Entropi deret waktu python

Gerakan Manusia, Ortopedi, Kedokteran Olahraga dan Metode Digital (HOSD), Institut Kesehatan Luksemburg (LIH), Eich, Luksemburg

Temukan artikel oleh Matthew W. Banjir

Bernd Grimm

Gerakan Manusia, Ortopedi, Kedokteran Olahraga dan Metode Digital (HOSD), Institut Kesehatan Luksemburg (LIH), Eich, Luksemburg

Temukan artikel oleh Bernd Grimm

Masya Allah Rezakazemi, Editor

Penafian

Gerakan Manusia, Ortopedi, Kedokteran Olahraga dan Metode Digital (HOSD), Institut Kesehatan Luksemburg (LIH), Eich, Luksemburg

Universitas Teknologi Shahrood, REPUBLIK ISLAM IRAN

Minat Bersaing. Para penulis telah menyatakan bahwa tidak ada kepentingan yang bersaing

* Surel. ul. hil@doolf. wehttam

Diterima 2021 Juli 1;

Hak Cipta © 2021 Banjir, Grimm

Ini adalah artikel akses terbuka yang didistribusikan di bawah ketentuan Lisensi Atribusi Creative Commons, yang mengizinkan penggunaan, distribusi, dan reproduksi tanpa batas dalam media apa pun, asalkan penulis dan sumber asli dikreditkan

Data Terkait

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Abstrak

An increasing number of studies across many research fields from biomedical engineering to finance are employing measures of entropy to quantify the regularity, variability or randomness of time series and image data. Entropi, yang berkaitan dengan teori informasi dan teori sistem dinamik, dapat diperkirakan dengan banyak cara, dengan metode yang baru dikembangkan terus diperkenalkan dalam literatur ilmiah. Terlepas dari meningkatnya minat dalam deret waktu entropik dan analisis gambar, ada kekurangan alat perangkat lunak sumber terbuka yang divalidasi yang memungkinkan peneliti untuk menerapkan metode ini. Hingga saat ini, paket untuk melakukan analisis entropi sering dijalankan menggunakan antarmuka pengguna grafis, tidak memiliki dokumentasi pendukung yang diperlukan, atau tidak menyertakan fungsi untuk metode entropi lanjutan, seperti entropi silang, entropi lintas multiskala, atau entropi bidimensi. Sehubungan dengan hal ini, makalah ini memperkenalkan EntropyHub, perangkat sumber terbuka untuk melakukan analisis deret waktu entropik di MATLAB, Python, dan Julia. EntropyHub (version 0. 1) menyediakan berbagai lebih dari empat puluh fungsi untuk memperkirakan entropi lintas, multiskala, lintas multiskala, dan bidimensi, masing-masing termasuk sejumlah argumen kata kunci yang memungkinkan pengguna untuk menentukan beberapa parameter dalam perhitungan entropi. Petunjuk pemasangan, deskripsi sintaks fungsi, dan contoh penggunaan dirinci sepenuhnya dalam dokumentasi pendukung, tersedia di situs web EntropyHub– www. EntropyHub. xyz. Kompatibel dengan sistem operasi Windows, Mac dan Linux, EntropyHub dihosting di GitHub, serta repositori paket asli untuk MATLAB, Python, dan Julia, masing-masing. Tujuan dari EntropyHub adalah untuk mengintegrasikan banyak metode entropi yang sudah mapan ke dalam satu sumber daya yang lengkap, menyediakan alat yang membuat analisis deret waktu entropik tingkat lanjut menjadi mudah dan dapat direproduksi

pengantar

Melalui lensa probabilitas, informasi dan ketidakpastian dapat dilihat sebagai hubungan yang berlawanan—semakin banyak ketidakpastian, semakin banyak informasi yang kita peroleh dengan menghilangkan ketidakpastian tersebut. Ini adalah prinsip di balik formulasi entropi Shannon (1) yang mengukur ketidakpastian karena berkaitan dengan proses acak []

H(X)=−∑i=1np(xi)logbp(xi)

