mpePy: A Python Package for Data Analysis with Multivariate Permutation Entropy for Time Series

mpepy is a pure Python module that implements data analysis methods based on Bandt and Pompe's [1] symbolic encoding scheme.

mpepy implements the following data analysis methods:

• Pooled Permutation Entropy [2];
• Multivariate Multiscale Permutation Entropy [3];
• Multivariate Weighted Permutation Entropy [4];
• Multivariate Ordinal Pattern Permutation Entropy [5];
• Multivariate Permutation Entropy based on Principal Component Analysis [5]

Installing

mpePy can be installed via the command line using

pip install mpepy

or you can directly clone its git repository:

git clone https://github.com/marisamohr/mpePy.git
cd mpepy
pip install -e .

Basic usage

# Computing different multivariate permutation entropies for fractional Brownian motion.

import subprocess
import csv
import pandas as pd
import mpepy as mpe


# Example of data simulation: multivariate fractional Brownian motion
# usage of R-package
def simulateMultiFracBrownMotion(n, H_1, H_2, H_3, H_4, H_5, rho):
    output_file_name = './intermediate_output/MultiFracBrownMotionOutput.csv'
    subprocess.check_call(['Rscript', './intermediate_output/simulation_mfBm.R', str(n), str(H_1), str(H_2), str(H_3), str(H_4), str(H_5), str(rho), output_file_name], shell=False)
    arr = []
    with open(output_file_name, 'r') as file:
        reader = csv.reader(file)
        for row in reader:
            arr.append(row)
    mfbm = pd.DataFrame.from_records(arr)
    mfbm = mfbm.apply(pd.to_numeric)
    return mfbm
# simulation
mfbm = simulateMultiFracBrownMotion(2000, 0.3, 0.6, None, None, None, 0.0)
mfbm = mfbm.T


# Examples of multivariate permutation entropy calculation
mpe.pooled_permutation_entropy(mfbm, order = 3 , delay = 1)
mpe.multivariate_weighted_permutation_entropy(mfbm, order = 3 , delay = 1)
mpe.multivariate_multiscale_permutation_entropy(mfbm, order = 3 , delay = 1, scale = 1)
mpe.multivariate_ordinal_pattern_permutation_entropy(mfbm, order = 2 , delay = 1)
mpe.multivariate_permutation_entropy_pca(mfbm, order = 2 , delay = 1, no_pc = 1)
mpe.multivariate_permutation_entropy_pca(mfbm, order = 3 , delay = 5, no_pc = "all")

Contributors

• Marisa Mohr(https://github.com/marisamohr)
• Nils Finke(https://github.com/FinkeNils)

References

[1]	Bandt, C., and Pompe, B. (2002). Permutation entropy: A Natural Complexity Measure for Time Series. Physical Review Letters, 88, 174102.

[2]	Keller, K., and Lauffer, H. (2003). Symbolic Analysis of High-Dimensional Time Series. International Journal of Bifurcation and Chaos, vol. 13,no. 09, pp. 2657–2668.

[3]	Morabito, F.C., Labate, D., La Foresta, F., Bramanti, A., Morabito, G., and Palamara I. (2012). Multivariate Multi-Scale Permutation Entropy for Complexity Analysis of Alzheimer’s Disease EEG. Entropy, vol. 14, no. 7.

[4]	Mohr, M., Wilhelm, F., and Möller, R. (2021). On the Behaviour of Weighted Permutation Entropy on Fractional Brownian Motion in the Univariate and Multivariate Setting. The International FLAIRS Conference Proceedings, vol. 34.

[5]	(1, 2) Mohr, M., Wilhelm, F., Hartwig, M., Möller, R., and Keller, K. (2020). New Approaches in Ordinal Pattern Representations for Multivariate Time Series. In: Proceedings of the 33rd International Florida Artificial Intelligence Research Society Conference (FLAIRS-33).