction. We develop supervised learning approaches for relationship (link) prediction in multi-relational networks, and demonstrate that a supervised approach to link prediction can enhance performance. We present results on three diverse, real-world heterogeneous information networks and discuss the trends and tradeoffs of supervised and unsupervised link prediction in a multi-relational setting. Feedforward multilayer networks trained by supervised learning have recently demonstrated state of the art performance on image labeling problems such as boundary prediction and scene parsing. As even very low error rates can limit practical usage of such systems, methods that perform closer to human accuracy remain desirable. In this work, we propose a new type of network with the following properties that address what we hypothesize to be limiting aspects of existing methods: (1) a wide' structure with thousands of features, (2) a large field of view, (3) recursive iterations that exploit statistical dependencies in label space, and (4) a parallelizable architecture that can be trained in a fraction of the time compared to benchmark multilayer convolutional networks. For the specific image labeling problem of boundary prediction, we also introduce a novel example weighting algorithm that improves segmentation accuracy. Experiments in the challenging domain of connectomic reconstruction of neural circuity from 3d electron microscopy data show that these "Deep And Wide Multiscale Recursive" (DAWMR) networks lead to new levels of image labeling performance. The highest performing architecture has twelve layers, interwoven supervised and unsupervised stages, and uses an input field of view of 157,464 voxels ( @math ) to make a prediction at each image location. We present an associated open source software package that enables the simple and flexible creation of DAWMR networks. We propose to solve the link prediction problem in graphs using a supervised matrix factorization approach. The model learns latent features from the topological structure of a (possibly directed) graph, and is shown to make better predictions than popular unsupervised scores. We show how these latent features may be combined with optional explicit features for nodes or edges, which yields better performance than using either type of feature exclusively. Finally, we propose a novel approach to address the class imbalance problem which is common in link prediction by directly optimizing for a ranking loss. Our model is optimized with stochastic gradient descent and scales to large graphs. Results on several datasets show the efficacy of our approach. With the development of deep learning, supervised learning has frequently been adopted to classify remotely sensed images using convolutional networks. However, due to the limited amount of labeled data available, supervised learning is often difficult to carry out. Therefore, we proposed an unsupervised model called multiple-layer feature-matching generative adversarial networks (MARTA GANs) to learn a representation using only unlabeled data. MARTA GANs consists of both a generative model @math and a discriminative model @math . We treat @math as a feature extractor. To fit the complex properties of remote sensing data, we use a fusion layer to merge the mid-level and global features. @math can produce numerous images that are similar to the training data; therefore, @math can learn better representations of remotely sensed images using the training data provided by @math . The classification results on two widely used remote sensing image databases show that the proposed method significantly improves the classification performance compared with other state-of-the-art methods. This paper examines important factors for link prediction in networks and provides a general, high-performance framework for the prediction task. Link prediction in sparse networks presents a significant challenge due to the inherent disproportion of links that can form to links that do form. Previous research has typically approached this as an unsupervised problem. While this is not the first work to explore supervised learning, many factors significant in influencing and guiding classification remain unexplored. In this paper, we consider these factors by first motivating the use of a supervised framework through a careful investigation of issues such as network observational period, generality of existing methods, variance reduction, topological causes and degrees of imbalance, and sampling approaches. We also present an effective flow-based predicting algorithm, offer formal bounds on imbalance in sparse network link prediction, and employ an evaluation method appropriate for the observed imbalance. Our careful consideration of the above issues ultimately leads to a completely general framework that outperforms unsupervised link prediction methods by more than 30 AUC. The problem of predicting links or interactions between objects in a network, is an important task in network analysis. Along this line, link prediction between co-authors in a co-author network is a frequently studied problem. In most of these studies, authors are considered in a homogeneous network, .e., only one type of objects(author type) and one type of links (co-authorship) exist in the network. However, in a real bibliographic network, there are multiple types of objects ( .g., venues, topics, papers) and multiple types of links among these objects. In this paper, we study the problem of co-author relationship prediction in the heterogeneous bibliographic network, and a new methodology called, .e., meta path-based relationship prediction model, is proposed to solve this problem. First, meta path-based topological features are systematically extracted from the network. Then, a supervised model is used to learn the best weights associated with different topological features in deciding the co-author relationships. We present experiments on a real bibliographic network, the DBLP network, which show that metapath-based heterogeneous topological features can generate more accurate prediction results as compared to homogeneous topological features. In addition, the level of significance of each topological feature can be learned from the model, which is helpful in understanding the mechanism behind the relationship building. Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Although this problem has been extensively studied, the challenge of how to effectively combine the information from the network structure with rich node and edge attribute data remains largely open. We develop an algorithm based on Supervised Random Walks that naturally combines the information from the network structure with node and edge level attributes. We achieve this by using these attributes to guide a random walk on the graph. We formulate a supervised learning task where the goal is to learn a function that assigns strengths to edges in the network such that a random walker is more likely to visit the nodes to which new links will be created in the future. We develop an efficient training algorithm to directly learn the edge strength estimation function. Our experiments on the Facebook social graph and large collaboration networks show that our approach outperforms state-of-the-art unsupervised approaches as well as approaches that are based on feature extraction. Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Although this problem has been extensively studied, the challenge of how to effectively combine the information from the network structure with rich node and edge attribute data remains largely open. We develop an algorithm based on Supervised Random Walks that naturally combines the information from the network structure with node and edge level attributes. We achieve this by using these attributes to guide a random walk on the graph. We formulate a supervised learning task where the goal is to learn a function that assigns strengths to edges in the network such that a random walker is more likely to visit the nodes to which new links will be created in the future. We develop an efficient training algorithm to directly learn the edge strength estimation function. Our experiments on the Facebook social graph and large collaboration networks show that our approach outperforms state-of-the-art unsupervised approaches as well as approaches that are based on feature extraction. One of the core tasks in social network analysis is to predict the formation of links (i.e. various types of relationships) over time. Previous research has generally represented the social network in the form of a graph and has leveraged topological and semantic measures of similarity between two nodes to evaluate the probability of link formation. Here we introduce a novel local probabilistic graphical model method that can scale to large graphs to estimate the joint co-occurrence probability of two nodes. Such a probability measure captures information that is not captured by either topological measures or measures of semantic similarity, which are the dominant measures used for link prediction. We demonstrate the effectiveness of the co-occurrence probability feature by using it both in isolation and in combination with other topological and semantic features for predicting co-authorship collaborations on real datasets. Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying a new formulation in deep networks. Three aspects in convolutional neural networks (CNN) style architectures are being looked at: (1) transparency of the intermediate layers to the overall classification; (2) discriminativeness and robustness of learned features, especially in the early layers; (3) effectiveness in training due to the presence of the exploding and vanishing gradients. We introduce "companion objective" to the individual hidden layers, in addition to the overall objective at the output layer (a different strategy to layer-wise pre-training). We extend techniques from stochastic gradient methods to analyze our algorithm. The advantage of our method is evident and our experimental result on benchmark datasets shows significant performance gain over existing methods (e.g. all state-of-the-art results on MNIST, CIFAR-10, CIFAR-100, and SVHN). Many interesting domains in machine learning can be viewed as networks, with relationships (e.g., friendships) connecting items (e.g., individuals). The Active Exploration (AE) task is to identify all items in a network with a desired trait (i.e., positive labels) given only partial information about the network. The AE process iteratively queries for labels or network structure within a limited budget; thus, accurate predictions prior to making each query is critical to maximizing the number of positives gathered. However, the targeted AE query process produces partially observed networks that can create difficulties for predictive modeling. In particular, we demonstrate that these partial networks can exhibit extreme label correlation bias, which makes it difficult for conventional relational learning methods to accurately estimate relational parameters. To overcome this issue, we model the joint distribution of possible edges and labels to improve learning and inference. Our proposed method, Probabilistic Relational Expectation Maximization (PR-EM), is the first AE approach to accurately learn the complex dependencies between attributes, labels, and structure to improve predictions. PR-EM utilizes collective inference over the missing relationships in the partial network to jointly infer unknown item traits. Further, we develop a linear inference algorithm to facilitate efficient use of PR-EM in large networks. We test our approach on four real world networks, showing that AE with PR-EM gathers significantly more positive items compared to state-of-the-art methods. Graph clustering has been widely applied in exploring regularities emerging in relational data. Recently, the rapid development of network theory correlates graph clustering with the detection of community structure, a common and important topological characteristic of networks. Most existing methods investigate the community structure at a single topological scale. However, as shown by empirical studies, the community structure of real world networks often exhibits multiple topological descriptions, corresponding to the clustering at different resolutions. Furthermore, the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree. It is very challenging to detect multiscale community structure in heterogeneous networks. In this paper, we propose a novel, unified framework for detecting community structure from the perspective of dimensionality reduction. Based on the framework, we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction. We then propose a novel method to detect communities at multiple topological scales within our framework. We further show that existing algorithms fail to deal with heterogeneous node degrees. We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework. Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks. Learning low-dimensional representations of networks has proved effective in a variety of tasks such as node classification, link prediction and network visualization. Existing methods can effectively encode different structural properties into the representations, such as neighborhood connectivity patterns, global structural role similarities and other high-order proximities. However, except for objectives to capture network structural properties, most of them suffer from lack of additional constraints for enhancing the robustness of representations. In this paper, we aim to exploit the strengths of generative adversarial networks in capturing latent features, and investigate its contribution in learning stable and robust graph representations. Specifically, we propose an Adversarial Network Embedding (ANE) framework, which leverages the adversarial learning principle to regularize the representation learning. It consists of two components, i.e., a structure preserving component and an adversarial learning component. The former component aims to capture network structural properties, while the latter contributes to learning robust representations by matching the posterior distribution of the latent representations to given priors. As shown by the empirical results, our method is competitive with or superior to state-of-the-art approaches on benchmark network embedding tasks. This work addresses graph-based semi-supervised classification and betweenness computation in large, sparse, networks (several millions of nodes). The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal. Two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph, which would be impractical for graphs containing millions of nodes. The first approach directly computes, for each class, the sum of the similarities between the nodes to classify and the labeled nodes of the class, as suggested initially in [1,2]. Along this approach, two algorithms exploiting different state-of-the-art kernels on a graph are developed. The same strategy can also be used in order to compute a betweenness measure. The second approach works on a trellis structure built from biased random walks on the graph, extending an idea introduced in [3]. These random walks allow to define a biased bounded betweenness for the nodes of interest, defined separately for each class. All the proposed algorithms have a linear computing time in the number of edges while providing good results, and hence are applicable to large sparse networks. They are empirically validated on medium-size standard data sets and are shown to be competitive with state-of-the-art techniques. Finally, we processed a novel data set, which is made available for benchmarking, for multi-class classification in a large network: the U.S. patents citation network containing 3M nodes (of six different classes) and 38M edges. The three proposed algorithms achieve competitive results (around 85 classification rate) on this large network-they classify the unlabeled nodes within a few minutes on a standard workstation. We propose a simple discrete time semi-supervised graph embedding approach to link prediction in dynamic networks. The learned embedding reflects information from both the temporal and cross-sectional network structures, which is performed by defining the loss function as a weighted sum of the supervised loss from past dynamics and the unsupervised loss of predicting the neighborhood context in the current network. Our model is also capable of learning different embeddings for both formation and dissolution dynamics. These key aspects contributes to the predictive performance of our model and we provide experiments with three real--world dynamic networks showing that our method is comparable to state of the art methods in link formation prediction and outperforms state of the art baseline methods in link dissolution prediction. Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database. Topological properties of networks are widely applied to study the link-prediction problem recently. Common Neighbors, for example, is a natural yet efficient framework. Many variants of Common Neighbors have been thus proposed to further boost the discriminative resolution of candidate links. In this paper, we reexamine the role of network topology in predicting missing links from the perspective of information theory, and present a practical approach based on the mutual information of network structures. It not only can improve the prediction accuracy substantially, but also experiences reasonable computing complexity. Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models - which potentially limits performance. In this work we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree - which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set - however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets - deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets. Abstract As network analysis methods prevail, more metrics are applied to co-word networks to reveal hot topics in a field. However, few studies have examined the relationships among these metrics. To bridge this gap, this study explores the relationships among different ranking metrics, including one frequency-based and six network-based metrics, in order to understand the impact of network structural features on ranking themes on co-word networks. We collected bibliographic data from three disciplines from Web of Science (WoS), and generated 40 simulation networks following the preferential attachment assumption. Correlation analysis on the empirical and simulated networks shows strong relationships among the metrics. Their relationships are consistent across disciplines. The metrics can be categorized into three groups according to the strength of their correlations, where Degree Centrality, H-index, and Coreness are in one group, Betweenness Centrality, Clustering Coefficient, and frequency in another, and Weighted PageRank by itself. Regression analysis on the simulation networks reveals that network topology properties, such as connectivity, sparsity, and aggregation, influence the relationships among selected metrics. In addition, when comparing the top keywords ranked by the metrics in the three disciplines, we found the metrics exhibit different discriminative capacity. Coreness and H-index may be better suited for categorizing keywords rather than ranking keywords. Findings from this study contribute to a better understanding of the relationships among different metrics and provide guidance for using them effectively in different contexts. Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks.