Multiscale Entropy

Computes the multiscale entropy (MSE; Costa, Goldberger & Peng, 2002) of a one-dimensional signal: the sample entropy of the signal after coarse-graining it at a series of time scales. At scale \(s\) the signal is partitioned into non-overlapping windows of length \(s\), each window is replaced by its mean, and the sample entropy (embedding m, tolerance r times the SD of the ORIGINAL signal, held fixed across scales) of that coarse-grained series is the MSE at scale \(s\). A signal whose MSE stays high or rises at coarse scales carries structure across time scales; white noise, by contrast, has an MSE that falls monotonically from scale 1.

Usage

multiscaleEntropy(x, m = 2L, r = 0.2, scales = 1:8)

Arguments

x

A numeric vector (the time series).

m

Embedding dimension for the sample entropy (default 2).

r

Tolerance as a fraction of the ORIGINAL signal's SD (default 0.2), held fixed across all scales (Costa's convention).

scales

Integer vector of time scales (default 1:8).

Value

A named numeric vector of sample entropies, one per scale (scale1, scale2, ...). NA for a scale whose coarse-grained series is too short or yields no template matches.

References

Costa, M., Goldberger, A. L., & Peng, C.-K. (2002). "Multiscale entropy analysis of complex physiologic time series." Physical Review Letters, 89(6), 068102. doi:10.1103/PhysRevLett.89.068102

See also

eegComplexity for the multi-measure wrapper; PhysioMoCap's sampleEntropy for the single-scale measure.

Examples

set.seed(1); multiscaleEntropy(rnorm(1000), scales = 1:5)  # noise: falls with scale
#>   scale1   scale2   scale3   scale4   scale5 
#> 2.157936 1.832660 1.524710 1.409100 1.163269