(1)

di mana H(X) adalah entropi (H) dari urutan (X) mengingat probabilitas (p) keadaan (xi). Perpanjangan dari entropi Shannon, entropi bersyarat (2) mengukur informasi yang diperoleh tentang proses (X) tergantung pada informasi sebelumnya yang diberikan oleh proses Y,

H(X. Y)=−∑i=1np(xi. Y=y)logbp(xi. Y=y)

(2)

di mana y dapat mewakili keadaan sistem yang terpisah atau keadaan sebelumnya dari sistem yang sama. Sejak saat itu, banyak varian telah diturunkan dari entropi bersyarat, dan pada tingkat yang lebih rendah entropi Shannon, untuk memperkirakan konten informasi data deret waktu di berbagai domain ilmiah [], menghasilkan apa yang baru-baru ini disebut "alam semesta entropi" []. Alam semesta entropi ini terus berkembang karena semakin banyak metode diturunkan dengan sifat statistik yang lebih baik dari prekursornya, seperti ketahanan terhadap panjang sinyal yang pendek [–], ketahanan terhadap noise [–], ketidakpekaan terhadap fluktuasi amplitudo [–]. Selain itu, varian entropi baru sedang diidentifikasi yang mengukur variabilitas data deret waktu dalam aplikasi spesifik, termasuk penilaian penyakit jantung dari elektrokardiogram [–], dan pemeriksaan kegagalan mesin dari sinyal getaran [, ]

Karena popularitas entropi menyebar di luar bidang matematika ke mata pelajaran mulai dari neurofisiologi [–] hingga keuangan [–], ada permintaan yang muncul untuk paket perangkat lunak yang dapat digunakan untuk melakukan analisis deret waktu entropik. Perangkat lunak sumber terbuka memainkan peran penting dalam mengatasi krisis replikasi dalam sains dengan menyediakan alat algoritme tervalidasi yang tersedia untuk semua peneliti [, ]. Tanpa akses ke alat perangkat lunak ini, peneliti yang kurang melek pemrograman komputer mungkin terpaksa meminjam algoritme dari sumber yang tidak diverifikasi yang rentan terhadap kesalahan pengkodean. Selain itu, paket perangkat lunak sering berfungsi sebagai titik masuk bagi peneliti yang tidak terbiasa dengan subjek untuk mengembangkan pemahaman tentang metode yang paling umum digunakan dan bagaimana penerapannya. Poin ini sangat relevan dalam konteks entropi, sebuah konsep yang sering disalahartikan [, , ], dan di mana metode varian nama dan nomor mungkin sulit untuk diikuti. Misalnya, turunan dari algoritme entropi sampel asli [], sudah merupakan peningkatan pada entropi perkiraan [], termasuk entropi sampel yang dimodifikasi (entropi fuzzy) [], entropi multiskala (sampel) [], entropi multiskala komposit [], entropi multiskala yang disempurnakan

Beberapa paket yang menawarkan fungsi terkait entropi telah dirilis dalam beberapa tahun terakhir [–], ditujukan terutama untuk analisis data fisiologis, Tabel 1. Although these packages offer some useful tools, they lack the capacity to perform extensive data analysis with multiple methods from the cross-entropy [], bidimensional entropy [], and multiscale entropy [] families of algorithms. Additionally, the utility of these packages is also limited for several reasons. The CEPS [], EZ Entropy [] and PyBioS [] packages all operate through graphical user interfaces (GUIs) with facilities to plot and process data interactively. The interactive nature of GUIs can be beneficial when analysing small datasets but becomes burdensome when analysing large datasets where automated processing tasks are advantageous. Both the CEPS [] and EZ Entropy [] are designed for the MATLAB programming environment (MathWorks, MA, USA) which requires a purchased license in order to use. This paywall prevents many users from accessing the software and consequently impedes the replication of results achieved by using these packages. Neither PyBioS nor EZ Entropy have accompanying documentation to describe how to use the software, and neither toolbox is hosted on the native package repository for MATLAB (MathWorks File Exchange) or Python (PyPi), which facilitate direct and simplified installation and updating.

