Title
Time Series Prediction By Chaotic Modeling Of Nonlinear Dynamical Systems
Abstract
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. Our main contributions are: multivariate phase space reconstruction for human actions and dynamic textures, a deterministic approach to model dynamics in contrast to the popular noise-driven approaches for dynamic textures, and video synthesis from kernel regression in the phase space. Experimental results provide qualitative and quantitative analysis of our approach on standard data sets. ©2009 IEEE.
Publication Date
12-1-2009
Publication Title
Proceedings of the IEEE International Conference on Computer Vision
Number of Pages
1941-1948
Document Type
Article; Proceedings Paper
Personal Identifier
scopus
DOI Link
https://doi.org/10.1109/ICCV.2009.5459429
Copyright Status
Unknown
Socpus ID
77953214241 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/77953214241
STARS Citation
Basharat, Arslan and Shah, Mubarak, "Time Series Prediction By Chaotic Modeling Of Nonlinear Dynamical Systems" (2009). Scopus Export 2000s. 11380.
https://stars.library.ucf.edu/scopus2000/11380