Decomposes the activity series into intrinsic mode functions by empirical mode decomposition, a data-adaptive, nonlinear alternative to the linear SSA decomposition (Huang et al. 1998). The intrinsic mode function whose period is nearest 24 hours is taken as the circadian component. Optional ensemble EMD adds noise to reduce mode mixing (Wu and Huang 2009).
Usage
circadian.emd(
counts,
timestamps,
max_imf = 10L,
ensemble = 1L,
noise_sd = 0.2,
period_range = c(20, 28),
epoch_length = 60,
seed = NULL
)Arguments
- counts
Numeric activity vector (a coarse epoch is recommended for speed).
- timestamps
POSIXct timestamps, one per value.
- max_imf
Maximum number of modes to extract (default 10).
- ensemble
Ensemble size for EEMD (default 1 = plain EMD).
- noise_sd
Added-noise SD as a fraction of the series SD (default 0.2).
- period_range
Period window (hours) for the circadian mode (default 20 to 28).
- epoch_length
Epoch length in seconds (default 60).
- seed
Optional seed for the EEMD noise.
Value
An object of class actiRhythm_emd: the IMF matrix, the residual
trend, per-IMF period and variance share, the circadian IMF index, and the
reconstruction error. The first and last epochs are unreliable (the spline
envelopes pin the IMFs near zero at the edges), so read the instantaneous
series away from the boundary. Never errors.
References
Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH (1998). “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.” Proceedings of the Royal Society A, 454(1971), 903–995. doi:10.1098/rspa.1998.0193 .
Wu Z, Huang NE (2009). “Ensemble empirical mode decomposition: a noise-assisted data analysis method.” Advances in Adaptive Data Analysis, 1(1), 1–41. doi:10.1142/S1793536909000047 .
Examples
ts <- seq(as.POSIXct("2024-01-01", tz = "UTC"), by = 600, length.out = 6 * 144)
th <- as.numeric(difftime(ts, ts[1], units = "hours"))
circadian.emd(100 + 60 * cos(2 * pi * th / 24), ts, epoch_length = 600)
#> Empirical Mode Decomposition
#>
#> IMFs: 3 reconstruction error: 7.11e-15
#> IMF period_h var_share
#> 1 22.15 0.737
#> 2 41.14 0.030
#> 3 72.00 0.232
#>
#> Circadian IMF: 1 (period 22.15 h)
#>