Shape Distributions of Nonlinear Dynamical Systems for Video-based Inference

—This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. An alternative idea we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation for quantification of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models like Lorenz and Rossler systems, and our feature representations (shape distribution) support our hypothesis that the shape of the reconstructed phase space can...

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Vinay Venkataraman, Pavan K. Turaga
• Keywords: CORR 2016, Education