Permutation Entropy

Estimates the complexity of a time series using permutation entropy (Bandt & Pompe 2002): the Shannon entropy of the distribution of ordinal patterns ("motifs") of length order found in the series. Ported from Lucas Franca's own mrpheus package (part of its AASM sleep-staging feature pipeline), itself validated for exact parity against the antropy Python library; re-validated here directly against antropy 0.2.2 on synthetic test data (exact match to displayed precision). See inst/COPYRIGHTS.

Usage

perm_entropy(x, order = 3L, delay = 1L, normalize = TRUE)

Arguments

x

Numeric vector. The time series to analyse.

order

Integer >= 2. Length of the ordinal pattern (embedding dimension). Default 3.

delay

Integer >= 1. Time delay between pattern elements. Default 1.

normalize

Logical. If TRUE (default), divide by log(order!) so the result falls in [0, 1]. If FALSE, return the raw Shannon entropy in nats (natural log). Note this differs from the antropy Python library, which computes the raw value in bits (log base 2); the normalized value is base-independent and matches antropy exactly, but the raw values are not directly comparable between the two. See inst/COPYRIGHTS.

Value

A length-1 numeric: the permutation entropy.

References

Bandt C, Pompe B. Permutation entropy: a natural complexity measure for time series. Phys Rev Lett 2002;88:174102.

Examples

set.seed(1)
perm_entropy(rnorm(1000))
#> [1] 0.9988401