Available in MatLab // Python // Julia
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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To install EntropyHub with Matlab, Python or Julia, please follow the instructions given in the relevant folder above.
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.
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.
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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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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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://github.com/MattWillFlood/EntropyHub
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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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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.
When new entropies are published in the scientific literature, efforts will be made to incorporate them in future releases.
| 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 |
| 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 |
| 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 |
| Entropy Type | Function Name |
|---|---|
| Multiscale Entropy | MSEn |
| Composite/Refined-Composite Multiscale Entropy | cMSEn |
| Refined Multiscale Entropy | rMSEn |
| Hierarchical Multiscale Entropy | hMSEn |
| 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 |
___ _ _ _____ _____ ____ ____ _ _
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| \_ | \| | | | | __/| || __| \ \_/ / / _______ \
| _|| \ \ | | | | \ | || | \ / | / ___ \ |
| \_ | |\ | | | | |\ \ | || | | | | | / \ | |
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| | | || | | || \ An open-source | /\______\__|_/
| |_| || | | || | toolkit for | | / \ | |
| _ || | | || \ entropic time- | | \___/ | |
| | | || |_| || \ series analysis | \_______/ |
|_| |_|\_____/|_____/ \___________/
