entropy.app_entropy

entropy.app_entropy(x, order=2, metric='chebyshev')

Approximate Entropy.

Parameters

xlist or np.array

One-dimensional time series of shape (n_times).

orderint

Embedding dimension. Default is 2.

metricstr

Name of the distance metric function used with sklearn.neighbors.KDTree. Default is to use the Chebyshev distance.

Returns

aefloat

Approximate Entropy.

Notes

Approximate entropy is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data. Smaller values indicates that the data is more regular and predictable.

The tolerance value (\(r\)) is set to \(0.2 * \text{std}(x)\).

Code adapted from the mne-features package by Jean-Baptiste Schiratti and Alexandre Gramfort.

References

Richman, J. S. et al. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), H2039-H2049.

https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.DistanceMetric.html

Examples

Fractional Gaussian noise with H = 0.5

>>> import numpy as np
>>> import entropy as ent
>>> import stochastic.processes.noise as sn
>>> rng = np.random.default_rng(seed=42)
>>> x = sn.FractionalGaussianNoise(hurst=0.5, rng=rng).sample(10000)
>>> print(f"{ent.app_entropy(x, order=2):.4f}")
2.1958

Same with order = 3 and metric = ‘euclidean’

>>> print(f"{ent.app_entropy(x, order=3, metric='euclidean'):.4f}")
1.5120

Fractional Gaussian noise with H = 0.9

>>> rng = np.random.default_rng(seed=42)
>>> x = sn.FractionalGaussianNoise(hurst=0.9, rng=rng).sample(10000)
>>> print(f"{ent.app_entropy(x):.4f}")
1.9681

Fractional Gaussian noise with H = 0.1

>>> rng = np.random.default_rng(seed=42)
>>> x = sn.FractionalGaussianNoise(hurst=0.1, rng=rng).sample(10000)
>>> print(f"{ent.app_entropy(x):.4f}")
2.0906

Random

>>> rng = np.random.default_rng(seed=42)
>>> print(f"{ent.app_entropy(rng.random(1000)):.4f}")
1.8177

Pure sine wave

>>> x = np.sin(2 * np.pi * 1 * np.arange(3000) / 100)
>>> print(f"{ent.app_entropy(x):.4f}")
0.2009

Linearly-increasing time-series

>>> x = np.arange(1000)
>>> print(f"{ent.app_entropy(x):.4f}")
-0.0010