Dispersion Entropy

Computes the dispersion entropy (DispEn) of a one-dimensional signal (Rostaghi & Azami, 2016) – a fast, robust symbolic-dynamics complexity measure. Unlike the amplitude-histogram entropies (renyiEntropy, tsallisEntropy) and the ordinal permutation entropy, DispEn maps the signal to c amplitude classes through the normal cumulative distribution function (NCDF), forms embedding vectors of length dimension (the dispersion patterns), and takes the Shannon entropy of the pattern distribution, normalized by \(\ln(c^{m})\). The NCDF mapping makes it insensitive to outliers and much cheaper than sample entropy, with no threshold-crossing boundary effects. Set reverse = TRUE to return the reverse dispersion entropy (RDEn), the mean-square deviation of the pattern distribution from uniformity (larger = more regular / less complex).

Usage

dispersionEntropy(x, c = 6L, dimension = 3L, delay = 1L, reverse = FALSE)

Arguments

x: A numeric vector (the time series).
c: Number of amplitude classes / symbols (default 6; Rostaghi & Azami recommend 4–8).
dimension: Embedding dimension \(m\) of the dispersion patterns (default 3).
delay: Time delay (lag) in samples (default 1).
reverse: If TRUE, return the reverse dispersion entropy (RDEn) instead of DispEn (default FALSE).

Value

A single numeric value: the dispersion entropy (or, if reverse = TRUE, the reverse dispersion entropy).

Details

This implementation reproduces NeuroKit2's entropy_dispersion bit-for-bit, including its normalization convention (a base-2 Shannon term divided by the natural-log \(\ln(c^{m})\), so DispEn ranges in \([0, 1/\ln 2]\)).

References

Rostaghi, M., & Azami, H. (2016). "Dispersion entropy: A measure for time-series analysis." IEEE Signal Processing Letters, 23(5), 610–614. doi:10.1109/LSP.2016.2542881

Examples

set.seed(1)
dispersionEntropy(rnorm(1000))                 # DispEn (c = 6, m = 3)
#> [1] 1.414845
dispersionEntropy(rnorm(1000), reverse = TRUE) # reverse dispersion entropy
#> [1] 0.0007654149