Multiscale Entropy (MSE)

Estimates the complexity of a time series across a range of temporal scales (Costa, Goldberger & Peng 2002): the series is coarse-grained (non-overlapping block-averaged) at each scale factor, and sample_entropy() is computed on each coarse-grained series, using a tolerance held fixed relative to the original (not the coarse-grained) series' standard deviation – this is the standard MSE convention and essential for entropy values to be comparable across scales. Direct C++ port of the coarse-graining + sample-entropy core in PhysioNet's reference mse.c (Costa), validated to reproduce the compiled reference binary's output exactly (to its own displayed precision) on synthetic test data. See inst/COPYRIGHTS.

Usage

multiscale_entropy(x, scale_max = 20L, m = 2L, r = 0.15)

Arguments

x

Numeric vector. The time series to analyse.

scale_max

Integer >= 1. Largest scale factor to evaluate; MSE is computed at every integer scale from 1 to scale_max. Default 20 (the standard MSE convention).

m

Integer >= 1. Template length, passed to sample_entropy(). Default 2 (the standard MSE convention).

r

Numeric > 0. Tolerance as a fraction of the original series' standard deviation, passed to sample_entropy(). Default 0.15 (the standard MSE convention).

Value

A list with:

scale

The scale factors evaluated, 1:scale_max.

mse

Sample entropy at each scale (may contain NA at large scales, where the coarse-grained series becomes too short to estimate reliably).

m, r

The parameters used, echoed back for reference.

References

Costa M, Goldberger AL, Peng CK. Multiscale entropy analysis of complex physiologic time series. Phys Rev Lett 2002;89:068102.

Examples

set.seed(1)
res <- multiscale_entropy(rnorm(2000), scale_max = 10)
plot(res$scale, res$mse, type = "b")