Fig. 4: Koopman eigenvalue analysis and the corresponding stable, unstable, and neutral modes.
From: Data-driven analysis and forecasting of highway traffic dynamics
a Plotting the color-coded eigenvalues on the unit circle confirms the findings of Kim59 in that slowly evolving patterns persist in time. b Plotting the average amplitude of the modes against their period confirms the findings of Gartner60 in that slower evolving patterns carry larger amplitudes. c Plotting the timescales identified for various choices of data demonstrates the KMD to be a robust methodology for extracting fundamental frequencies regardless of the modality of observation and verify the existence of intra-day patterns. d–i Plots of the corresponding stable, unstable, and neutral modes and various superpositions of them. These figures verify that the individual modes correspond to coherent and dynamically important sub-patterns and when superimposed reconstruct the data.