Tabel 1

Daftar sumber daya yang menyediakan alat analisis entropi

NamaBahasaAntarmukaAkses TautanDetailEntropiHubMATLABBaris Perintah• MATLAB Add-On Explorer
• Indeks Paket Python (PyPi)
• JuliaHub
• GitHub
• Repo Julia GitHub
• www. EntropyHub. xyzLihat Tabel 2 untuk daftar lengkap fungsi di versi 0. 1. EntropyHub menyediakan 18 metode entropi Basis untuk analisis data univariat (mis. g. entropi sampel, entropi fuzzy, dll. ), dan 8 Metode lintas-entropi (mis. g. entropi lintas permutasi, entropi lintas distribusi). Ada juga 4 metode entropi dua dimensi untuk analisis 2D/gambar (mis. g. entropi dispersi dua dimensi, entropi sampel dua dimensi). Ada juga beberapa varian entropi multiskala yang tersedia yang dapat memanfaatkan masing-masing metode Base dan Cross-entropy. PythonJuliaCEPS []MATLABGUIBitBucketTermasuk Shannon, Rényi, minimum, Tsallis, Kolmogorov-Sinai, kondisional, koreksi-kondisional, perkiraan, sampel, fuzzy, permutasi, distribusi, dispersi, fase, kemiringan, gelembung, spektral, diferensial, difusi, dan metode entropi multiskala. PyBios []PythonGUIKontak PenulisTermasuk sampel, fuzzy, permutasi, distribusi, dispersi, fase, metode entropi multiskala. EZ Entropy []MATLABGUIGitHubMencakup perkiraan, sampel, fuzzy, permutasi, distribusi, dan metode entropi bersyarat. PhysioNet []MATLAB C*Command Linewww. PhysioNet. orgMenyediakan fungsi mandiri untuk entropi sampel, multiskala, dan transfer*.

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Tercantum di samping setiap alat adalah bahasa pemrograman yang mereka dukung, antarmuka tempat mereka beroperasi, tautan untuk mengakses perangkat lunak, dan garis besar singkat dari alat analisis entropi yang mereka sediakan.

* Implementasi pemrograman C dari entropi transfer saat ini tidak tersedia di PhysioNet

Dengan latar belakang ini, makalah ini memperkenalkan EntropyHub, perangkat sumber terbuka untuk analisis deret waktu entropik dalam lingkungan pemrograman MATLAB, Python [] dan Julia []. Menggabungkan estimator entropi dari teori informasi, teori probabilitas, dan teori sistem dinamis, EntropyHub menampilkan berbagai fungsi untuk menghitung entropi, dan entropi silang antara, data deret waktu univariat. Berbeda dengan toolbox lain yang berfokus pada entropi, EntropyHub berjalan dari baris perintah tanpa menggunakan GUI dan memberikan banyak manfaat baru, termasuk

• ■ Fungsi untuk melakukan analisis entropi multiskala halus, komposit, komposit halus, dan hirarkis menggunakan lebih dari dua puluh lima estimator entropi dan lintas entropi yang berbeda (perkiraan entropi, entropi sampel silang, dll.)

• ■ Fungsi untuk menghitung entropi dua dimensi dari data (gambar) dua dimensi

• ■ Berbagai argumen fungsi untuk menentukan nilai parameter tambahan dalam perhitungan entropi, termasuk opsi untuk rekonstruksi ruang-keadaan yang tertunda waktu dan normalisasi nilai entropi jika memungkinkan

• ■ Ketersediaan dalam berbagai bahasa pemrograman–MATLAB, Python, Julia–untuk mengaktifkan akses sumber terbuka dan menyediakan terjemahan metode lintas platform melalui sintaks fungsi yang konsisten. Sejauh pengetahuan Penulis, ini adalah perangkat khusus entropi pertama untuk bahasa Julia

