The automated analysis of social networks has become an important problem due to the proliferation of social networks, such as LiveJournal, Flickr and Facebook. The scale of these social networks is massive and continues to grow rapidly. An important problem in social network analysis is proximity estimation that infers the closeness of different users. Link prediction, in turn, is an important application of proximity estimation. However, many methods for computing proximity measures have high computational complexity and are thus prohibitive for large-scale link prediction problems. One way to address this problem is to estimate proximity measures via low-rank approximation. However, a single low-rank approximation may not be sufficient to represent the behavior of the entire network. In this paper, we propose Multi-Scale Link Prediction (MSLP), a framework for link prediction, which can handle massive networks. The basis idea of MSLP is to construct low rank approximations of the network at multiple scales in an efficient manner. Based on this approach, MSLP combines predictions at multiple scales to make robust and accurate predictions. Experimental results on real-life datasets with more than a million nodes show the superior performance and scalability of our method.
Efficient proximity estimation is essential for scalable link prediction. However, one should be able to make accurate and robust predictions with the estimated measures. For example, @cite_0 @cite_9 explore the low rank approximation of social networks to speed up large-scale link prediction. Another way to improve the link prediction performance is to explore the community structure of a network. For example, LinkBoost @cite_5 explores the community structure by a novel degree dependent cost function and shows that minimization of the associated risk can lead to more links predicted within communities than between communities. However, considering a single community structure may not lead to robust predictions, because even detecting the best' community structure itself is still an open question.
@cite_0 @cite_5 @cite_9
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Link prediction is a challenging task due to the inherent skew ness of network data. Typical link prediction methods can be categorized as either local or global. Local methods consider the link structure in the immediate neighborhood of a node pair to determine the presence or absence of a link, whereas global methods utilize information from the whole network. This paper presents a community (cluster) level link prediction method without the need to explicitly identify the communities in a network. Specifically, a variable-cost loss function is defined to address the data skew ness problem. We provide theoretical proof that shows the equivalence between maximizing the well-known modularity measure used in community detection and minimizing a special case of the proposed loss function. As a result, any link prediction method designed to optimize the loss function would result in more links being predicted within a community than between communities. We design a boosting algorithm to minimize the loss function and present an approach to scale-up the algorithm by decomposing the network into smaller partitions and aggregating the weak learners constructed from each partition. Experimental results show that our proposed Link Boost algorithm consistently performs as good as or better than many existing methods when evaluated on 4 real-world network datasets. In this work, we address the problem of joint modeling of text and citations in the topic modeling framework. We present two different models called the Pairwise-Link-LDA and the Link-PLSA-LDA models. The Pairwise-Link-LDA model combines the ideas of LDA [4] and Mixed Membership Block Stochastic Models [1] and allows modeling arbitrary link structure. However, the model is computationally expensive, since it involves modeling the presence or absence of a citation (link) between every pair of documents. The second model solves this problem by assuming that the link structure is a bipartite graph. As the name indicates, Link-PLSA-LDA model combines the LDA and PLSA models into a single graphical model. Our experiments on a subset of Citeseer data show that both these models are able to predict unseen data better than the baseline model of Erosheva and Lafferty [8], by capturing the notion of topical similarity between the contents of the cited and citing documents. Our experiments on two different data sets on the link prediction task show that the Link-PLSA-LDA model performs the best on the citation prediction task, while also remaining highly scalable. In addition, we also present some interesting visualizations generated by each of the models. We investigate an unsupervised generative approach for network embedding. A multi-task Siamese neural network structure is formulated to connect embedding vectors and our objective to preserve the global node ranking and local proximity of nodes. We provide deeper analysis to connect the proposed proximity objective to link prediction and community detection in the network. We show our model can satisfy the following design properties: scalability, asymmetry, unity and simplicity. Experiment results not only verify the above design properties but also demonstrate the superior performance in learning-to-rank, classification, regression, and link prediction tasks. Proximity measures quantify the closeness or similarity between nodes in a social network and form the basis of a range of applications in social sciences, business, information technology, computer networks, and cyber security. It is challenging to estimate proximity measures in online social networks due to their massive scale (with millions of users) and dynamic nature (with hundreds of thousands of new nodes and millions of edges added daily). To address this challenge, we develop two novel methods to efficiently and accurately approximate a large family of proximity measures. We also propose a novel incremental update algorithm to enable near real-time proximity estimation in highly dynamic social networks. Evaluation based on a large amount of real data collected in five popular online social networks shows that our methods are accurate and can easily scale to networks with millions of nodes. To demonstrate the practical values of our techniques, we consider a significant application of proximity estimation: link prediction, i.e., predicting which new edges will be added in the near future based