In this paper we address the problem of modeling relational data, which appear in many applications such as social network analysis, recommender systems and bioinformatics. Previous studies either consider latent feature based models but disregarding local structure in the network, or focus exclusively on capturing local structure of objects based on latent blockmodels without coupling with latent characteristics of objects. To combine the benefits of the previous work, we propose a novel model that can simultaneously incorporate the effect of latent features and covariates if any, as well as the effect of latent structure that may exist in the data. To achieve this, we model the relation graph as a function of both latent feature factors and latent cluster memberships of objects to collectively discover globally predictive intrinsic properties of objects and capture latent block structure in the network to improve prediction performance. We also develop an optimization transfer algorithm based on the generalized EM-style strategy to learn the latent factors. We prove the efficacy of our proposed model through the link prediction task and cluster analysis task, and extensive experiments on the synthetic data and several real world datasets suggest that our proposed LFBM model outperforms the other state of the art approaches in the evaluated tasks.
: The latent structure based models provide building latent blocks for complex networks and allow us to understand and predict unknown interactions between network nodes. For example, stochastic blockmodels @cite_8 adopt mixture models for relational data. In this model, each node is sampled from a cluster based on a multinomial distribution. To allow a node belonging to multiple groups, @cite_4 developed mixed membership stochastic blockmodels, which use a latent Dirichlet allocation prior to model latent membership variables. in @cite_15 proposed the Predictive Discrete Latent Factor (PDLF) model to predict large scale dyadic response variables. The model simultaneously incorporates the effect of covariates and estimates local structure that is induced by interactions among the dyads through a discrete latent factor model. There is also similar work in @cite_12 . Another related research is the relational clustering. @cite_6 and @cite_13 has proposed a general model for relational clustering based on symmetric convex coding.
@cite_4 @cite_8 @cite_6 @cite_15 @cite_13 @cite_12
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We consider the statistical analysis of a collection of unipartite graphs, i.e., multiple matrices of relations among objects of a single type. Such data arise, for example, in biological settings, collections of author-recipient email, and social networks. In many applications, clustering the objects of study or situating them in a low dimensional space (e.g., a simplex) is only one of the goals of the analysis. Begin able to estimate relational structures among the clusters themselves is often times as important. For example, in biological applications we are interested in estimating how stable protein complexes (i.e., clusters of proteins) interact. To support such integrated data analyses, we develop the family of “stochastic block models of mixed membership”. Our models combine features of mixed-membership models (Erosheva & Fienberg, 2005) and block models for relational data (, 1983) in a hierarchical Bayesian framework. We develop a novel “nested” variational inference scheme, which is necessary to successfully perform fast approximate posterior inference in our models of relational data. We present evidence to support our claims, using both synthetic data and biological case study. Relational data appear frequently in many machine learning applications. Relational data consist of the pairwise relations (similarities or dissimilarities) between each pair of implicit objects, and are usually stored in relation matrices and typically no other knowledge is available. Although relational clustering can be formulated as graph partitioning in some applications, this formulation is not adequate for general relational data. In this paper, we propose a general model for relational clustering based on symmetric convex coding. The model is applicable to all types of relational data and unifies the existing graph partitioning formulation. Under this model, we derive two alternative bound optimization algorithms to solve the symmetric convex coding under two popular distance functions, Euclidean distance and generalized I-divergence. Experimental evaluation and theoretical analysis show the effectiveness and great potential of the proposed model and algorithms. We propose a novel statistical method to predict large scale dyadic response variables in the presence of covariate information. Our approach simultaneously incorporates the effect of covariates and estimates local structure that is induced by interactions among the dyads through a discrete latent factor model. The discovered latent factors provide a redictive model that is both accurate and interpretable. We illustrate our method by working in a framework of generalized linear models, which include commonly used regression techniques like linear regression, logistic regression and Poisson regression as special cases. We also provide scalable generalized EM-based algorithms for model fitting using both "hard" and "soft" cluster assignments. We demonstrate the generality and efficacy of our approach through large scale simulation studies and analysis of datasets obtained from certain real-world movie recommendation and internet advertising applications. Relational clustering has attracted more and more attention due to its phenomenal impact in various important applications which involve multi-type interrelated data objects, such as Web mining, search marketing, bioinformatics, citation analysis, and epidemiology. In this paper, we propose a probabilistic model for relational clustering, which also provides a principal framework to unify various important clustering tasks including traditional attributes-based clustering, semi-supervised clustering, co-clustering and graph clustering. The proposed model seeks to identify cluster structures for each type of data objects and interaction patterns between different types of objects. Under this model, we propose parametric hard and soft relational clustering algorithms under a large number of exponential family distributions. The algorithms are applicable to relational data of various structures and at the same time unifies a number of stat-of-the-art clustering algorithms: co-clustering algorithms, the k-partite graph clustering, Bregman k-means, and semi-supervised clustering based on hidden Markov random fields. We consider the problem of learning probabilistic models for complex relational structures between various types of objects. A model can help us "understand" a dataset of relational facts in at least two ways, by finding interpretable structure in the data, and by supporting predictions, or inferences about whether particular unobserved relations are likely to be true. Often there is a tradeoff between these two aims: cluster-based models yield more easily interpretable representations, while factorization-based approaches have given better predictive performance on large data sets. We introduce the Bayesian Clustered Tensor Factorization (BCTF) model, which embeds a factorized representation of relations in a nonparametric Bayesian clustering framework. Inference is fully Bayesian but scales well to large data sets. The model simultaneously discovers interpretable clusters and yields predictive performance that matches or beats previous probabilistic models for relational data.