• ■ Kompatibel dengan sistem operasi Windows, Mac dan Linux

• ■ Dokumentasi komprehensif yang menjelaskan penginstalan, sintaks fungsi, contoh penggunaan, dan referensi ke literatur sumber. Dokumentasi tersedia online di www. EntropyHub. xyz (atau di MattWillFlood. github. io/EntropyHub), yang juga dapat diunduh sebagai buklet (Panduan EntropyHub. pdf). Dokumentasi khusus untuk edisi MATLAB juga dapat ditemukan di bagian 'perangkat lunak tambahan' di browser bantuan MATLAB setelah instalasi. Dokumentasi khusus untuk edisi Julia juga dapat ditemukan di MattWillFlood. github. io/EntropyHub. jl/stabil

• ■ Menghosting repositori paket asli untuk MATLAB (MathWorks File Exchange), Python (PyPi), dan Julia (Julia General Registry), untuk memfasilitasi pengunduhan, penginstalan, dan pemutakhiran secara langsung. Rilis pengembangan terbaru juga dapat diunduh dari repositori EntropyHub GitHub - www. github. com/MattWillFlood/EntropyHub

Saat ukuran-ukuran baru memasuki alam semesta entropi yang terus berkembang, EntropyHub bertujuan untuk memasukkan ukuran-ukuran ini sesuai dengan itu. EntropyHub dilisensikan di bawah lisensi Apache (versi 2. 0) dan tersedia untuk digunakan oleh semua dengan syarat bahwa makalah ini dikutip pada keluaran ilmiah apa pun yang direalisasikan menggunakan perangkat EntropyHub

Bagian makalah berikut menguraikan isi toolkit, langkah-langkah untuk menginstal dan mengakses dokumentasi

Konten dan fungsi Toolkit

Fungsi dalam toolkit EntropyHub terbagi dalam lima kategori. Tiga kategori pertama—Base, Cross, dan Bidimensional—mengacu pada estimator entropi mandiri yang dibedakan menurut jenis data input yang dianalisis

• ■ Fungsi dasar mengembalikan entropi dari deret waktu univariat tunggal, mis. g. entropi sampel (SampEn), entropi gelembung (BubbEn), entropi fase (PhasEn), dll

• ■ Fungsi silang mengembalikan entropi silang antara dua deret waktu univariat, mis. g. cross-fuzzy entropy (XFuzzEn), cross-permutation entropy (XPermEn), dll

• ■ Fungsi dua dimensi mengembalikan entropi dari matriks data dua dimensi univariat, mis. g. entropi distribusi dua dimensi (DistEn2D), dll

Dua kategori yang tersisa–Multiscale dan Multiscale Cross–berkaitan dengan metode entropi multiskala menggunakan estimator entropi dari masing-masing kategori Basis dan Lintas

• ■ Fungsi multiskala mengembalikan entropi multiskala dari deret waktu univariat tunggal, yang dihitung menggunakan salah satu penaksir entropi Basis,

  ■ e. g. entropi multiskala (MSEn), entropi multiskala komposit (cMSEn), dll

• ■ Fungsi Silang Multiskala menampilkan entropi silang multiskala antara dua deret waktu univariat yang dihitung menggunakan salah satu estimator Entropi Silang,

  ■ e. g. entropi lintas multiskala (XMSEn), entropi lintas multiskala halus (rXMSEn), dll

Daftar semua fungsi yang tersedia di versi 0. 1 dari toolkit EntropyHub tersedia di Tabel 2 . Semakin banyak metode entropi yang teridentifikasi, ini akan ditambahkan ke versi toolkit yang lebih baru.

Meja 2

Daftar fungsi lintas-entropi basis, silang, bidimensi, multiskala, dan multiskala tersedia dalam versi 0. 1 dari perangkat EntropyHub

Metode EntropiNama FungsiReferensiFungsi Entropi BasisPerkiraan EntropiApEn[]EntropiPerhatianAttnEn[]Entropi GelembungBubbEn[](diperbaiki) Entropi BersyaratKonden[]Cosinus Kesamaan EntropiCoSiEn[]EntropiDispersiDispEn[, –]Distribusi EntropiDistEn[]Entropi EntropiEnofEn[]EntropiFuzzyEntropiFuzzDistribusi Berakhir[, ]

