In recent years, the amount of user-generated opinionated texts (e.g., reviews, user comments) continues to grow at a rapid speed: featured news stories on a major event easily attract thousands of user comments on a popular online News service. How to consume subjective information of this volume becomes an interesting and important research question. In contrast to previous work on review analysis that tried to filter or summarize information for a generic average user, we explore a different direction of enabling personalized recommendation of such information. For each user, our task is to rank the comments associated with a given article according to personalized user preference (i.e., whether the user is likely to like or dislike the comment). To this end, we propose a factor model that incorporates rater-comment and rater-author interactions simultaneously in a principled way. Our full model significantly outperforms strong baselines as well as related models that have been considered in previous work. 1

averaging and dimension selection for the singular value decomposition

A new model of random graphs, the random dot product graph (RDPG) is described. This model is well suited to social networks, since it defines the edges in the graph in terms of a vector of “attributes”. The edge probabilities are modeled as the dot product of vectors associated with the vertices. A small set of distinct vectors is used, allowing the automatic grouping of vertices according to their attributes. We discuss various issues of model fitting and model selection for the reduced vector set version of the RDPG. We extend the basic model to model time series of graphs, and illustrate the model through application to a time series of graphs defined by the alliances between nation states.

Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. The matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that includes linear and quadratic terms, and arises as a posterior distribution in a latent factor model for network and graph data. This article describes a Gibbs sampling algorithm for generating approximate samples from this distribution, and illustrates its use in the analysis of a protein-protein interaction network.

Social network data are typically characterized by a set of binary link variables yi,j measured on pairs a set of objects or nodes. The presence of a link from i to j is expressed as yi,j = 1, and the absence of such a link by yi,j = 0. The situation in which it is not known whether or not there is a link from i to j is denoted as yi,j = NA, indicating the information about the relationship from i to

latent space representation of overdispersed relative propensity in “How many X’s do you know? ” data

Abstract. This paper discusses the use of spatial graph models for the analysis of networks that do not have a direct spatial reality, such as web graphs, on-line social networks, or citation graphs. In a spatial graph model, nodes are embedded in a metric space, and link formation depends on the relative position of nodes in the space. It is argued that spatial models form a good basis for link mining: assuming a spatial model, the link information can be used to infer the spatial position of the nodes, and this information can then be used for clustering and recognition of node similarity. This paper gives a survey of spatial graph models, and discusses their suitability for link mining. 1

This paper discusses work on graphs defined in terms of alliances between countries. Scan statistics are used to investigate years in which there are an unusual number of agreements, not just between one country and its allies, but amongst the allies themselves. This is related to work on email ``chatter' ' discussed in Priebe et al. (2005). The scan statistic detects unusually high (or low) values for a graph invariant within a local region of the graph (an induced subgraph). Thus, without a priori knowledge of where in the graph the detection might occur, we seek to detect a region of the graph that is very different from the other regions. We will use a particular graph invariant, the size, or number of edges in the graph, to help detect interesting changes in the alliance graphs that we investigate. We will be more precise below, but the idea is as follows: A detection at scale 0 corresponds to a single country making an unusually large number of alliances; a detection at scale 1 corresponds to a country and its allies making a large number of alliances among themselves. This can be a measure of the cohesiveness of the group; a detection at scale 2 (and higher) corresponds to a larger spreading of the alliances. It means that not only are there more alliances among the countries allied with the central country, but among their allies there are more alliances. This paper seeks to perform two tasks: the first is to introduce scan statistics to those in the social network community not familiar with this work; the second is to determine whether, in the case of interstate alliances, there are any interesting detections at scales above 0. We will demonstrate that sometimes this type of behavior is interesting.

We present a unified approach to modelling dyadic relational data, namely that seen in social, biological and technological networks, without restriction to the binary format. The approach involves three principles: considering the marginal specification of any edge as the fundamental unit, embedding as much dependence as possible in latent structural forms, and using distributional forms that favour high-throughput computational methods for their solution. We show that this approach allows for an extremely flexible and generalizable way of describing the structural properties of relational systems; namely, we offer alternate explanations for two approaches popular in the networks literature, the “small-world” and “scale-free ” mechanisms, and demonstrate the ability of marginal hierarchical modelling to expand beyond them. 1

The focus of this paper is an approach to the modeling of longitudinal social network or relational data. Such data arise from measurements on pairs of objects or actors made at regular temporal intervals, resulting in a social network for each point in time. In this article we represent the network and temporal dependencies with a random effects model, resulting in a stochastic process defined by a set of stationary covariance matrices. Our approach builds upon the social relations models of Warner, Kenny and Stoto [Journal of Personality and Social Psychology 37 (1979) 1742–1757] and Gill and Swartz [Canad. J. Statist. 29 (2001) 321–331] and allows for an intra- and inter-temporal representation of network structures. We apply the methodology to two longitudinal data sets: international trade (continuous response) and militarized interstate disputes (binary response).