Computes Multiscale Sample Entropy (Costa et al., 2002, 2005), which applies Sample Entropy (Richman & Moorman, 2000) to coarse-grained versions of an activity time series across a range of temporal scales. MSE distinguishes genuinely complex signals (whose entropy is sustained or increases across scales, e.g. 1/f-like physiological signals) from uncorrelated random signals (whose entropy falls monotonically with scale).
Arguments
- x
Numeric vector of activity counts (minute-level recommended). Internally analyzed on the longest continuous non-NA segment.
- scales
Integer vector of coarse-graining scale factors tau. Default
1:20.- m
Integer embedding dimension (template length) for Sample Entropy. Default 2.
- r
Numeric tolerance as a fraction of the standard deviation of the ORIGINAL (scale-1) series. The Chebyshev matching radius used at every scale is
r * sd(x_original), following the standard MSE convention of holding r fixed in absolute units across scales. Default 0.15.
Value
A list with class "actiRhythm_mse" containing:
- mse
Numeric vector of SampEn values, one per requested scale (NA where the coarse-grained series is too short or yields no matches).
- scales
Integer vector of the scale factors used.
- area
Sum of
mseover scales (complexity index),sum(mse, na.rm = TRUE).- slope
Slope of
lm(mse ~ scales)over the non-NA points (negative => entropy declines with scale, typical of noise).- r_absolute
The absolute tolerance
r * sd(x_original)used.- n_used
Length of the analyzed (longest non-NA) segment.
On an unusable series the entropy vector is all NA with the same structure (never an error).
Details
For each scale tau the series is coarse-grained into non-overlapping means of
length tau, then Sample Entropy is computed on the coarse-grained series with
embedding dimension m and the FIXED absolute tolerance
r * sd(x_original). Sample Entropy is the negative natural log of the
conditional probability that two sub-sequences matching for m points
(within the tolerance, Chebyshev distance, self-matches excluded) also match
for m + 1 points.
Examples
# \donttest{
set.seed(1)
# White noise: entropy decreases with scale
multiscale.entropy(rnorm(2000))$mse
#> [1] 2.446324 2.105090 1.935192 1.777846 1.621644 1.552057 1.569350 1.427566
#> [9] 1.357506 1.303940 1.305857 1.384235 1.256591 1.199179 1.138336 1.120196
#> [17] 1.254367 1.146115 1.051494 0.892656
# 1/f-like (random walk): flatter / sustained entropy
multiscale.entropy(cumsum(rnorm(2000)))$mse
#> [1] 0.1147112 0.1594668 0.2091053 0.2474783 0.2828905 0.3114901 0.3333711
#> [8] 0.3486852 0.3554676 0.3622740 0.4004146 0.3876029 0.4276109 0.4148211
#> [15] 0.4246965 0.4166384 0.4553923 0.4447822 0.5024574 0.4326161
# }