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* Objek entropi multiskala yang dikembalikan oleh fungsi MSobject adalah argumen yang diperlukan untuk fungsi Multiskala dan Silang Multiskala

** Contoh deret waktu dan data gambar dapat diimpor menggunakan fungsi ExampleData. Penggunaan fungsi ini membutuhkan koneksi internet. Data yang diimpor sama dengan yang digunakan dalam contoh yang diberikan dalam dokumentasi EntropyHub

† Berbeda dengan entropi Basis lainnya, entropi spektral (SpecEn) tidak diturunkan dari teori informasi atau teori sistem dinamik, melainkan mengukur entropi spektrum frekuensi

§ Entropi lintas-Kolmogorov dan lintas-spektral, meskipun termasuk dalam perangkat, belum diverifikasi dalam literatur ilmiah

Salah satu keuntungan utama EntropyHub adalah kemampuan untuk menentukan banyak parameter yang digunakan dalam perhitungan entropi dengan memasukkan argumen fungsi kata kunci opsional. Nilai default dari setiap argumen kata kunci didasarkan pada nilai yang diusulkan dalam literatur sumber asli untuk metode tersebut. Namun, menganalisis data deret waktu secara membabi buta menggunakan argumen ini sangat tidak dianjurkan. Menarik kesimpulan tentang data berdasarkan nilai entropi hanya valid ketika parameter yang digunakan untuk menghitung nilai tersebut secara akurat menangkap dinamika data yang mendasarinya

Dengan fungsi Basis dan Silang tertentu, dimungkinkan untuk menghitung entropi menggunakan metode varian penaksir utama. Misalnya, dengan fungsi untuk entropi permutasi (PermEn) seseorang dapat menghitung tepi [], [berbobot], [] sadar amplitudo [], [] dimodifikasi, [] halus [], dan varian entropi permutasi [] kuantisasi seragam, . Penting untuk dicatat bahwa meskipun variabel utama yang dikembalikan oleh setiap fungsi adalah perkiraan nilai entropi, sebagian besar fungsi menyediakan variabel sekunder dan tersier yang mungkin menarik bagi pengguna. Beberapa contoh termasuk fungsi entropi dispersi (DispEn) [] yang juga mengembalikan entropi dispersi balik [], fungsi entropi spektral (SpecEn) [] yang juga mengembalikan entropi pita-spektral [], dan fungsi entropi Kolmogorov (K2En) . Selain itu, setiap fungsi Multiscale dan Multiscale Cross memiliki opsi untuk memplot kurva entropi multiskala (silang) ( Gambar 1 ), serta beberapa fungsi Basis yang . ​(Figs22 and ​and33).

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Gambar 1

Plot representatif dari kurva entropi multiskala yang dikembalikan oleh fungsi entropi Multiskala atau Lintas Multiskala

Kurva yang ditunjukkan sesuai dengan entropi gelembung multiskala dari sinyal derau putih Gaussian (N = 5000, μ = 0, σ = 1), dihitung selama 5 skala waktu berbutir kasar, dengan parameter penaksir. dimensi penyisipan (m) = 2, waktu tunda (τ) = 1

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Gambar 2

Plot perbedaan orde kedua dikembalikan oleh fungsi fase entropi (PhasEn)

Plot perbedaan orde kedua yang representatif dari komponen x dari himpunan persamaan Henon (α = 1. 4, β = 0. 3), dihitung dengan waktu tunda (τ) = 2 dan partisi (K) = 9

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Gambar 3

Plot poincaré dan histogram bivariat dikembalikan oleh fungsi entropi distribusi grid (GridEn)

Plot representatif Pioncaré dan histogram bivariat komponen x dari sistem persamaan Lorenz (σ = 10, β = 8/3, ρ = 28), dihitung dengan partisi kisi (m) = 5 dan penundaan waktu (τ)

Instalasi dan dependensi

Rilis versi utama dari toolkit EntropyHub dapat langsung diinstal melalui repositori paket asli untuk lingkungan pemrograman MATLAB, Python, dan Julia. Versi pengembangan beta dapat diunduh dan diinstal dari direktori setiap bahasa pemrograman yang dihosting di repositori EntropyHub GitHub– github. com/MattWillFlood/EntropyHub. EntropyHub kompatibel dengan sistem operasi Windows, Mac dan Linux

