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Stationarity is a key assumption in many statistical models for randomprocesses. With recent developments in the field of graph signal processing,the conventional notion of wide-sense stationarity has been extended to randomprocesses defined on the vertices of graphs. It has been shown that well-knownspectral graph kernel methods assume that the underlying random process over agraph is stationary. While many approaches have been proposed, both in machinelearning and signal processing literature, to model stationary random processesover graphs, they are too restrictive to characterize real-world datasets asmost of them are non-stationary processes. In this paper, to well-characterizea non-stationary process over graph, we propose a novel model and acomputationally efficient algorithm that partitions a large graph into disjointclusters such that the process is stationary on each of the clusters butindependent across clusters. We evaluate our model for traffic prediction on alarge-scale dataset of fine-grained highway travel times in the Dallas--FortWorth area. The accuracy of our method is very close to the state-of-the-artgraph based deep learning methods while the computational complexity of ourmodel is substantially smaller.

Piecewise Stationary Modeling of Random Processes Over Graphs With an Application to Traffic Prediction