on past snapshots of a social network. Our results reveal that (i) the effectiveness of different proximity measures for link prediction varies significantly across different online social networks and depends heavily on the fraction of edges contributed by the highest degree nodes, and (ii) combining multiple proximity measures consistently yields the best link prediction accuracy. Community detection and edge prediction are both forms of link mining: they are concerned with discovering the relations between vertices in networks. Some of the vertex similarity measures used in edge prediction are closely related to the concept of community structure. We use this insight to propose a novel method for improving existing community detection algorithms by using a simple vertex similarity measure. We show that this new strategy can be more effective in detecting communities than the basic community detection algorithms. Social network analysis has attracted increasing attention in recent years. In many social networks, besides friendship links among users, the phenomenon of users associating themselves with groups or communities is common. Thus, two networks exist simultaneously: the friendship network among users, and the affiliation network between users and groups. In this article, we tackle the affiliation recommendation problem, where the task is to predict or suggest new affiliations between users and communities, given the current state of the friendship and affiliation networks. More generally, affiliations need not be community affiliations---they can be a user’s taste, so affiliation recommendation algorithms have applications beyond community recommendation. In this article, we show that information from the friendship network can indeed be fruitfully exploited in making affiliation recommendations. Using a simple way of combining these networks, we suggest two models of user-community affinity for the purpose of making affiliation recommendations: one based on graph proximity, and another using latent factors to model users and communities. We explore the affiliation recommendation algorithms suggested by these models and evaluate these algorithms on two real-world networks, Orkut and Youtube. In doing so, we motivate and propose a way of evaluating recommenders, by measuring how good the top 50 recommendations are for the average user, and demonstrate the importance of choosing the right evaluation strategy. The algorithms suggested by the graph proximity model turn out to be the most effective. We also introduce scalable versions of these algorithms, and demonstrate their effectiveness. This use of link prediction techniques for the purpose of affiliation recommendation is, to our knowledge, novel. With hundreds of millions of participants, social media services have become commonplace. Unlike a traditional social network service, a microblogging network like Twitter is a hybrid network, combining aspects of both social networks and information networks. Understanding the structure of such hybrid networks and predicting new links are important for many tasks such as friend recommendation, community detection, and modeling network growth. We note that the link prediction problem in a hybrid network is different from previously studied networks. Unlike the information networks and traditional online social networks, the structures in a hybrid network are more complicated and informative. We compare most popular and recent methods and principles for link prediction and recommendation. Finally we propose a novel structure-based personalized link prediction model and compare its predictive performance against many fundamental and popular link prediction methods on real-world data from the Twitter microblogging network. Our experiments on both static and dynamic data sets show that our methods noticeably outperform the state-of-the-art. Prediction is one of the most attractive aspects in data mining. Link prediction has recently attracted the attention of many researchers as an effective technique to be used in graph based models in general and in particular for social network analysis due to the recent popularity of the field. Link prediction helps to understand associations between nodes in social communities. Existing link prediction-related approaches described in the literature are limited to predict links that are anticipated to exist in the future. To the best of our knowledge, none of the previous works in this area has explored the prediction of links that could disappear in the future. We argue that the latter set of links are important to know about; they are at least equally important as and do complement the positive link prediction process in order to plan better for the future. In this paper, we propose a link prediction model which is capable of predicting both links that might exist and links that may disappear in the future. The model has been successfully applied in two different though very related domains, namely health care and gene expression networks. The former application concentrates on physicians and their interactions while the second application covers genes and their interactions. We have tested our model using different classifiers and the reported results are encouraging. Finally, we compare our approach with the internal links approach and we reached the conclusion that our approach performs very well in both bipartite and non-bipartite graphs. The explosive growth of social networks has created numerous exciting research opportunities. A central concept in the analysis of social networks is a proximity measure, which captures the closeness or similarity between nodes in the network. Despite much research on proximity measures, there is a lack of techniques to efficiently and accurately compute proximity measures for large-scale social networks. In this paper, we embed the original massive social graph into a much smaller graph, using a novel dimensionality reduction technique termed Clustered Spectral Graph Embedding. We show that the embedded graph captures the essential clustering and spectral structure of the original graph and allow a wide range of analysis to be performed on massive social graphs. Applying the clustered embedding to proximity measurement of social networks, we develop accurate, scalable, and flexible solutions to three important social network analysis tasks: proximity estimation, missing link inference, and link prediction. We demonstrate the effectiveness of our solutions to the tasks in the context of large real-world social