MATLAB

Ada dua toolbox tambahan dari keluarga produk MATLAB yang diperlukan untuk mengalami fungsionalitas penuh dari toolkit EntropyHub — Kotak Alat Pemrosesan Sinyal dan Kotak Alat Statistik dan Pembelajaran Mesin. Namun, sebagian besar fungsi akan berfungsi tanpa kotak peralatan ini. EntropyHub dimaksudkan untuk digunakan dengan versi MATLAB ≥ 2016a. Dalam beberapa kasus, toolkit dapat berfungsi pada versi 2015a & 2015b, meskipun tidak disarankan untuk menginstal pada versi MATLAB yang lebih lama dari 2016

Ada dua cara untuk menginstal EntropyHub di MATLAB

Pilihan 1. Catatan. Opsi 1 mengharuskan pengguna untuk masuk ke akun MathWorks mereka

1. Di aplikasi MATLAB, buka browser Add-Ons di bawah tab 'Home' dengan mengklik 'Get Add-Ons' ()

2. Di bilah pencarian, cari "EntroypHub" (Gambar S1b)

3. Buka tautan yang dihasilkan dan klik 'tambahkan' di sudut kanan atas (Gambar S1c)

4. Ikuti petunjuk untuk menginstal toolbox ()

pilihan 2

1. Buka direktori 'EntropyHub–MatLab' di repositori EntropyHub di GitHub (). https. //github. com/MattWillFlood/Entropi Hub/tiga/utama/Entropi Hub%20-%20 MatLab

2. Unduh file kotak alat MATLAB (EntropyHub. file mltbx) ()

3. Open the MATLAB application and change the current folder to the directory where the EntropyHub. mltbx file is saved ()

4. Double-click the EntropyHub. mltbx file to open it and click install ()

To check that EntropyHub has been correctly installed, enter “EntropyHub” at the command line and the EntropyHub logo should be displayed ()

Python

There are several modules required to use EntropyHub in Python—NumPy [], SciPy [], Matplotlib [], PyEMD [], and Requests. These modules will be automatically installed alongside EntropyHub if not already installed. EntropyHub was designed using Python3 and thus is not intended for use with Python2 or Python versions < 3. 6. EntropyHub Python functions are primarily built on top of the NumPy module for mathematical computation [], so vector or matrix variables are returned as NumPy array objects

There are 2 ways to install EntropyHub in Python. Option 1 is strongly recommended

Option 1. Note. Option 1 requires the ‘pip’ Python package installer

• ■ Using pip, enter the following at the command line ()

          pip install EntropyHub

  *Note. this command is case sensitive

pilihan 2

1. Go to the ‘EntropyHub–Python’ directory in the EntropyHub repository on GitHub (). https. //github. com/MattWillFlood/EntropyHub/tree/main/EntropyHub%20-%20Python

2. Download the EntropyHub. x. x. x. tar. gz folder and unzip it ()

3. Open a command prompt (cmd on Windows, terminal on Mac) or the Anaconda prompt if Anaconda is the user’s python package distribution ()

4. In the command prompt/terminal, navigate to the directory where the EntropyHub. x. x. x. tar. gz folder was saved and extracted ()

5. Enter the following in the command line ()

           python setup. py install

6. Ensure that an up-to-date version of the setuptools module is installed

           python -m pip install—upgrade setuptools

Untuk menggunakan EntropyHub, impor modul dengan perintah berikut ()

        import EntropyHub as EH

To check that EntropyHub has been correctly installed and loaded, enter ()

        EH. greet()

Julia

There are a number of modules required to use EntropyHub in Julia—DSP, FFTW, HTTP, DelimitedFiles, Random, Plots, StatsBase, StatsFuns, Statistics, GroupSlices, Combinatorics, Clustering, LinearAlgebra, and Dierckx []. These modules will be automatically installed alongside EntropyHub if not already installed. EntropyHub was designed using Julia 1. 5 and is intended for use with Julia versions ≥ 1. 2

