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

EntropyHub Git

Available in MatLab // Python // Julia

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.

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Installation

To install EntropyHub with Matlab, Python or Julia, please follow the instructions given in the relevant folder above.

Requirements


MatLab

There are two additional MatLab toolboxes required to exploit the full functionality of the EntropyHub toolkit:

Signal Processing Toolbox and Statistics and Machine Learning Toolbox.

However, most functions will work without these toolboxes.

EntropyHub is intended for use with MatLab versions >= 2016a. In some cases the toolkit may work on versions 2015a and 2015b, but it is not recommended to install on MatLab versions older than 2016.


Python

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

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


Julia

There are several package dependencies which will be installed alongside EntropyHub (if not already installed):

DSP, FFTW, HTTP, Random, Plots, StatsBase, StatsFuns, GroupSlices, Statistics, DelimitedFiles, Combinatorics, LinearAlgebra, Dierckx, Clustering

EntropyHub was designed using Julia 1.5 and is intended for use with Julia versions >= 1.2.

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Documentation & Help

The EntropyHub Guide is a .pdf booklet written to help you use the toolkit effectively. (available here)

In this guide you will find descriptions of function syntax, examples of function use, and references to the source literature of each function.

The MatLab version of the toolkit has a comprehensive help section which can be accessed through the help browser.

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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, 
    EntropyHub: An Open-Source Toolkit for Entropic Time Series Analysis,
    2021 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://github.com/MattWillFlood/EntropyHub

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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.

If you have any questions about the package or identify any issues, please do not hesitate to contact us at: info@entropyhub.xyz

Thank you for using EntropyHub.

Yours in research,

Matt

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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

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
     ___  _   _  _____  _____  ____  ____  _     _          
    |  _|| \ | ||_   _||     \|    ||    || \   / |   ___________ 
    | \_ |  \| |  | |  |   __/|    ||  __| \ \_/ /   /  _______  \
    |  _|| \ \ |  | |  |   \  |    || |     \   /   |  /  ___  \  |
    | \_ | |\  |  | |  | |\ \ |    || |      | |    | |  /   \  | | 
    |___||_| \_|  |_|  |_| \_||____||_|      |_|   _|_|__\___/  | | 
     _   _  _   _  ____                           / |__\______\/  | 
    | | | || | | ||    \     An open-source      |  /\______\__|_/ 
    | |_| || | | ||    |     toolkit for         | |  /   \  | | 
    |  _  || | | ||    \     entropic time-      | |  \___/  | |          
    | | | || |_| ||     \    series analysis     |  \_______/  |
    |_| |_|\_____/|_____/                         \___________/ 

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