Community detection has been an active research area for decades. Among all probabilistic models, Stochastic Block Model has been the most popular one. This paper introduces a novel probabilistic model: RW-HDP, based on random walks and Hierarchical Dirichlet Process, for community extraction. In RW-HDP, random walks conducted in a social network are treated as documents; nodes are treated as words. By using Hierarchical Dirichlet Process, a nonparametric Bayesian model, we are not only able to cluster nodes into different communities, but also determine the number of communities automatically. We use Stochastic Variational Inference for our model inference, which makes our method time efficient and can be easily extended to an online learning algorithm.
Nonparametric Bayesian models are becoming popular these days due to their flexibility @cite_17 , @cite_31 and new posterior inference methods such as Variational Inference @cite_15 , @cite_6 . Teh, Jordan, Beal, and Blei @cite_5 extended the Dirichlet Process to the Hierarchical Dirichlet Process which can also be viewed as an extension of LDA model. Hoffman, Blei, Wang, and Paisley @cite_30 developed the Stochastic Variational Inference for several non-parametric Bayesian models including HDP. In social network research, Morup and Schmidt @cite_11 , @cite_7 formulated a non-parametric Bayesian community generative model for social network analysis. Kim, Gopalan, Blei, and Sudderth @cite_25 proposed the hierarchical Dirichlet process relational model which allowed nodes to have mixed membership in an unbounded set of communities. Guo and Nordman @cite_19 introduced a series of Bayesian nonparametric statistical models for community detection. Blundell and Teh @cite_14 proposed an efficient Bayesian nonparametric model for discovering hierarchical community structure in social networks.
@cite_30 @cite_11 @cite_14 @cite_7 @cite_15 @cite_6 @cite_19 @cite_5 @cite_31 @cite_25 @cite_17
2004029027 2096297741 2149021215 2166851633
We propose a series of Bayesian nonparametric statistical models for community detection in graphs. We model the probability of the presence or absence of edges within the graph. Using these models, we naturally incorporate uncertainty and variability and take advantage of nonparametric techniques, such as the Chinese restaurant process and the Dirichlet process. Some of the contributions include: (a) the community structure is directly modeled without specifying the number of communities a priori; (b) the probabilities of edges within or between communities may be modeled as varying by community or pairs of communities; (c) some nodes can be classified as not belonging to any community; and (d) Bayesian model diagnostics are used to compare models and help with appropriate model selection. We start by fitting an initial model to a well-known network dataset, and we develop a series of increasingly complex models. We propose Markov chain Monte Carlo algorithms to carry out the estimation as well as an app... We propose an efficient Bayesian nonparametric model for discovering hierarchical community structure in social networks. Our model is a tree-structured mixture of potentially exponentially many stochastic blockmodels. We describe a family of greedy agglomerative model selection algorithms that take just one pass through the data to learn a fully probabilistic, hierarchical community model. In the worst case, Our algorithms scale quadratically in the number of vertices of the network, but independent of the number of nested communities. In practice, the run time of our algorithms are two orders of magnitude faster than the Infinite Relational Model, achieving comparable or better accuracy. We propose a novel unsupervised learning framework to model activities and interactions in crowded and complicated scenes. Hierarchical Bayesian models are used to connect three elements in visual surveillance: low-level visual features, simple "atomic" activities, and interactions. Atomic activities are modeled as distributions over low-level visual features, and multi-agent interactions are modeled as distributions over atomic activities. These models are learnt in an unsupervised way. Given a long video sequence, moving pixels are clustered into different atomic activities and short video clips are clustered into different interactions. In this paper, we propose three hierarchical Bayesian models, Latent Dirichlet Allocation (LDA) mixture model, Hierarchical Dirichlet Process (HDP) mixture model, and Dual Hierarchical Dirichlet Processes (Dual-HDP) model. They advance existing language models, such as LDA [1] and HDP [2]. Our data sets are challenging video sequences from crowded traffic scenes and train station scenes with many kinds of activities co-occurring. Without tracking and human labeling effort, our framework completes many challenging visual surveillance tasks of board interest such as: (1) discovering typical atomic activities and interactions; (2) segmenting long video sequences into different interactions; (3) segmenting motions into different activities; (4) detecting abnormality; and (5) supporting high-level queries on activities and interactions. We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Using stochastic variational inference, we analyze several large collections of documents: 300K articles from Nature, 1.8M articles from The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can easily handle data sets of this size and outperforms traditional variational inference, which can only handle a smaller subset. (We also show that the Bayesian nonparametric topic model outperforms its parametric counterpart.) Stochastic variational inference lets us apply complex Bayesian models to massive data sets.