Modeling homophily and stochastic equivalence in symmetric relational data

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.

• Publication year

  2007

• Venue

  Neural Information Processing Systems

• Publication date

  2007-11-07

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 0711.1146
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• METHODS AND

  2006cited by this paper
• Interaction network containing conserved and essential protein complexes in Escherichia coli

  2005cited by this paper
• A latent mixed membership model for relational data

  2005cited by this paper
• Bilinear Mixed-Effects Models for Dyadic Data

  2005influential reference
• Discovering Latent Classes in Relational Data

  2004cited by this paper
• Bilinear Mixed Eects Models for Dyadic Data

  2003cited by this paper
• Latent Space Approaches to Social Network Analysis

  2002cited by this paper
• Estimation and Prediction for Stochastic Blockstructures

  2001cited by this paper
• Social Network Analysis: Methods and Applications

  1994cited by this paper
• École d'été de probabilités de Saint-Flour XIII - 1983

  1985cited by this paper
• Exchangeability and related topics

  1985cited by this paper

• Balanced Stochastic Block Model for Community Detection in Signed Networks

  2026cites this paper
• Network Model Averaging Prediction for Latent Space Models by K-Fold Edge Cross-Validation

  2025cites this paper
• Covariate-assisted graph matching

  2025cites this paper
• Adaptive Bayesian Joint Latent Space Modeling via Cumulative Shrinkage

  2025cites this paper
• Local Information for Global Network Estimation in Latent Space Models

  2025cites this paper
• Latent space-based network analysis for brain–behavior linking in neuroimaging

  2025cites this paper
• Spherical latent space models for social network analysis

  2025cites this paper
• LOBSTUR: A Local Bootstrap Framework for Tuning Unsupervised Representations in Graph Neural Networks

  2025cites this paper
• Community detection in heterogeneous signed networks

  2025cites this paper
• Tensor State Space-based Dynamic Multilayer Network Modeling

  2025cites this paper
• Network analysis of multivariate time series data in biological systems: methods and applications

  2025cites this paper
• How Low Can You Go? Searching for the Intrinsic Dimensionality of Complex Networks using Metric Node Embeddings

  2025influential citation
• The Deep Latent Position Block Model for Block Clustering and Latent Representation of Nodes in Networks

  2025cites this paper
• Bayesian Sociality Models: A Scalable and Flexible Alternative for Network Analysis

  2025influential citation
• Self-Organizing Models of Brain Wiring: Developmental Programs for Evolving Intelligence

  2025cites this paper
• Euclidean Ideal Point Estimation From Roll-Call Data via Distance-Based Bipartite Network Models

  2025cites this paper
• Stochastic gradient variational Bayes in the stochastic blockmodel

  2025cites this paper
• Hybrid Bayesian Models for Community Detection with Application to a Colombian Conflict Network

  2025influential citation
• Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings

  2024cites this paper
• Optimal Nonparametric Inference on Network Effects with Dependent Edges

  2024cites this paper
• Influence networks: Bayesian modeling and diffusion

  2024cites this paper
• Hybrid of node and link communities for graphon estimation

  2024cites this paper
• An unified approach to link prediction in collaboration networks

  2024cites this paper
• Evaluating methods for estimating influence effects in social networks: a simulation study

  2024cites this paper
• Sex‐specific topological structure associated with dementia via latent space estimation

  2024cites this paper
• Nested exemplar latent space models for dimension reduction in dynamic networks

  2024cites this paper
• A latent variable approach for modeling relational data with multiple receivers

  2024cites this paper
• Stochastic Gradient Descent-based Inference for Dynamic Network Models with Attractors

  2024influential citation
• Transfer Learning for Latent Variable Network Models

  2024cites this paper
• Impossibility of Latent Inner Product Recovery via Rate Distortion

  2024cites this paper
• IRWE: Inductive Random Walk for Joint Inference of Identity and Position Network Embedding

  2024cites this paper
• Bayesian Transfer Learning

  2023cites this paper
• Establishing group-level brain structural connectivity incorporating anatomical knowledge under latent space modeling

  2023cites this paper
• Latent Position Network Models

  2023cites this paper
• Fast inference of latent space dynamics in huge relational event networks

  2023cites this paper
• Identifying World Events in Dynamic International Relations Data Using a Latent Space Model

  2023cites this paper
• Group fairness without demographics using social networks

  2023cites this paper
• Predictability of cortico-cortical connections in the mammalian brain

  2023cites this paper
• Network Inference Using the Hub Model and Variants

  2023cites this paper
• Asymmetric Learning for Graph Neural Network based Link Prediction

  2023cites this paper
• Community informed experimental design

  2023cites this paper
• A Hybrid Membership Latent Distance Model for Unsigned and Signed Integer Weighted Networks

  2023influential citation
• Inference-based statistical network analysis uncovers star-like brain functional architectures for internalizing psychopathology in children

  2023cites this paper
• A Spike-and-Slab Prior for Dimension Selection in Generalized Linear Network Eigenmodels

