Modeling homophily and stochastic equivalence in symmetric relational data

By Peter D. Hoff. Neural Information Processing Systems, 2007

303 citations recorded by the source corpus.

This article discusses a latent variable model for inference and prediction of symmetric relational data. The model, based on the idea of the eigenvalue decomposition, represents the relationship between two nodes as the weighted inner-product of node-specific vectors of latent characteristics. This "eigenmodel" generalizes other popular latent variable models, such as latent class and distance models: It is shown mathematically that any latent class or distance model has a representation as an eigenmodel, but not vice-versa. The practical implications of this are examined in the context of three real datasets, for which the eigenmodel has as good or better out-of-sample predictive performance than the other two models.

Subfields: Artificial Intelligence, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/87ba290234c3b2f23b3bba5d85f4c82ea50cf275

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Citations in the corpus

Semantic Proximity Search on Heterogeneous Graph by Proximity Embedding (2017, background): “Similarly, latent eigenmodel (Hoff 2008) also looks for a latent vector for each node in network modeling.”
Discovering Latent Network Structure in Point Process Data (2014, methodology): “A rich literature has arisen in recent years for applying statistical machine learning models to this type of problem, e.g., Liben-Nowell & Kleinberg (2007); Hoﬀ (2008); Goldenberg et al. (2010).”
Link Prediction via Matrix Factorization (2011, unknown): “This underpins the approaches of [24,16,15,23].”
A Survey of Statistical Network Models (2009, background): “Hoff [145] provides a nice comparison, both theoretical and empirical, of these two types of models with the eigenmodel.”
Generalized Latent Factor Models for Social Network Analysis (2011, methodology): “In this paper, we focus on latent variable models [Bartholomew and Knott, 1999] which have been successfully applied to model social networks [Hoff, 2008; Nowicki and Snijders, 2001; Hoff et al., 2002; Kemp et al., 2006; Airoldi et al., 2008; Hoff, 2009].”
Pseudo-likelihood methods for community detection in large sparse networks (2012, background): “These include the popular stochastic block model [20], its extensions to include varying degree distributions within communities [22] and overlapping communities [2, 4], and various latent variable models [17, 19].”
Consistency of community detection in networks under degree-corrected stochastic block models (2011, methodology): “Other models include a recently introduced degree-corrected stochastic block model [20], mixture models for directed networks [27], multivariate latent variable models [16], latent feature models [17] and mixed membership stochastic block models for modeling overlapping communities [2].”
LRBM: A Restricted Boltzmann Machine Based Approach for Representation Learning on Linked Data (2014, methodology): “In other models such as the latent eigen model [12] and the latent feature relational model [13], [14], Ψ(μi, μj) is defined as Ψ(μi, μj) = μi Wμj , where W is a parameter matrix subsuming the interacting patterns between node i and node j.”
FAST COMMUNITY DETECTION BY SCORE (2012, background): “A problem that is of major interest is “network community detection” [7, 8, 9, 14, 22, 23, 24, 25, 32, 33].”
Dropout Training of Matrix Factorization and Autoencoder for Link Prediction in Sparse Graphs (2015, background): “non-cohesive distinction of graph structure has previously been investigated in [29, 9].”