Jul 2026· Signal Processing and Communications Applications Conference· pp. 1-4· 0 citations· 11 references
Abstract
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.
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.
Understanding temporal dynamics in complex systems often requires identifying abrupt structural changes, known as change points in multivariate time series. Traditional vector autoregressive (VAR) models have been widely used for modeling dependencies across time, yet their parameter space grows quadratically with the number of variables, leading to computational and estimation challenges in high‐dimensional settings. The recently proposed network autoregressive (NAR) modeling framework offers a computationally efficient alternative by reducing parameter complexity through a network‐based representation. However, existing NAR models either assume homogeneous temporal behavior across all nodes, overlooking node‐specific dynamics that frequently arise in environmental and socio‐economic systems, or do not allow for structural breaks. In this work, we propose
NLDNAR‐CP
, a novel change point detection method within a node‐specific NAR framework that accommodates heterogeneous temporal dependencies across variables. The proposed approach efficiently detects multiple structural breaks while preserving scalability to high‐dimensional networks. We demonstrate the method's superior empirical performance through extensive simulations and a real‐world environmental application.
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation. In this paper, we analyze continuous normalized flow models parameterized by GNNs and show that permutation equivariance is preserved for both the resulting continuous-time ordinary differential equations and their discrete numerical approximations used as graph signal samplers. Our primary contribution is to derive explicit stability bounds on the generated probability distributions, which quantify how relative graph perturbations affect the final sampled signals. Motivated by these theoretical bounds, we introduce a stability-promoting regularized flow matching strategy that actively penalizes the spatial Lipschitz constant of the vector field during model training. Experiments using synthetic smooth signals on stochastic block model graphs and real-world fMRI signals on brain connectomes demonstrate that this bound-oriented approach yields generative models that are more robust to structural noise, without sacrificing output quality.
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.
Complex dynamical systems often display extreme fluctuations of an observed variable that constitute significant deviations from the long-term average, and which are often associated with severe impacts on the system. By definition, extreme events are therefore usually explored from time series recordings. In this work, we characterize extreme values in time series using visibility graphs, a method that non-parametrically maps a time series onto a network, whose topological structure is known to inherit important characteristics of the original time series dynamics. Unlike threshold-based approaches, extreme values in this framework can be identified without the need to introduce external parameters and can be applied to time series generated by both stationary and nonstationary processes. For stationary processes, we exploit a known property of visibility graphs in which the degree of a node is monotonically and nonlinearly related to the corresponding data value. This nonlinear amplification enhances the contribution of large values while suppressing noise, while the monotonic relationship enables a direct ranking of data points according to node degree. This procedure identifies global extreme values and locally prominent ones. For nonstationary processes, the degree ranking in the visibility graph still provides a robust indicator of relative importance. We validate our findings with synthetic time series and with real climatological data. Our results show that extreme-value characterization in stationary time series is enhanced when combining standard methods with visibility-graph-based detection, whereas for nonstationary data, where conventional approaches are often ill-posed, visibility graphs provide an effective alternative. We discuss how sub-sampling the time series using only peak values preserves the ability to identify extreme values while reducing computational cost.
The definition of directed graph wide-sense stationarity is revisited, and the surrogate signals preserve covariance under the stationary assumption to demonstrate the feasibility of the scheme to detect irregular node covariance and benchmark the method against conventional schemes using the symmetrized graph.
Chun Hei Michael Chan, Alexandre Cionca, D. Ville· 0 citations