# Latent Space Models for Dynamic Networks

arXiv: https://arxiv.org/abs/2005.08808 · HTML: https://mlsanity.com/paper/2005.08808/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2020.

## Built on by (most cited first, 29 of 29)

- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks](https://mlsanity.com/paper/2205.09263/) (2022)
- [Piecewise-Velocity Model for Learning Continuous-time Dynamic Node Representations](https://mlsanity.com/paper/2212.12345/) (2022)
- [A Hierarchical Block Distance Model for Ultra Low-Dimensional Graph Representations](https://mlsanity.com/paper/2204.05885/) (2022)
- [Mutually exciting point process graphs for modelling dynamic networks](https://mlsanity.com/paper/2102.06527/) (2021)
- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [A Scalable Factorization Approach for High-Order Structured Tensor Recovery](https://mlsanity.com/paper/2506.16032/) (2025)
- [Transfer Learning for Latent Variable Network Models](https://mlsanity.com/paper/2406.03437/) (2024)
- [A Latent Space Model for Multilayer Network Data](https://mlsanity.com/paper/2102.09560/) (2021)
- [Structured Optimal Variational Inference for Dynamic Latent Space Models](https://mlsanity.com/paper/2209.15117/) (2022)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis](https://mlsanity.com/paper/2208.01365/) (2022)
- [A Latent Space Model for HLA Compatibility Networks in Kidney Transplantation](https://mlsanity.com/paper/2211.02234/) (2022)
- [Fast inference of latent space dynamics in huge relational event networks](https://mlsanity.com/paper/2303.17460/) (2023)
- [Enhanced Safety in Autonomous Driving: Integrating Latent State Diffusion Model for End-to-End Navigation](https://mlsanity.com/paper/2407.06317/) (2024)
- [A Frequentist Statistical Introduction to Variational Inference, Autoencoders, and Diffusion Models](https://mlsanity.com/paper/2510.18777/) (2025)
- [A Dynamic Atlas of Persian Poetic Symbolism: Families, Fields, and the Historical Rewiring of Meaning](https://mlsanity.com/paper/2604.01467/) (2026)
- [A Deep Latent Space Model for Graph Representation Learning](https://mlsanity.com/paper/2106.11721/) (2021)
- [A Probit Tensor Factorization Model For Relational Learning](https://mlsanity.com/paper/2111.03943/) (2021)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [Efficient Estimation for Longitudinal Networks via Adaptive Merging](https://mlsanity.com/paper/2211.07866/) (2022)
- [Time to Cite: Modeling Citation Networks using the Dynamic Impact Single-Event Embedding Model](https://mlsanity.com/paper/2403.00032/) (2024)
- [Unsupervised Attributed Dynamic Network Embedding with Stability Guarantees](https://mlsanity.com/paper/2503.02859/) (2025)
- [Tensor State Space-based Dynamic Multilayer Network Modeling](https://mlsanity.com/paper/2506.02413/) (2025)
- [Unfolded Laplacian Spectral Embedding: A Theoretically Grounded Approach to Dynamic Network Representation](https://mlsanity.com/paper/2508.12674/) (2025)
- [Nonparametric estimation of time-varying network connections by multi-stage smoothing](https://mlsanity.com/paper/2605.06862/) (2026)
- [Dynamic Latent Space Modeling of Inhomogeneous Poisson Network Processes with Applications to International Relations](https://mlsanity.com/paper/2609.08813/) (2026)

## Abstract (arXiv)

Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov chain Monte Carlo algorithm is proposed to estimate the model parameters and latent positions of the actors in the network. The model yields meaningful visualization of dynamic networks, giving the researcher insight into the evolution and the structure, both local and global, of the network. The model handles directed or undirected edges, easily handles missing edges, and lends itself well to predicting future edges. Further, a novel approach is given to detect and visualize an attracting influence between actors using only the edge information. We use the case-control likelihood approximation to speed up the estimation algorithm, modifying it slightly to account for missing data. We apply the latent space model to data collected from a Dutch classroom, and a cosponsorship network collected on members of the U.S. House of Representatives, illustrating the usefulness of the model by making insights into the networks.