import numpy as np
import pandas as pd
from ..stats import rescale
[docs]
def fractal_sevcik(signal):
"""**Sevcik Fractal Dimension (SFD)**
The SFD algorithm was proposed to calculate the fractal dimension of waveforms by Sevcik
(1998). This method can be used to quickly measure the complexity and randomness of a signal.
.. note:: Some papers (e.g., Wang et al. 2017) suggest adding ``np.log(2)`` to the numerator,
but it's unclear why, so we sticked to the original formula for now. But if you have an idea,
please let us know!
Parameters
----------
signal : Union[list, np.array, pd.Series]
The signal (i.e., a time series) in the form of a vector of values.
Returns
---------
sfd : float
The sevcik fractal dimension.
info : dict
An empty dictionary returned for consistency with the other complexity functions.
See Also
--------
fractal_petrosian
Examples
----------
.. ipython:: python
import neurokit2 as nk
signal = nk.signal_simulate(duration=2, frequency=5)
sfd, _ = nk.fractal_sevcik(signal)
sfd
References
----------
* Sevcik, C. (2010). A procedure to estimate the fractal dimension of waveforms. arXiv preprint
arXiv:1003.5266.
* Kumar, D. K., Arjunan, S. P., & Aliahmad, B. (2017). Fractals: applications in biological
Signalling and image processing. CRC Press.
* Wang, H., Li, J., Guo, L., Dou, Z., Lin, Y., & Zhou, R. (2017). Fractal complexity-based
feature extraction algorithm of communication signals. Fractals, 25(04), 1740008.
* Goh, C., Hamadicharef, B., Henderson, G., & Ifeachor, E. (2005, June). Comparison of fractal
dimension algorithms for the computation of EEG biomarkers for dementia. In 2nd International
Conference on Computational Intelligence in Medicine and Healthcare (CIMED2005).
"""
# Sanity checks
if isinstance(signal, (np.ndarray, pd.DataFrame)) and signal.ndim > 1:
raise ValueError(
"Multidimensional inputs (e.g., matrices or multichannel data) are not supported yet."
)
# 1. Normalize the signal (new range to [0, 1])
y_ = rescale(signal, to=[0, 1])
n = len(y_)
# 2. Derive x* and y* (y* is actually the normalized signal)
x_ = np.linspace(0, 1, n)
# 3. Compute L (because we use np.diff, hence n-1 below)
L = np.sum(np.sqrt(np.diff(y_) ** 2 + np.diff(x_) ** 2))
# 4. Compute the fractal dimension (approximation)
sfd = 1 + np.log(L) / np.log(2 * (n - 1))
# Some papers (e.g., Wang et al. 2017) suggest adding np.log(2) to the numerator:
# sfd = 1 + (np.log(L) + np.log(2)) / np.log(2 * (n - 1))
# But it's unclear why. Sticking to the original formula for now.
# If you have an idea, let us know!
return sfd, {}