network datasets: Flickr, LiveJournal, and MySpace with up to 2 million nodes and 90 million links. How does online content propagate on social networks? Billions of users generate, consume, and spread tons of information every day. This unprecedented scale of dynamics becomes invaluable to reflect our zeitgeist. However, most present diffusion extraction works have only touched individual user level and cannot obtain comprehensive clues. This paper introduces a new approach, i.e., COmmunity Level Diffusion (COLD), to uncover and explore temporal diffusion. We model topics and communities in a unified latent framework, and extract inter-community influence dynamics. With a well-designed multi-component model structure and a parallel inference implementation on GraphLab, the COLD method is expressive while remaining efficient. The extracted community level patterns enable diffusion exploration from a new perspective. We leverage the compact yet robust representations to develop new prediction and analysis applications. Extensive experiments on large social datasets show significant improvement in prediction accuracy. We can also find communities play very different roles in diffusion processes depending on their interest. Our method guarantees high scalability with increasing data size. Many datasets of interest today are best described as a linked collection of interrelated objects. These may represent homogeneous networks, in which there is a single-object type and link type, or richer, heterogeneous networks, in which there may be multiple object and link types (and possibly other semantic information). Examples of homogeneous networks include single mode social networks, such as people connected by friendship links, or the WWW, a collection of linked web pages. Examples of heterogeneous networks include those in medical domains describing patients, diseases, treatments and contacts, or in bibliographic domains describing publications, authors, and venues. Link mining refers to data mining techniques that explicitly consider these links when building predictive or descriptive models of the linked data. Commonly addressed link mining tasks include object ranking, group detection, collective classification, link prediction and subgraph discovery. While network analysis has been studied in depth in particular areas such as social network analysis, hypertext mining, and web analysis, only recently has there been a cross-fertilization of ideas among these different communities. This is an exciting, rapidly expanding area. In this article, we review some of the common emerging themes. Our understanding of how individual mobility patterns shape and impact the social network is limited, but is essential for a deeper understanding of network dynamics and evolution. This question is largely unexplored, partly due to the difficulty in obtaining large-scale society-wide data that simultaneously capture the dynamical information on individual movements and social interactions. Here we address this challenge for the first time by tracking the trajectories and communication records of 6 Million mobile phone users. We find that the similarity between two individuals' movements strongly correlates with their proximity in the social network. We further investigate how the predictive power hidden in such correlations can be exploited to address a challenging problem: which new links will develop in a social network. We show that mobility measures alone yield surprising predictive power, comparable to traditional network-based measures. Furthermore, the prediction accuracy can be significantly improved by learning a supervised classifier based on combined mobility and network measures. We believe our findings on the interplay of mobility patterns and social ties offer new perspectives on not only link prediction but also network dynamics. The effects of social influence and homophily suggest that both network structure and node-attribute information should inform the tasks of link prediction and node-attribute inference. Recently, [2010a, 2010b] proposed an attribute-augmented social network model, which we call Social-Attribute Network (SAN), to integrate network structure and node attributes to perform both link prediction and attribute inference. They focused on generalizing the random walk with a restart algorithm to the SAN framework and showed improved performance. In this article, we extend the SAN framework with several leading supervised and unsupervised link-prediction algorithms and demonstrate performance improvement for each algorithm on both link prediction and attribute inference. Moreover, we make the novel observation that attribute inference can help inform link prediction, that is, link-prediction accuracy is further improved by first inferring missing attributes. We comprehensively evaluate these algorithms and compare them with other existing algorithms using a novel, large-scale Googlep dataset, which we make publicly available (rlhttp: www.cs.berkeley.edu ∼stevgong gplus.html). The ability to predict linkages among data objects is central to many data mining tasks, such as product recommendation and social network analysis. Substantial literature has been devoted to the link prediction problem either as an implicitly embedded problem in specific applications or as a generic data mining task. This literature has mostly adopted a static graph representation where a snapshot of the network is analyzed to predict hidden or future links. However, this representation is only appropriate to investigate whether a certain link will ever occur and does not apply to many applications for which the prediction of the repeated link occurrences are of primary interest (e.g., communication network surveillance). In this paper, we introduce the time-series link prediction problem, taking into consideration temporal evolutions of link occurrences to predict link occurrence probabilities at a particular time. Using Enron e-mail data and high-energy particle physics literature coauthorship data, we have demonstrated that time-series models of single-link occurrences achieve comparable link prediction performance with commonly used static graph link prediction algorithms. Furthermore, a combination of static graph link prediction algorithms and time-series models produced significantly better predictions over static graph link prediction methods, demonstrating the great potential of integrated methods that exploit both interlink structural dependencies and intralink temporal dependencies. