EntropyHub: An open-source toolkit for entropic data analysis

Julia Edition

Latest Update

v2.0

----- New multivariate methods -----
Five new multivariate entropy functions incorporating several method-specific variations
> Multivariate Sample Entropy
> Multivariate Fuzzy Entropy [++ many fuzzy functions]
> Multivariate Dispersion Entropy [++ many symbolic sequence transforms]
> Multivariate Cosine Similarity Entropy
> Multivariate Permutation Entropy [++ amplitude-aware, edge, phase, weighted and modified variants]

----- New multivariate multiscale methods -----
Two new multivariate multiscale entropy functions
> Multivariate Multiscale Entropy [++ coarse, modified and generalized graining procedures]
> Composite and Refined-composite Multivariate Multiscale Entropy

----- Extra signal processing tools -----
WindowData() is a new function that allows users to segment data (univariate or multivariate time series) into windows with/without overlapping samples! This allows users to calculate entropy on subsequences of their data to perform analyses with greater time resolution.

Other little fixes...

----- Docs edits -----
- Examples in the www.EntropyHub.xyz documentation were updated to match the latest package syntax.

Welcome

This toolkit provides a wide range of functions to calculate different entropy statistics. There is an ever-growing range of information-theoretic and dynamical systems entropy measures presented in the scientific literature. The goal of EntropyHub is to integrate the many established entropy methods in one open-source package.

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. 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.

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 Julia.

Method 1:

In Julia, open the package REPL by typing ]. The command line should appear as:

@vX.Y. pkg>

Where X and Y refer to your version of Julia.
Type:

add EntropyHub

(Note: this is case sensitive)

Alternatively, one can use the Pkg module to perform the same procedure:

using Pkg

Pkg.add("EntropyHub")

Method 2:

In Julia, open the package REPL by typing ]. The command line should appear as:

@vX.Y. pkg>

Where X and Y refer to your version of Julia.
Type:

add https://github.com/MattWillFlood/EntropyHub.jl

(Note: this is case sensitive)

System Requirements

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, DataInterpolations, Clustering

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

Documentation & Help

A key advantage of EntropyHub is the comprehensive documentation available to help users to make the most of the toolkit.

To learn more about a specific function, one can do so easily from the command line by typing: ?, which will open the julia help system, and then typing the function name.

For example:

julia> ?  
help?> SampEn	  # Documentation on sample entropy function

julia> ?  
help?> XSpecEn    # Documentation on cross-spectral entropy function

julia> ?
help?> hXMSEn     # Documentation on hierarchical multiscale cross-entropy function

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

Functions

EntropyHub functions fall into 8 categories:

* Base                       functions for estimating the entropy of a single univariate time series.
* Cross                      functions for estimating the entropy between two univariate time series.
* Multivariate               functions for estimating the entropy of a multivariate dataset.
* 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.
* Multivariate Multiscale    functions for estimating the multivariate multiscale entropy of multivariate dataset using any of the Multivariate-entropy functions.
* Other                      Supplementary functions for various tasks related to EntropyHub and signal processing.

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 Range Entropy | RangEn Diversity Entropy | DivEn

Cross Entropies:

Multivariate Entropies:

Bidimensional Entropies

EntropyHub.jl

Install / Use

README