To install EntropyHub in Julia,

1. In the Julia programming environment, open the package REPL by typing ‘]’ ()

2. At the command line, enter ()

           add EntropyHub

   *Note. this command is case sensitive

   Alternatively, one can install EntropyHub from the EntropyHub. jl GitHub repository

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

Untuk menggunakan EntropyHub, impor modul dengan perintah berikut ()

        using EntropyHub

To check that EntropyHub has been correctly installed and loaded, type ()

        EntropyHub. greet()

Supporting documentation and help

To help users to get the most out of EntropyHub, extensive documentation has been developed to cover all aspects of the toolkit, . Included in the documentation are

• ■ Instructions for installation

• ■ Thorough descriptions of the application programming interface (API) syntax–function names, keyword arguments, output values, etc

• ■ References to the original source literature for each method

• ■ Licensing and terms of use

• ■ Examples of use

Supporting documentation is available in various formats from the following sources

www. EntropyHub. xyz

The EntropyHub website, www. EntropyHub. xyz (also available at MattWillFlood. github. io/EntropyHub) is the primary source of information on the toolkit with dedicated sections to MATLAB, Python and Julia, as well as release updates and links to helpful internet resources

EntropyHub guide

The EntropyHub Guide. pdf is the toolkit user manual and can be downloaded from the or from the EntropyHub GitHub repository. In addition to the information given on the website, the EntropyHub Guide. pdf document provides some extra material, such as plots of fuzzy functions used for fuzzy entropy (FuzzEn) calculation, or plots of symbolic mapping procedures used in dispersion (DispEn) or symbolic-dynamic entropy (SyDyEn)

MATLAB help browser

Custom built documentation for the MATLAB edition of the toolkit is accessible through the MATLAB help browser after installation. Every function has its own help page featuring several examples of use ranging from basic to advanced. To access this documentation, open the help browser in the MATLAB application and at the bottom of the contents menu on the main page, under ‘Supplemental Software’, click on the link ‘EntropyHub Toolbox’

EntropyHub. jl

Custom documentation for the Julia edition of the toolkit can also be found at MattWillFlood. github. io/EntropyHub. jl (linked to the EntropyHub website). Following Julia package convention, the Julia edition is given the suffix ‘. jl’ and is hosted in a standalone GitHub repository linked to the main EntropyHub repository

Seeking further help

Within each programming environment, information about a specific function can be displayed in the command prompt by accessing the function docstrings. For example, to display information about the approximate entropy function (ApEn), type

• MATLAB.     help ApEn

• Python.         help(EntropyHub. ApEn)        (if imported as EntropyHub)

• Julia.         julia>?                 (to open help mode in the REPL)

•                         help?> ApEn

Contact

For help with topics not addressed in the documentation, users can seek help by contacting the toolkit developers at zyx. buhyportne@pleh. Every effort will be made to promptly respond to all queries received

To ensure that EntropyHub works as intended, with accurate and robust algorithms at its core, users are encouraged to report any potential bugs or errors discovered. The recommended way to report issues is to place an issue post under the ‘Issues’ tab on the EntropyHub GitHub repository. Doing so allows other users to find answers to common issues and contribute their own solutions. Alternatively, one can notify the package developers of any issues via email to zyx. buhyportne@xif

Continuous integration of new and improved entropy methods into the toolkit is a core principle of the EntropyHub project. Thus, requests and suggestions for new features are welcomed, as are contributions and offers for collaboration. EntropyHub developers will work with collaborators to ensure that contributions are valid, translated into MATLAB, Python and Julia, and follow the formatting adopted throughout the toolkit. Please contact zyx. buhyportne@ofni regarding any proposals that wish to be made

