spkit.entropy_permutation

spkit.entropy_permutation(x, order=3, delay=1, base=2, normalize=False)

Permutation Entropy \(H_{\pi}(X)\)

Permutation Entropy extracts the patterns as order of embeddings, and compute the entropy of the distribuation of the patterns.

The order of embeddings is the sorting order. For example, pattern of embedding e1 = [1,2,-2], is same as pattern of embedding e2 = [1,20,-5].

Parameters:

x1d-array, shape (n,)

• input signal

orderint, default=3

• Embedding dimension (order).

delayint, default=1

• Delay.

base: scalar>0, deafult=2

• base of log, 2, 10, ‘e’

normalize: bool, default=False

• if True, Hx is normalised

Returns:

H_pi: scalar,

• Permutation Entropy

See also

entropy

Entropy

entropy_sample

Sample Entropy

entropy_approx

Approximate Entropy

dispersion_entropy

Dispersion Entropy

entropy_spectral

Spectral Entropy

entropy_svd

SVD Entropy

entropy_differential

Differential Entropy

References

• Bandt, Christoph, and Bernd Pompe. “Permutation entropy: a natural complexity measure for time series.” Physical review letters 88.17 (2002): 174102.

Examples

>>> import numpy as np
>>> import spkit as sp
>>> t = np.linspace(0,2,200)
>>> x1 = np.sin(2*np.pi*1*t) + 0.01*np.random.randn(len(t))  # less noisy
>>> x2 = np.sin(2*np.pi*1*t) + 0.5*np.random.randn(len(t))  # very noisy
>>> H_x1 = sp.entropy_permutation(x1,order=3, delay=1)
>>> H_x2 = sp.entropy_permutation(x2,order=3, delay=1)
>>> print('Permutation Entropy ')
>>> print('Entropy of x1: H_p(x1) = ',H_x1)
>>> print('Entropy of x2: H_p(x2) = ',H_x2)
Permutation Entropy 
Entropy of x1: H_p(x1) =  1.5156504111997058
Entropy of x2: H_p(x2) =  2.556358399367036