# Fuzzy network jump models for soft dynamic clustering of graph-structured data

arXiv: https://arxiv.org/abs/2608.05786 · HTML: https://mlsanity.com/paper/2608.05786/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [A Review of Stochastic Block Models and Extensions for Graph Clustering](https://mlsanity.com/paper/1903.00114/) (2019)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [Learning Latent Block Structure in Weighted Networks](https://mlsanity.com/paper/1404.0431/) (2014)
- [Fitting Jump Models](https://mlsanity.com/paper/1711.09220/) (2017)
- [Significance-based community detection in weighted networks](https://mlsanity.com/paper/1601.05630/) (2016)
- [Spatio-Temporal Jump Model for Urban Thermal Comfort Monitoring](https://mlsanity.com/paper/2411.09726/) (2024)
- [Robust fuzzy clustering with cellwise outliers](https://mlsanity.com/paper/2508.03310/) (2025)
- [Fuzzy Jump Models for Soft and Hard Clustering of Multivariate Time Series Data](https://mlsanity.com/paper/2509.26029/) (2025)
- [Robust State-Conditional Feature-Weighted Jump Models for Temporal Clustering](https://mlsanity.com/paper/2606.13146/) (2026)

## Abstract (arXiv)

We introduce a fuzzy network jump model for clustering time-varying observations indexed by the nodes of a weighted graph. The framework allows flexible graph representations with spatial and temporal regularization promoting smooth soft cluster assignments across connected nodes and consecutive time points. Estimation is performed through an efficient alternating optimization scheme that exploits the quadratic structure of the regularization terms. A simulation study covering different levels of spatial dependence and cluster overlap shows that the proposed method accurately recovers the true membership probabilities and outperforms competing clustering methods. An application to traffic-network data for the city of San Francisco identifies interpretable traffic regimes and reveals their evolution over time and across connected road segments.