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.
Homophily and stochastic equivalence are two primary features of interest in social networks. Recently, the multiplicative latent factor model (MLFM) is proposed to model social networks with directed links. Although MLFM can capture stochastic equivalence, it cannot model well homophily in networks. However, many real-world networks exhibit homophily or both homophily and stochastic equivalence, and hence the network structure of these networks cannot be modeled well by MLFM. In this paper, we propose a novel model, called generalized latent factor model (GLFM), for social network analysis by enhancing homophily modeling in MLFM. We devise a minorization-maximization (MM) algorithm with linear-time complexity and convergence guarantee to learn the model parameters. Extensive experiments on some real-world networks show that GLFM can effectively model homophily to dramatically outperform state-of-the-art methods. In dyadic prediction, labels must be predicted for pairs (dyads) whose members possess unique identifiers and, sometimes, additional features called side-information. Special cases of this problem include collaborative filtering and link prediction. We present a new log-linear model for dyadic prediction that is the first to satisfy several important desiderata: (i) labels may be ordinal or nominal, (ii) side-information can be easily exploited if present, (iii) with or without side-information, latent features are inferred for dyad members, (iv) the model is resistant to sample-selection bias, (v) it can learn well-calibrated probabilities, and (vi) it can scale to large datasets. To our knowledge, no existing method satisfies all the above criteria. In particular, many methods assume that the labels are binary or numerical, and cannot use side-information. Experimental results show that the new method is competitive with previous specialized methods for collaborative filtering and link prediction. Other experimental results demonstrate that the new method succeeds for dyadic prediction tasks where previous methods cannot be used. In particular, the new method predicts nominal labels accurately, and by using side-information it solves the cold-start problem in collaborative filtering. We discuss a statistical model of social network data derived from matrix representations and symmetry considerations. The model can include known predictor information in the form of a regression term, and can represent additional structure via sender-specific and receiver-specific latent factors. This approach allows for the graphical description of a social network via the latent factors of the nodes, and provides a framework for the prediction of missing links in network data.