EntropyHub 0.2

An open-source toolkit for entropic time series analysis.

EntropyHub: An open-source toolkit for entropic time series analysis

Python Edition

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About

Information and uncertainty can be regarded as two sides of the same coin: the more uncertainty there is, the more information we gain by removing that uncertainty. In the context of information and probability theory, Entropy quantifies that uncertainty.

The concept of entropy has its origins in classical physics under the second law of thermodynamics, a law considered to underpin our fundamental understanding of time in physics. Attempting to analyse the analog world around us requires that we measure time in discrete steps, but doing so compromises our ability to measure entropy accurately. Various measures have been derived to estimate entropy (uncertainty) from discrete time series, each seeking to best capture the uncertainty of the system under examination. This has resulted in many entropy statistics from approximate entropy and sample entropy, to multiscale sample entropy and refined-composite multiscale cross-sample entropy.

As the number of statisitcal entropy measures grows, it becomes more difficult to identify, contrast and compare the performance of each measure. To overcome this, we have developed EntropyHub - an open-source toolkit designed to integrate the many established entropy methods into one package. The goal of EntropyHub is to provide a comprehensive set of functions with a simple and consistent syntax that allows the user to augment parameters at the command line, enabling a range from basic to advanced entropy methods to be implemented with ease.

It is important to clarify that the entropy functions herein described estimate entropy in the context of probability theory and information theory as defined by Shannon, and not thermodynamic or other entropies from classical physics.

Installation

There are two ways to install EntropyHub for Python. Method 1 is strongly recommended.

Method 1:

1. Using pip in your python IDE, type: pip install EntropyHub

Method 2:

1. Download the folder above (EntropyHub.x.x.x.tar.gz) and unzip it.
2. Open a command terminal (cmd on Windows, terminal on Mac) or use the Anaconda prompt if you use Anaconda as your python package distribution.
3. In the command prompt/terminal, navigate to the directory where you saved and extracted the .tar.gz folder.
4. Enter the following in the command line: python setup.py install

System Requirements & Dependencies

There are several package dependencies which will be installed alongside EntropyHub: Numpy, Scipy, Matplotlib, PyEMD

EntropyHub was designed using Python 3 and thus is not intended for use with Python 2. Python versions > 3.6 are required for using EntropyHub.

Documentation & Help

A key advantage of EntropyHub is the comprehensive documentation available to help users to make the most of the toolkit. One can simply access the docstrings of a function (like any Python function) by typing help FunctionName in the command line, which will print the docstrings.

All information on the EntropyHub package is detailed in the EntropyHub Guide, a .pdf document available here.

Functions

EntropyHub functions fall into 5 categories:

* Base                functions for estimating the entropy of a single univariate time series.
* Cross               functions for estimating the entropy between two univariate time series.
* Bidimensional       functions for estimating the entropy of a two-dimensional univariate matrix.
* Multiscale          functions for estimating the multiscale entropy of a single univariate time series using any of the Base entropy functions.
* Multiscale Cross    functions for estimating the multiscale entropy between two univariate time series using any of the Cross-entropy functions.

The following tables outline the functions available in the EntropyHub package.

When new entropies are published in the scientific literature, efforts will be made to incorporate them in future releases.

Base Entropies:

Entropy Type	Function Name
Approximate Entropy	ApEn
Sample Entropy	SampEn
Fuzzy Entropy	FuzzEn
Kolmogorov Entropy	K2En
Permutation Entropy	PermEn
Conditional Entropy	CondEn
Distribution Entropy	DistEn
Spectral Entropy	SpecEn
Dispersion Entropy	DispEn
Symbolic Dynamic Entropy	SyDyEn
Increment Entropy	IncrEn
Cosine Similarity Entropy	CoSiEn
Phase Entropy	PhasEn
Slope Entropy	SlopEn
Bubble Entropy	BubbEn
Gridded Distribution Entropy	GridEn
Entropy of Entropy	EnofEn
Attention Entropy	AttnEn

---

Cross Entropies:

Entropy Type	Function Name
Cross Sample Entropy	XSampEn
Cross Approximate Entropy	XApEn
Cross Fuzzy Entropy	XFuzzEn
Cross Permutation Entropy	XPermEn
Cross Conditional Entropy	XCondEn
Cross Distribution Entropy	XDistEn
Cross Spectral Entropy	XSpecEn
Cross Kolmogorov Entropy	XK2En

---

Bidimensional Entropies

Entropy Type	Function Name
Bidimensional Sample Entropy	SampEn2D
Bidimensional Fuzzy Entropy	FuzzEn2D
Bidimensional Distribution Entropy	DistEn2D
Bidimensional Dispersion Entropy	DispEn2D
Bidimensional Permutation Entropy	PermEn2D
Bidimensional Espinosa Entropy	EspEn2D

---

Multiscale Entropy Functions

Entropy Type	Function Name
Multiscale Entropy	MSEn
Composite/Refined-Composite Multiscale Entropy	cMSEn
Refined Multiscale Entropy	rMSEn
Hierarchical Multiscale Entropy	hMSEn

---

Multiscale Cross-Entropy Functions

Entropy Type	Function Name
Multiscale Cross-Entropy	XMSEn
Composite/Refined-Composite Multiscale Cross-Entropy	cXMSEn
Refined Multiscale Cross-Entropy	rXMSEn
Hierarchical Multiscale Cross-Entropy	hXMSEn

License and Terms of Use

EntropyHub is licensed under the Apache License (Version 2.0) and is free to use by all on condition that the following reference be included on any outputs realized using the software:

    Matthew W. Flood and Bernd Grimm (2021), 
    EntropyHub: An Open-Source Toolkit for Entropic Time Series Analysis,
    PLoS ONE 16(11):e0259448
    DOI: 10.1371/journal.pone.0259448
    www.EntropyHub.xyz

---

    © Copyright 2021 Matthew W. Flood, EntropyHub
    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

             http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.

    For Terms of Use see https://www.EntropyHub.xyz

Contact

If you find this package useful, please consider starring it on GitHub, MatLab File Exchange, PyPI or Julia Packages as this helps us to gauge user satisfaction.

For general queries and information about EntropyHub, contact: [e-mail] If you have any questions or need help using the package, please contact us at: [e-mail] If you notice or identify any issues, please do not hesitate to contact us at: [e-mail]

Thank you for using EntropyHub.

Yours in research,

Matt