Dr. Michael Small, The University of Western Australia
Choosing embedding lag and why it matters
May 29, 2023 – 7:30 PM IST
Zoom Link: https://us06web.zoom.us/webinar/register/WN_zJqiJvZbSBy26hC6k8WFjw
Abstract: Takens’ theorem guarantees a faithful embedding of a deterministic nonlinear dynamical system from time series data under fairly generic conditions. Embedding, in this way, is the foundation of nonlinear time series analysis and modelling. Since the 1980s many methods have been proposed to estimate the time between observations to provide an embedding – the embedding lag. The basic premise is that time interval should ensure independence but not irrelevance. Almost all methods to choose this lag are based on the application of some heuristic to this premise. I will review some of the more interesting ones and introduce a new topologically well-founded way of doing the same. The method I describe is based on using concepts from persistent homology and topological data analysis to ensure that one achieves the “best” attractor for the given data.
Michael Small is the CSIRO-UWA Chair of Complex Systems and holds academic positions at The University of Western Australia and with CSIRO (the Australian government research agency). He is Deputy Editor with Chaos and Main Editor at Physica A. Michael’s research is in nonlinear dynamics, nonlinear time series analysis, complex systems and networks. His work spans a range of application areas and focuses on data-driven methods for understanding complexity and chaos. Applications that he is currently working on include traffic modelling, mineral exploration, mental health, and disease modelling.
Photo credits: https://research-repository.uwa.edu.au/en/persons/michael-small