Graf arma süreçleri ile zamanda değişen graf sinyallerinin tahmini

Graph models provide efficient tools for analyzing data defined over irregular domains such as social networks, sensor networks, and transportation networks. Real-world graph signals are usually time-varying signals. The characterization of the joint behavior of time-varying graph signals in the time and the vertex domains has recently arisen as an interesting research problem, contrasted to the independent processing of graph signals acquired at different time instants. The concept of wide sense stationarity, which facilitates the analysis of random time processes in statistical signal processing, has been extended to graph domains for the joint time-vertex analysis of time-varying graph random processes. In this thesis, we study the problem of learning parametric joint wide sense stationary models to analyze and estimate time-varying graph signals. Since parametric models with few parameters typically require less training data than nonparametric models, they are expected to perform better in case of incomplete observations. We model time-varying graph signals as autoregressive moving average (ARMA) processes in this study. The graph ARMA process parameters are learnt from a prior coarse estimation of the joint power spectral density (JPSD) of the process that models a given set of time-varying graph signals with missing observations. The JPSD estimation is then refined and improved based on the learnt graph ARMA process model. The estimated JPSD is finally used to recover the missing observations of the given time-varying graph signals. Experiments performed on synthetic and real data show that using ARMA graph process models to analyze time-varying graph signals yields promising results.