Slope Entropy

Computes the slope entropy (SlopEn) of a one-dimensional signal (Cuesta-Frau, 2019) – a symbolic complexity measure defined on the slopes between successive samples. Each first difference is turned into the angle \(\theta = \arctan(\Delta x)\) (in degrees) and mapped to one of five symbols by two angle thresholds: steep-up (\(> \gamma\)), gentle-up (\((\delta, \gamma]\)), flat (\([-\delta, \delta]\)), gentle-down and steep-down; SlopEn is the Shannon entropy of the resulting length-(m-1) slope patterns. By combining a coarse (steep/gentle) and fine (flat) angular resolution it captures the shape of local trends, a mechanism distinct from the amplitude, NCDF-pattern, template-matching and increment-magnitude entropies.

Usage

slopeEntropy(x, dimension = 3L, thresholds = c(0.1, 45), delay = 1L)

Arguments

x: A numeric vector (the time series).
dimension: Embedding dimension \(m\) (default 3); slope patterns have length dimension - 1.
thresholds: Increasing positive angle thresholds (degrees) that split the slope into symbol classes (default c(0.1, 45): a flat band within +/-0.1 deg, a gentle band up to +/-45 deg, and a steep class beyond).
delay: Time delay (lag) in samples for the difference (default 1).

Value

A single numeric value, the slope entropy (bits).

Details

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

References

Cuesta-Frau, D. (2019). "Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information." Entropy, 21(12), 1167. doi:10.3390/e21121167

Examples

set.seed(1)
slopeEntropy(rnorm(1000), dimension = 3)
#> [1] 3.865113