Method for cycle detection in sparse, irregularly sampled, long-term neuro-behavioral timeseries: Basis pursuit denoising with polynomial detrending of long-term, inter-ictal epileptiform activity
Fig 5
Impact of varying sample density on Basis Pursuit with Polynomial Detrending (BPWP) outputs, participant 1.
(A) Raw data showing hourly rate of inter-ictal epileptiform discharges (IED) detected from the left hippocampus, updated every 20 minutes. Timeseries consists of over 20,000 samples. (Bi) Raw data are in gray and one random sample per day is in orange. (Bii) Raw data are in gray and the reconstructed signal using BPWP outputs based on input data of one random sample per day is in orange. (C) Average complex wavelet transform (CWT) spectrum from the raw data in (A) is in gray. The BPWP spectrum based on one sample per day input is shown in orange. Black stars denote significant peaks; peaks whose amplitude was above the 99th percentile of the distribution created by shuffling the input data and re-calculating the method 100 times. Random samples, signal reconstructions, and BPWP spectra are shown again for sampling rates of three and five per day in (D) and (E) and in (F) and (G) respectively. Agreement between BPWP output and raw data and CWT spectra improves as the signal is sampled more densely. Part (H) shows agreement between the BPWP and CWT spectra as a function of frequency of random sampling. For each sampling frequency, the raw data were resampled and BPWP was re-calculated 10 times. For each peak in the CWT spectrum, the offset between the period of the CWT peak and the nearest BPWP peak was calculated in terms of days and divided by the period of the CWT peak. This offset-to-cycle-length ratio was averaged across the 10 iterations and plotted as a log value on the y axis. The associated frequency of random sampling was plotted on the x axis. Shaded areas denote 95% confidence intervals. The offset ratio decreases and stabilizes as sampling density increases.