Abstract: Informed by physiology, the wave-shape oscillatory model for biomedical time series asserts that cycles lie on or near a low-dimensional manifold.
Recovering this manifold provides insight into the dynamics of the underlying system. I present a manifold learning framework for biomedical time series analysis, and I provide a guarantee on the dynamical information which can be recovered using this framework. We will discuss several applications in the analysis of electrocardiograms and blood pressure monitoring. Time-permitting, we will examine further approaches to biomedical time series analysis which fuse traditional signal processing with modern mathematics.