A Framework for Spatio-Temporal Data Analysis and Hypothesis Exploration

We present a general framework for pattern discovery and hypothesis exploration in spatio-temporal data sets that is based on delay-embedding. This is a remarkable method of nonlinear time-series analysis that allows the full phase-space behaviour of a system to be reconstructed from only a single observable (accessible variable). Recent extensions to the theory that focus on a probabilistic interpretation extend its scope and allow practical application to noisy, uncertain and high-dimensional systems. The framework uses these extensions to aid alignment of spatio-temporal sub-models (hypotheses) to empirical data - for example satellite images plus remote-sensing - and to explore modifications consistent with this alignment. The novel aspect of the work is a mechanism for linking global and local dynamics using a holistic spatio-temporal feedback loop. An example framework is devised for an urban based application, transit centric developments, and its utility is demonstrated with real data