A fuzzy network jump model for clustering time-varying observations indexed by the nodes of a weighted graph that accurately recovers the true membership probabilities and outperforms competing clustering methods is introduced.
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.
The framework gives a nonparametric baseline for dynamic network analysis with explicit convergence guarantees and establishes nonparametric convergence rates in both block-model and Holder-smooth regimes.
Spectral clustering for community detection is analysed in multivariate time series models whose dependence structure is determined by an unobserved stochastic blockmodel. We establish that spectral clustering of the sample covariance matrix achieves exact recovery of the underlying communities. The recovery rates depend explicitly on the network size, sample length, block separation, and degree of data dependence. This demonstrates that exact community recovery under a stochastic blockmodel is possible even when the adjacency matrix is unobserved. Our theory provides extensions of both classical and fine-grained matrix perturbation theory to the setting of dependent data, which may be of independent interest.
Brendan Martin, Joshua Agterberg, Mihai Cucuringu et al.· 0 citations
Graph signal processing provides a powerful framework for analyzing data defined over irregular network structures. Estimation of effective models from a set of timevarying graph signals requires capturing both temporal dynamics and graph-dependent statistical structures. Existing approaches that model time-vertex signals as stochastic processes typically assume a globally stationary model, which often fails to represent local variations that naturally arise across both temporal and graph dimensions. In this work, we address the problem of learning parametric models for graph signals exhibiting locally stationary behavior over time and graph. We propose a locally stationary time-vertex signal model that extends stationarity to a locally adaptive setting and develop an algorithm to learn the model parameters. Experiments on synthetic and real datasets demonstrate improved estimation accuracy over existing time-vertex methods.
Deniz Aslan, Elif Vural· Signal Processing and Commun...· 0 citations
By specifying a stochastically evolving hidden Markov network model, this work addresses two important directions for further investigation identified by Chang et al. (2022): robustness to non-identical network replicates, and efficient aggregation of multiple available network snapshots.
A generative model for temporal networks that jointly controls community evolution and dynamic node sets and is used as a benchmark to study the impact of the rate at which nodes join/leave the network on the performance of dynamic community detection algorithms.
Peijie Zhong, Raúl Mondragón, Richard Clegg· 0 citations
