This work provides a comprehensive analysis and interpretation of the graph spectral representation of traffic scenarios. Based on a spatio-temporal vehicle interaction graph, an observed traffic scenario can be transformed into the graph spectral domain by means of the multidimensional Graph Fourier Transformation. Since these spectral scenario representations have shown to successfully incorporate the complex and interactive nature of traffic scenarios, the beneficial feature representation is employed for the purpose of predicting vehicle trajectories. This work introduces GFTNNv2, a deep learning network predicting vehicle trajectories in the graph spectral domain. Evaluation of the GFTNNv2 on the publicly available datasets highD and NGSIM shows a performance gain of up to 25% in comparison to state-of-the-art prediction approaches.

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to algorithms for reconstructing missing information from graph signals via sparse representations, and yield new graph analysis tools. While previous work has focused on generalizing notions of spreads of a graph signal in the vertex and graph spectral domains, our approach is to generalize the methods of Lieb in order to develop uncertainty principles that provide limits on the concentration of the analysis coefficients of any graph signal under a dictionary transform whose atoms are jointly localized in the vertex and graph spectral domains. One challenge we highlight is that due to the inhomogeneity of the underlying graph data domain, the local structure in a single small region of the graph can drastically affect the uncertainty bounds for signals concentrated in different regions of the graph, limiting the information provided by global uncertainty principles. Accordingly, we suggest a new way to incorporate a notion of locality, and develop local uncertainty principles that bound the concentration of the analysis coefficients of each atom of a localized graph spectral filter frame in terms of quantities that depend on the local structure of the graph around the center vertex of the given atom. Finally, we demonstrate how our proposed local uncertainty measures can improve the random sampling of graph signals.