Irregular time-varying series prediction on graphs with nonlinear expansion functions

Predicting irregular time-varying series is challenging due to the complex interdependencies among variables. To capture the nonlinear spatiotemporal relationships in the data evolution process, we propose two nonlinear prediction methods that incorporate nonlinear expansion functions and graph signal processing (GSP). First, we develop a nonlinear graph vector autoregressive (NL-GVAR) model equipped with a nonlinear expansion module. This model maps graph signals from low-dimensional to high-dimensional spaces to enhance the nonlinear representation capability. Second, to address the impact of fluctuations in non-stationary time series, we integrate empirical mode decomposition (EMD) into the NL-GVAR framework. This integration allows for the efficient capture of the underlying nonlinear interdependencies within the time series. Furthermore, we derive closed-form solutions for parameter optimization under the minimum mean square error (MSE) criterion. Numerical results using various synthetic and real-world datasets demonstrate the superior performance of the proposed methods compared to existing methods.