HFD {musclesyneRgies}

Higuchi's fractal dimension

Description

Higuchi's fractal dimension

Usage

HFD(P, k_max = 10)

Arguments

P

A time series (numeric)

k_max

Maximum window length in points

Details

The Higuchi’s fractal dimension is a measure of local complexity and it increases together with the “roughness” of the time series at a single cycle level (thus the term “local”). Higuchi’s fractal dimension values range from 1 to 2, with increasing values correlating to increasingly complex data and Higuchi’s fractal dimension = 1.5 indicating random Gaussian noise (Higuchi, 1988; Anmuth et al., 1994; Kesić & Spasić, 2016) For motor primitives, only the most linear part of the log-log plot should be used, as reported in Santuz, Akay (2020).

Value

A list with elements:

• loglog containing the log-log plot from which the HFD is calculated
  

• Higuchi containing the Higuchi's fractal dimension of the time series.

References

Higuchi, T. Approach to an irregular time series on the basis of the fractal theory. Phys. D Nonlinear Phenom. 31, 277–283 (1988).

Anmuth C. J., Goldberg G. & Mayer N. H. Fractal dimension of electromyographic signals recorded with surface electrodes during isometric contractions is linearly correlated with muscle activation. Muscle Nerve 17, 953–954 (1994).

Kesić S. & Spasić S. Z. Application of Higuchi’s fractal dimension from basic to clinical neurophysiology: A review. Comput Methods Programs Biomed 133, 55–70 (2016).

Santuz, A. & Akay, T. Fractal analysis of muscle activity patterns during locomotion: pitfalls and how to avoid them. J. Neurophysiol. 124, 1083–1091 (2020).

Examples

# Measurements of the annual flow of the river Nile at Aswan
flow <- datasets::Nile

# Calculate HFD
fractal_dimension <- HFD(flow)$Higuchi
message("Higuchi's fractal dimension: ", round(fractal_dimension, 3))

# Thirty-cycle locomotor primitive from Santuz & Akay (2020)
data(primitive)
fractal_dimension <- HFD(primitive$signal)$Higuchi
message("Higuchi's fractal dimension: ", round(fractal_dimension, 3))