  2023influential citation
• Perfect Spectral Clustering with Discrete Covariates

  2022cites this paper
• A Hierarchical Block Distance Model for Ultra Low-Dimensional Graph Representations

  2022cites this paper
• A Nonlinear Matrix Decomposition for Mining the Zeros of Sparse Data

  2022influential citation
• Dynamic latent space relational event model

  2022cites this paper
• Stochastic Block Smooth Graphon Model

  2022cites this paper
• HM-LDM: A Hybrid-Membership Latent Distance Model

  2022influential citation
• Estimating Social Influence from Observational Data

  2022cites this paper
• Structured Optimal Variational Inference for Dynamic Latent Space Models

  2022cites this paper
• Statistical Network Data Analysis in Economics

  2022cites this paper
• Dependence matters: Statistical models to identify the drivers of tie formation in economic networks

  2022cites this paper
• A latent space model and Hotelling's T2 control chart to monitor the networks of Covid-19 symptoms

  2022influential citation
• AntiConcealer: Reliable Detection of Adversary Concealed Behaviors in EdgeAI-Assisted IoT

  2022cites this paper
• A de Finetti-type representation of joint hierarchically exchangeable arrays on DAGs

  2022cites this paper
• A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks

  2022cites this paper
• A robust Bayesian latent position approach for community detection in networks with continuous attributes

  2022cites this paper
• Latent Community Adaptive Network Regression

  2021cites this paper
• Recent Integrations of Latent Variable Network Modeling With Psychometric Models

  2021influential citation
• Consistent estimation of the number of communities in stochastic block models using cross‐validation

  2021cites this paper
• Measuring and Modeling Group Dynamics in Open-Source Software Development: A Tensor Decomposition Approach

  2021cites this paper
• Network-aware credit scoring system for telecom subscribers using machine learning and network analysis

  2021cites this paper
• Developing a method for modeling and monitoring of dynamic networks using latent variables

  2021influential citation
• Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold

  2021cites this paper
• Subset Node Representation Learning over Large Dynamic Graphs

  2021cites this paper
• Who are in charge, who do i work with, and who are my friends: A latent space approach to understanding elite coappearances in China

  2021cites this paper
• Network Estimation by Mixing: Adaptivity and More

  2021influential citation
• An Eigenmodel for Dynamic Multilayer Networks

  2021influential citation
• Continuous latent position models for instantaneous interactions

  2021cites this paper
• A Latent Space Model for Multilayer Network Data

  2021cites this paper
• Covariate-Informed Latent Interaction Models: Addressing Geographic & Taxonomic Bias in Predicting Bird–Plant Interactions

  2021cites this paper
• Conflict resolution using relation classification: High-level data fusion in data integration

  2021cites this paper
• Taking dyads seriously

  2021cites this paper
• Pseudo-Euclidean Attract-Repel Embeddings for Undirected Graphs

  2021cites this paper
• A Latent Variable Model for Relational Events with Multiple Receivers

  2021cites this paper
• Toward Community-Driven Big Open Brain Science: Open Big Data and Tools for Structure, Function, and Genetics.

  2020cites this paper
• Equilibrium homophily in networks

  2020cites this paper
• Do Birds of a Feather Flock Together? Rebel Constituencies and Civil War Alliances

  2020cites this paper
• Tail Risk Transmission: A Study of the Iran Food Industry

  2020cites this paper
• Improving collaborative filtering's rating prediction coverage in sparse datasets by exploiting the 'friend of a friend' concept

  2020cites this paper
• Best Subset, Forward Stepwise or Lasso? Analysis and Recommendations Based on Extensive Comparisons

  2020cites this paper
• Bayesian Generalized Sparse Symmetric Tensor-on-Vector Regression

  2020cites this paper
• On the structural equivalence of coresidents and the measurement of village social structure

  2020cites this paper
• Advancements in latent space network modelling

  2020influential citation
• Central limit theorems for local network statistics

  2020cites this paper
• The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks

  2020cites this paper
• Universal Latent Space Model Fitting for Large Networks with Edge Covariates

  2020influential citation
• Stratified Stochastic Variational Inference for High-Dimensional Network Factor Model

  2020cites this paper
• Community detection in sparse latent space models

  2020cites this paper
• Unsupervised evaluation of multiple node ranks by reconstructing local structures

  2020cites this paper
• A de Finetti-type representation of joint hierarchically exchangeable arrays on directed acyclic graphs

  2020cites this paper
• A network model that combines latent factors and sparse graphs

  2020cites this paper
• Community Detection of Multi-Layer Attributed Networks via Penalized Alternating Factorization

  2020cites this paper
• A Bayesian Covariance Graph and Latent Position Model for Multivariate Financial Time Series

  2020influential citation
• Spectral Clustering via Adaptive Layer Aggregation for Multi-Layer Networks

  2020influential citation
• Identifiability and consistency of network inference using the hub model and variants: a restricted class of Bernoulli mixture models

  2020cites this paper
• Generative model for reciprocity and community detection in networks

  2020influential citation
• Information-Theoretic Limits for the Matrix Tensor Product

  2020cites this paper