ArXiv

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

2026-08-06 · 09:19 UTC ·Federico P. Cortese ·1 min read
Authors
Federico P. Cortese
Categories
stat.ME, stat.AP, stat.ML
arXiv
https://arxiv.org/abs/2608.05786v1
PDF
https://arxiv.org/pdf/2608.05786v1

Brief

The paper presents a fuzzy network jump model that clusters time-varying, node-indexed data on weighted graphs by estimating soft membership probabilities with spatial and temporal smoothness penalties. Estimation proceeds via an alternating-optimization algorithm exploiting quadratic regularizers. Simulations (varying spatial dependence and cluster overlap) show accurate recovery and empirical superiority to competitors; an application maps evolving traffic regimes in San Francisco. Full text available on arXiv; this summary is based on the abstract.

Why it matters

Federico P. Cortese (ArXiv 2608.05786v1, posted 2026-08-06) introduces the "fuzzy network jump model" for clustering time-varying observations on nodes of a weighted graph, producing soft (probabilistic) cluster memberships with spatial and temporal regularization.

Key details

  • Estimation uses an efficient alternating-optimization scheme that leverages the quadratic form of the spatial and temporal regularizers to enforce smooth membership across connected nodes and consecutive time points; a simulation study (varying spatial dependence and cluster overlap) reports accurate recovery of true membership probabilities and outperformance of competing clustering methods.
  • Applied to San Francisco traffic-network data, the model identifies interpretable traffic regimes and their evolution across road segments and time; full paper available at https://arxiv.org/abs/2608.05786v1 (PDF linked).
Source evidence

Abstract

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.