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18
Multiplicative Attribute Graph Model of Real-World Networks
, 1009
"... Large scale real-world network data, such as social networks, Internet and Web graphs, are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, especially in social networks, nodes have a rich set ..."
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Cited by 46 (4 self)
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Large scale real-world network data, such as social networks, Internet and Web graphs, are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, especially in social networks, nodes have a rich set of attributes (e.g., age, gender) associated with them. However, many existing network models focus on modeling the network structure while ignoring the features of the nodes. Here we present a model that we refer to as the Multiplicative Attribute Graphs (MAG), which naturally captures the interactions between the network structure and node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes then depends on the product of individual attribute-attribute similarities. This model yields itself to mathematical analysis and we derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to graphs with a constant diameter. We analyze the degree distribution to show that the model can produce networks with either log-normal or power-law degree distribution depending on certain conditions. 1
An Infinite Latent Attribute Model for Network Data
- In Proceedings of the International Conference on Machine Learning (ICML
, 2012
"... Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes then depends only on their cluster assignment. Currently av ..."
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Cited by 27 (7 self)
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Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes then depends only on their cluster assignment. Currently available models can be classified by whether clusters are disjoint or are allowed to overlap. These models can explain a “flat ” clustering structure. Hierarchical Bayesian models provide a natural approach to capture more complex dependencies. We propose a model in which objects are characterised by a latent feature vector. Each feature is itself partitioned into disjoint groups (subclusters), corresponding to a second layer of hierarchy. In experimental comparisons, the model achieves significantly improved predictive performance on social and biological link prediction tasks. The results indicate that models with a single layer hierarchy over-simplify real networks. 1.
Scalable Inference of Overlapping Communities
"... We develop a scalable algorithm for posterior inference of overlapping communities in large networks. Our algorithm is based on stochastic variational inference in the mixed-membership stochastic blockmodel (MMSB). It naturally interleaves subsampling the network with estimating its community struct ..."
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Cited by 22 (4 self)
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We develop a scalable algorithm for posterior inference of overlapping communities in large networks. Our algorithm is based on stochastic variational inference in the mixed-membership stochastic blockmodel (MMSB). It naturally interleaves subsampling the network with estimating its community structure. We apply our algorithm on ten large, real-world networks with up to 60,000 nodes. It converges several orders of magnitude faster than the state-of-the-art algorithm for MMSB, finds hundreds of communities in large real-world networks, and detects the true communities in 280 benchmark networks with equal or better accuracy compared to other scalable algorithms. 1
Latent multi-group membership graph model
"... We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as the node feature structure. The LMMG can be used to summarize ..."
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Cited by 15 (3 self)
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We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as the node feature structure. The LMMG can be used to summarize the network structure, to predict links between the nodes, and to pre-dict missing features of a node. We derive effi-cient inference and learning algorithms and eval-uate the predictive performance of the LMMG on several social and document network datasets. 1.
Jointly Predicting Links and Inferring Attributes using a Social-Attribute Network (SAN)
, 1112
"... 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, Yin et al. [28, 29] proposed Social-Attribute Network (SAN), an attribute-augmented social network, to i ..."
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Cited by 15 (7 self)
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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, Yin et al. [28, 29] proposed Social-Attribute Network (SAN), an attribute-augmented social network, to integrate network structure and node attributes to perform both link prediction and attribute inference. They focused on generalizing the random walk with restart algorithm to the SAN framework and showed improved performance. In this paper, 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, i.e., 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, largescale Google+ dataset, which we make publicly available 1.
Testing and Modeling Dependencies Between a Network and Nodal Attributes
, 2013
"... Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by modeling the attributes as a function of the network. These met ..."
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Cited by 6 (1 self)
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Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by modeling the attributes as a function of the network. These methods require specification of the exact nature of the association between the network and attributes, reduce the network data to a small number of summary statistics, and are unable provide predictions simultaneously for missing attribute and network information. Existing methods that model the attributes and network jointly also assume the data are fully observed. In this article we introduce a unified approach to analysis that addresses these shortcomings. We use a latent variable model to obtain a low dimensional representation of the network in terms of node-specific network factors and use a test of dependence between the network factors and attributes as a surrogate for a test of dependence between the network and attributes. We propose a formal testing procedure to determine if dependencies exists between the network factors and attributes. We also introduce a joint model for the network and attributes, for use if the test rejects, that can capture a variety of dependence patterns and be used to make inference and predictions for missing observations.
Nonparametric Multi-group Membership Model for Dynamic Networks
"... Relational data—like graphs, networks, and matrices—is often dynamic, where the relational struc-ture evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entitie ..."
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Cited by 4 (0 self)
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Relational data—like graphs, networks, and matrices—is often dynamic, where the relational struc-ture evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on the intuition that changes in the network structure are driven by the dy-namics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components: We model the birth and death of individual groups with respect to the dynamics of the network structure via a distance dependent In-dian Buffet Process. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model. And, we explain the dynamics of the network structure by explicitly mod-eling the connectivity structure of groups. We demonstrate our model’s capability of identifying the dynamics of latent groups in a number of different types of network data. Experimental results show that our model provides improved predictive performance over existing dynamic network models on future network forecasting and missing link prediction. 1
0 Joint Link Prediction and Attribute Inference using a Social-Attribute Network
"... 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, Yin et al. [Yin et al. 2010a; 2010b] proposed an attribute-augmented social network model, which we call ..."
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Cited by 3 (1 self)
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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, Yin et al. [Yin et al. 2010a; 2010b] proposed an attribute-augmented social network model, which we call as 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 restart algorithm to the SAN framework and showed improved performance. In this paper, 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, i.e., link prediction accuracy is further improved by first inferring missing attributes. We comprehensively evaluate these algorithms and compare them with
Ranking Networks
"... Latent space models for network formation assume that nodes possess latent attributes that determine their propensity to connect. We propose a new model for network formation, ranking networks, in which these attributes are rankings over some space of alternatives. Such rankings may reflect user pre ..."
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Cited by 2 (2 self)
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Latent space models for network formation assume that nodes possess latent attributes that determine their propensity to connect. We propose a new model for network formation, ranking networks, in which these attributes are rankings over some space of alternatives. Such rankings may reflect user preferences, relevance/quality judgements, etc., while ranking networks capture correlations of, say, user preferences across a social network. We present preliminary theoretical and empirical analyses of structural properties of such networks, and develop algorithmic approximations to help efficiently predict these properties. Empirical results demonstrate the quality of these approximations. 1
Quilting Stochastic Kronecker Product Graphs to Generate Multiplicative Attribute Graphs
"... We describe the first sub-quadratic sampling algorithm for the Multiplicative Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close connection between MAGM and the Kronecker Product Graph Model (KPGM) of Leskovec et al. (2010), and show that to sample a graph from a MAGM it s ..."
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Cited by 1 (0 self)
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We describe the first sub-quadratic sampling algorithm for the Multiplicative Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close connection between MAGM and the Kronecker Product Graph Model (KPGM) of Leskovec et al. (2010), and show that to sample a graph from a MAGM it suffices to sample small number of KPGM graphs and quilt them together. Under a restricted set of technical conditions our algorithm runs in O (log 2(n)) 3 |E | time, where n is the number of nodes and |E | is the number of edges in the sampled graph. We demonstrate the scalability of our algorithm via extensive empirical evaluation; we can sample a MAGM graph with 8 million nodes and 20 billion edges in under 6 hours. 1
