Fuzzy Entropy

Computes the fuzzy entropy (FuzzyEn) of a one-dimensional signal (Chen et al., 2007) – the fuzzy generalization of the sample entropy. Sample entropy counts template matches with a crisp threshold (a Heaviside step: two vectors either match within tolerance \(r\) or do not); fuzzy entropy replaces that hard step with a smooth exponential membership \(\mu = \exp(-(d^{n})/r)\), so near-matches contribute partially. This makes FuzzyEn markedly more robust and continuous than sample entropy, especially on short or noisy segments where the crisp count is unstable. Each embedding vector has its own baseline (mean) removed before the Chebyshev distance is taken, following Chen et al.

Usage

fuzzyEntropy(x, dimension = 2L, r = 0.2, delay = 1L, n = 1)

Arguments

x: A numeric vector (the time series).
dimension: Embedding dimension \(m\) (default 2).
r: Tolerance as a fraction of the signal's standard deviation; the distance tolerance is r * sd(x) (default 0.2, matching NeuroKit2's tolerance = "sd").
delay: Time delay (lag) in samples (default 1).
n: Fuzzy power (exponent) of the membership function (default 1).

Value

A single numeric value, the fuzzy entropy.

Details

This implementation reproduces NeuroKit2's entropy_fuzzy bit-for-bit (the default tolerance = "sd" there corresponds to r = 0.2).

References

Chen, W., Zhuang, J., Yu, W., & Wang, Z. (2009). "Measuring complexity using FuzzyEn, ApEn, and SampEn." Medical Engineering & Physics, 31(1), 61–68. doi:10.1016/j.medengphy.2008.04.005

Examples

set.seed(1)
fuzzyEntropy(rnorm(300), dimension = 2)   # fuzzy generalization of sample entropy
#> [1] 1.647206