A Framework for Spatio-Temporal Data Analysis and Hypothesis Exploration

We present a general framework for pattern discovery and hypothesis exploration in spatio-temporaldata sets that is based on delay-embedding. This is a remarkable method of nonlinear time-series analysis thatallows the full phase-space behaviour of a system to be reconstructed from only a single observable (accessiblevariable). Recent extensions to the theory that focus on a probabilistic interpretation extend its scope and allowpractical application to noisy, uncertain and high-dimensional systems. Our framework uses these extensions toaid alignment of spatio-temporal sub-models (hypotheses) to empirical data - for example, satellite images plusremote-sensing - and to explore behaviours consistent with this alignment. The novel aspect of the work is amechanism for linking global and local dynamics using a holistic spatio-temporal feedback loop. An exampleframework is devised for an urban planning application, transit-oriented developments, and its feasibility isdemonstrated with real data.