Increment Entropy

Computes the increment entropy (IncrEn) of a one-dimensional signal (Liu et al., 2016) – a symbolic complexity measure defined on the signal's increments (successive differences) rather than its amplitudes. Each increment in an embedding vector is mapped to a word letter combining its sign (\(-, 0, +\)) with a magnitude class in \(\{0, 1, \dots, q\}\) obtained by quantizing \(|{\rm increment}|\) relative to the vector's own standard deviation; IncrEn is the Shannon entropy of the resulting word distribution, normalized by \(m - 1\). Because it encodes both the direction and the graded size of changes, it is sensitive to dynamics that amplitude-based entropies miss, and is a distinct mechanism from the amplitude-histogram (renyiEntropy, tsallisEntropy), NCDF-pattern (dispersionEntropy) and template-matching (fuzzyEntropy) entropies.

Usage

incrementEntropy(x, dimension = 2L, q = 4L)

Arguments

x: A numeric vector (the time series).
dimension: Embedding dimension \(m\) of the increment words (default 2).
q: Number of magnitude quantization levels (default 4); each increment is binned into one of q + 1 magnitude classes by its size relative to the embedding vector's standard deviation.

Value

A single numeric value, the increment entropy.

Details

This implementation reproduces NeuroKit2's entropy_increment bit-for-bit.

References

Liu, X., Jiang, A., Xu, N., & Xue, J. (2016). "Increment Entropy as a Measure of Complexity for Time Series." Entropy, 18(1), 22. doi:10.3390/e18010022

Examples

set.seed(1)
incrementEntropy(rnorm(1000), dimension = 2, q = 4)
#> [1] 4.588031