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled. Link prediction in protein-protein interaction networks (PPINs) is an important task in biology, since the vast majority of biological functions involve such protein interactions. Link prediction is also important for online social networks (OSNs), which provide predictions about who is a friend of whom. Many link prediction methods for PPINs OSNs are local-based and do not exploit all network structure, which limits prediction accuracy. On the other hand, there are global approaches to detect the overall path structure in a network, being computationally prohibitive for huge-size PPINs OSNs. In this paper, we enhance a previously proposed multi-way spectral clustering method by introducing new ways to capture node proximity in both PPINs OSNs. Our new enhanced method uses information obtained from the top few eigenvectors of the normalized Laplacian matrix. As a result, it produces a less noisy matrix, which is smaller and more compact than the original one. In this way, we are able to provide faster and more accurate link predictions. Moreover, our new spectral clustering model is based on the well-known Bray-Curtis coefficient to measure proximity between two nodes. Compared to traditional clustering algorithms, such as k-means and DBSCAN, which assume globular (convex) regions in Euclidean space, our approach is more flexible in capturing the non-connected components of a social graph and a wider range of cluster geometries. We perform an extensive experimental comparison of the proposed method against existing link prediction algorithms and k-means algorithm, using two synthetic data sets, three real social networks and three real human protein data sets. Our experimental results show that our SpectralLink algorithm outperforms the local approaches, the k-means algorithm and another spectral clustering method in terms of effectiveness, whereas it is more efficient than the global approaches. Many networks can be modeled as signed graphs. These include social networks, and relationships interactions networks. Detecting sub-structures in such networks helps us understand user behavior, predict links, and recommend products. In this paper, we detect dense sub-structures from a signed graph, called quasi antagonistic communities (QACs). An antagonistic community consists of two groups of users expressing positive relationships within each group but negative relationships across groups. Instead of requiring complete set of negative links across its groups, a QAC allows a small number of inter-group negative links to be missing. We propose an algorithm, Mascot, to find all maximal quasi antagonistic communities (MQACs). Mascot consists of two stages: pruning and enumeration stages. Based on the properties of QAC, we propose four pruning rules to reduce the size of candidate graphs in the pruning stage. We use an enumeration tree to enumerate all strongly connected subgraphs in a top---down fashion in the second stage before they are used to construct MQACs. We have conducted extensive experiments using synthetic signed graphs and two real networks to demonstrate the efficiency and accuracy of the Mascot algorithm. We have also found that detecting MQACs helps us to predict the signs of links. In many applications we have a social network of people and would like to identify the members of an interesting but unlabeled group or community. We start with a small number of exemplar group members -- they may be followers of a political ideology or fans of a music genre -- and need to use those examples to discover the additional members. This problem gives rise to the seed expansion problem in community detection: given example community members, how can the social graph be used to predict the identities of remaining, hidden community members? In contrast with global community detection (graph partitioning or covering), seed expansion is best suited for identifying communities locally concentrated around nodes of interest. A growing body of work has used seed expansion as a scalable means of detecting overlapping communities. Yet despite growing interest in seed expansion, there are divergent approaches in the literature and there still isn't a systematic understanding of which approaches work best in different domains. Here we evaluate several variants and uncover subtle trade-offs between different approaches. We explore which properties of the seed set can improve performance, focusing on heuristics that one can control in practice. As a consequence of this systematic understanding we have found several opportunities for performance gains. We also consider an adaptive version in which requests are made for additional membership labels of particular nodes, such as one finds in field studies of social communities. This leads to interesting connections and contrasts with active learning and the trade-offs of exploration and exploitation. Finally, we explore topological properties of communities and seed sets that correlate with algorithm performance, and explain these empirical observations with theoretical ones. We evaluate our methods across multiple domains, using publicly available datasets with labeled, ground-truth communities. Link analysis typically focuses on a single type of connection, e.g., two journal papers are linked because they are written by the same author. However, often we want to analyze data that has multiple linkages between objects, e.g., two papers may have the same keywords and one may cite the other. The goal of this paper is to show that multilinear algebra provides a tool for multilink analysis. We analyze five years of publication data from journals published by the Society for Industrial and Applied Mathematics. We explore how papers can be grouped in the context of multiple link types using a tensor to represent all the links between them. A PARAFAC decomposition on the resulting tensor yields information similar to the SVD decomposition of a standard adjacency matrix. We show how the PARAFAC decomposition can be used to understand the structure of the document space and define paper-paper similarities based on multiple linkages. Examples are presented where the decomposed tensor data is used to find papers similar to a body of work (e.g., related by topic or similar to a particular author's papers), find related authors using linkages other than explicit co-authorship or citations, distinguish between papers written bymore » different authors with the same name, and predict the journal in which a paper was published.« less