Locally stationary time vertex process models

Date

2026-1-13

Author

Aslan, Deniz

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Graph signal processing provides a powerful framework for analyzing data defined over irregular network structures. In many real-world applications, time-vertex signals are observed only partially due to sensing failures, communication constraints, or limited data availability, making the learning of reliable signal models a challenging task. In particular, estimating parametric models from incomplete time-vertex observations requires capturing both temporal dynamics and graph-dependent statistical structures. Existing approaches based on joint wide-sense stationarity (JWSS) offer effective tools for modeling global statistical properties of time-vertex signals; however, their global stationarity assumptions often fail to represent local variations that naturally arise across both temporal and graph dimensions. In this thesis, we address the problem of estimating time-vertex signals with missing observations by learning parametric models that exhibit locally stationary behavior over time and graph. The proposed framework extends the concept of local stationarity to the time-vertex setting by modeling a structured covariance matrix derived from the sample covariance through a JWSS-inspired formulation. Model parameters are estimated via an alternating optimization algorithm that efficiently exploits the covariance structure for model fitting. Experimental results on synthetic and real data demonstrate that the proposed approach achieves lower normalized mean error (NME) and mean absolute error (MAE) compared to reference time-vertex methods. Overall, this study introduces a covariance-driven parametric framework for learning locally stationary time-vertex processes, enabling more reliable modeling of complex graph-temporal signals.

Subject Keywords

Graph signal processing, Locally stationary time-vertex processes, Local stationarity, Moving average processes

URI

https://hdl.handle.net/11511/118401

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Graduate School of Natural and Applied Sciences, Thesis