ordpy 1.0.0

A Python package for data analysis with permutation entropy and ordinal networks methods.

ordpy: A Python Package for Data Analysis with Permutation Entropy and Ordinal Network Methods

ordpy is a pure Python module [1] that implements data analysis methods based on Bandt and Pompe’s [2] symbolic encoding scheme.

Note

If you have used ordpy in a scientific publication, we would appreciate citations to the following reference [1]:

• A. A. B. Pessa, H. V. Ribeiro, ordpy: A Python package for data analysis with permutation entropy and ordinal network methods, ????, ??-?? (2021).

@article{pessa2021ordpy,
  title    = {ordpy: A Python Package for Data Analysis with Permutation
              Entropy and Ordinal Network Methods},
  author   = {Pessa, Arthur A. B. and Ribeiro, Haroldo V.},
  journal  = {?},
  volume   = {?},
  number   = {?},
  pages    = {?},
  year     = {2021},
  doi      = {?}
}

ordpy implements the following data analysis methods:

• Permutation entropy for time series [2] and images [3];

• Complexity-entropy plane for time series [4], [5] and images [3];

• Multiscale complexity-entropy plane for time series [6] and images [7];

• Tsallis [8] and Rényi [9] generalized complexity-entropy curves for time series and images;

• Ordinal networks for time series [10], [11] and images [12];

• Global node entropy of ordinal networks for time series [13], [11] and images [12].

Installing

Ordpy can be installed via the command line using

pip install ordpy

or you can directly clone its git repository:

git clone https://github.com/arthurpessa/ordpy.git
cd ordpy
pip install -e .

Basic usage

We provide a notebook illustrating how to use ordpy. This notebook reproduces all figures of our article [1]. The code below shows simple applications of ordpy.

#Complexity-entropy plane for logistic map and Gaussian noise.

import numpy as np
import ordpy
from matplotlib import pylab as plt

def logistic(a=4, n=100000, x0=0.4):
    x = np.zeros(n)
    x[0] = x0
    for i in range(n-1):
        x[i+1] = a*x[i]*(1-x[i])
    return(x)

time_series = [logistic(a) for a in [3.05, 3.55, 4]]
time_series += [np.random.normal(size=100000)]

HC = [ordpy.complexity_entropy(series, dx=4) for series in time_series]


f, ax = plt.subplots(figsize=(8.19, 6.3))

for HC_, label_ in zip(HC, ['Period-2 (a=3.05)',
                            'Period-8 (a=3.55)',
                            'Chaotic (a=4)',
                            'Gaussian noise']):
    ax.scatter(*HC_, label=label_, s=100)

ax.set_xlabel('Permutation entropy, $H$')
ax.set_ylabel('Statistical complexity, $C$')

ax.legend()

#Ordinal networks for logistic map and Gaussian noise.

import numpy as np
import igraph
import ordpy
from matplotlib import pylab as plt
from IPython.core.display import display, SVG

def logistic(a=4, n=100000, x0=0.4):
    x = np.zeros(n)
    x[0] = x0
    for i in range(n-1):
        x[i+1] = a*x[i]*(1-x[i])
    return(x)

time_series = [logistic(a=4), np.random.normal(size=100000)]

vertex_list, edge_list, edge_weight_list = list(), list(), list()
for series in time_series:
    v_, e_, w_   = ordpy.ordinal_network(series, dx=4)
    vertex_list += [v_]
    edge_list   += [e_]
    edge_weight_list += [w_]

def create_ig_graph(vertex_list, edge_list, edge_weight):

    G = igraph.Graph(directed=True)

    for v_ in vertex_list:
        G.add_vertex(v_)

    for [in_, out_], weight_ in zip(edge_list, edge_weight):
        G.add_edge(in_, out_, weight=weight_)

    return G

graphs = []

for v_, e_, w_ in zip(vertex_list, edge_list, edge_weight_list):
    graphs += [create_ig_graph(v_, e_, w_)]

def igplot(g):
    f = igraph.plot(g,
                    layout=g.layout_circle(),
                    bbox=(500,500),
                    margin=(40, 40, 40, 40),
                    vertex_label = [s.replace('|','') for s in g.vs['name']],
                    vertex_label_color='#202020',
                    vertex_color='#969696',
                    vertex_size=20,
                    vertex_font_size=6,
                    edge_width=(1 + 8*np.asarray(g.es['weight'])).tolist(),
                   )
    return f

for graph_, label_ in zip(graphs, ['Chaotic (a=4)',
                                   'Gaussian noise']):
    print(label_)
    display(SVG(igplot(graph_)._repr_svg_()))

References

[1] (1,2,3)

Pessa, A. A., & Ribeiro, H. V. (2021). ordpy: A Python package for data analysis with permutation entropy and ordinal networks methods. arXiv preprint arXiv:2007.03090.

[2] (1,2)

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

[3] (1,2)

Ribeiro, H. V., Zunino, L., Lenzi, E. K., Santoro, P. A., & Mendes, R. S. (2012). Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns. PLOS ONE, 7, e40689.

[4]

Lopez-Ruiz, R., Mancini, H. L., & Calbet, X. (1995). A Statistical Measure of Complexity. Physics Letters A, 209, 321-326.

[5]

Rosso, O. A., Larrondo, H. A., Martin, M. T., Plastino, A., & Fuentes, M. A. (2007). Distinguishing Noise from Chaos. Physical Review Letters, 99, 154102.

[6]

Zunino, L., Soriano, M. C., & Rosso, O. A. (2012). Distinguishing Chaotic and Stochastic Dynamics from Time Series by Using a Multiscale Symbolic Approach. Physical Review E, 86, 046210.

[7]

Zunino, L., & Ribeiro, H. V. (2016). Discriminating Image Textures with the Multiscale Two-Dimensional Complexity-Entropy Causality Plane. Chaos, Solitons & Fractals, 91, 679-688.

[8]

Ribeiro, H. V., Jauregui, M., Zunino, L., & Lenzi, E. K. (2017). Characterizing Time Series Via Complexity-Entropy Curves. Physical Review E, 95, 062106.

[9]

Jauregui, M., Zunino, L., Lenzi, E. K., Mendes, R. S., & Ribeiro, H. V. (2018). Characterization of Time Series via Rényi Complexity-Entropy Curves. Physica A, 498, 74-85.

[10]

Small, M. (2013). Complex Networks From Time Series: Capturing Dynamics. In 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013) (pp. 2509-2512). IEEE.

[11] (1,2)

Pessa, A. A., & Ribeiro, H. V. (2019). Characterizing Stochastic Time Series With Ordinal Networks. Physical Review E, 100, 042304.

[12] (1,2)

Pessa, A. A., & Ribeiro, H. V. (2020). Mapping Images Into Ordinal Networks. Physical Review E, 102, 052312.

[13]

McCullough, M., Small, M., Iu, H. H. C., & Stemler, T. (2017). Multiscale Ordinal Network Analysis of Human Cardiac Dynamics. Philosophical Transactions of the Royal Society A, 375, 20160292.

[14]

Amigó, J. M., Zambrano, S., & Sanjuán, M. A. F. (2007). True and False Forbidden Patterns in Deterministic and Random Dynamics. Europhysics Letters, 79, 50001.

[15]

Martin, M. T., Plastino, A., & Rosso, O. A. (2006). Generalized Statistical Complexity Measures: Geometrical and Analytical Properties, Physica A, 369, 439–462.