Paper of Jane Lyle and Philip Aston on higher-order embeddings for the SPAR method published in Chaos

The paper “Symmetric projection attractor reconstruction: Embedding in higher dimensions” by Jane Lyle and Philip Aston has been published in Chaos: An Interdisciplinary Journal of Nonlinear Science. A link to the published paper is here. The Symmetric Projection Attractor Reconstruction (SPAR) method provides an intuitive visualisation and simple quantification of the morphology and variability of approximately periodic signals. The original method takes a three-dimensional delay coordinate embedding of a signal and projects the phase space reconstruction to a two-dimensional image with threefold symmetry. This paper presents an extension of the original work to apply delay coordinate embedding in any dimension 𝑁≥3 while still deriving a two-dimensional output with some rotational symmetry property that provides a meaningful visualisation of the higher dimensional attractor. The potential clinical utility of this approach is illustrated by its application to some ECG signals. The image below shows Figure 14 from the paper.