Symmetric Projection Attractor Reconstruction: Multi-dimensional Embedding of Physiological Signals

Abstract

Physiological signals are typically analysed by identifying local extrema, but this discards the detail of the waveform morphology which is of clinical importance. We can apply delay coordinate embedding to a single time series to reconstruct an attractor in three-dimensional phase space. Our Symmetric Projection Attractor Reconstruction (SPAR) technique adapts this to provide an image of the waveform that is easily quantified and from which we can extract information about the whole waveform. We exemplify our method by discriminating gender from the electrocardiogram (ECG) using machine learning and quantify an individual's response to cardioactive drugs.