Time Series Prediction by Chaotic Modeling of Nonlinear Dynamical Systems

We use concepts from chaos theory in order to model nonlinear dynamical systems that exhibit deterministic behavior. Observed time series from such a system can be embedded into a higher dimensional phase space without the knowledge of an exact model of the underlying dynamics. Such an embedding warps the observed data to a strange attractor, in the phase space, which provides precise information about the dynamics involved. We extract this information from the strange attractor and utilize it to predict future observations. Given an initial condition, the predictions in the phase space are computed through kernel regression. This approach has the advantage of modeling dynamics without making any assumptions about the exact form (linear, polynomial, radial basis, etc.) of the mapping function. The predicted points are then warped back to the observed time series. We demonstrate the utility of these predictions for human action synthesis, and dynamic texture synthesis. ...

• Type: Conference
• Year: 2009
• Where: ICCV
• Authors: Arslan Basharat, Mubarak Shah
• Keywords: Chaotic Modeling, Computer Vision, ICCV 2009, Nonlinear Dynamical Systems, Time Series Prediction