Quadrant scan for multi-scale transition detection

Transition detection in temporal and nontemporal signals is a problem encountered in various disciplines. We investigate the quadrant scan technique to analyze recurrence plots to identify tipping points of a dynamical system. We define two types of transition, state-transition and dynamic-transition, and prove analytically the ability of quadrant scans to detect both types. We then provide an extension by considering a weighting scheme to overcome limitations of the standard scheme. We further highlight the merits of the quadrant scan and our extension by studying several applications. The ability of the quadrant scan and its extension to deal with nontemporal, multivariate, or large data sets as well as their capability to classify multiscale transitions are demonstrated in detail through several examples and settings.