Validation

Included in EntropyHub are a number of sample time series and image datasets which can be used to test the validity of the toolkit functions ( Fig 4 ). Included in these datasets are random number sequences (gaussian, uniform, random integers), chaotic attractors (Lorenz, Hénon), and matrix representations of images (Mandelbrot fractal, random numbers, etc. ). Importing these datasets into the programming environment is done using the ExampleData function ( Table 2 ), which requires an internet connection . Every example presented in the supporting documentation on the EntropyHub website, in the MATLAB help browser, or in the EntropyHub Guide. pdf, employs the same sample datasets provided by the ExampleData function. Therefore, users can replicate these examples verbatim to verify that the toolkit functions properly on their computer system. The following subsections demonstrate the implementation of several Base, Cross-, Bidimensional, Multiscale and Multiscale Cross-entropy methods as a proof-of-principle validation. Note. the examples in the following subsections use MATLAB syntax, but the implementation of these functions and the values they return are the same when using Python and Julia.

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Fig 4

Sample datasets available with the EntropyHub toolkit through the ExampleData function

(a) A gaussian white noise time series, (b) the Lorenz system of equations, (c) a Mandelbrot fractal

Base entropy

Urutan angka acak yang terdistribusi normal ( Gambar 4A ; N = 5000, rata-rata = 0, SD = 1) diimpor dan didekati . 2*SD[X]).

>> X = ContohData('gaussian');

>> Apen(X)

2. 33505 2. 29926 2. 10113

Urutan bilangan acak menghasilkan nilai entropi yang tinggi karena urutan tersebut memiliki ketidakpastian dan ketidakpastian maksimum. Nilai entropi perkiraan tinggi (> 2) yang dikembalikan dalam contoh ini, sesuai dengan perkiraan untuk dimensi penyematan 0, 1, dan 2, berada dalam kisaran yang diharapkan untuk deret waktu tersebut

Lintas-entropi

Komponen x, y dan z dari sistem persamaan Lorenz ( Gambar 4B ; N = 5917, σ = 10, β = .

>> X = ExampleData(‘lorenz’);

>> XPermEn(X(. ,1. 2))

0. 17771

The Lorenz system is commonly employed in nonlinear dynamics as its attractor exhibits chaotic behaviour. Thus, the low cross-permutation entropy estimate returned here (0. 1771) reflects the high degree of deterministic structure shared between the x and y components of the Lorenz system

Bidimensional entropy

A matrix of normally distributed (Gaussian) random numbers is imported ( Fig 4C ; N = 60x120, mean = 0, SD = 1) and bidimensional dispersion entropy is estimated with a template submatrix size of 5 and all other parameters set to default values (time delay = 1, number of symbols = 3, symbolic mapping transform = normal cumulative distribution function).

>> X = ExampleData(‘gaussian_Mat’);

>> DispEn2D(X, ‘m’, 5)

8. 77894

The high value of the bidimensional dispersion entropy estimate corresponds to those previously reported for Gaussian white noise []

Multiscale entropy

A chirp signal (N = 5000, t0 = 1, t0 = 4000, normalised instantaneous frequency at t0 = 0. 01Hz, instantaneous frequency at t1 = 0. 025Hz) is imported and multiscale sample entropy is estimated over 5 coarse-grained temporal scale using the default parameters (embedding dimension = 2, time delay = 1, threshold = 0. 2*SD[X]). Note. a multiscale entropy object (Mobj) must be used with multiscale entropy functions

>> X = ExampleData(‘chirp’);

>> Mobj = MSobject(‘SampEn’);

>> MSEn(X, Mobj, ’Scales’, 5)

0. 2738 0. 3412 0. 4257 0. 5452 0. 6759

The chirp signal imported in this example represents a swept-frequency cosine with a linearly decreasing period length. The coarse-graining procedure of multiscale entropy [] functions as a low-pass filter of the original time series, with a lower cut-off frequency at each increasing time scale. Therefore, the coarse-graining procedure increasingly diminishes the localised auto-correlation of the chirp signal at each temporal scale, increasing the entropy. Ini mencerminkan peningkatan nilai entropi sampel dari rendah (0. 2738) to moderate (0. 6759) returned by the MSEn function

Multiscale cross-entropy

Two sequences of uniformly distributed random numbers (N = 4096, range = [0, ]) are imported and multiscale cross-distribution entropy is estimated over 7 coarse-grained temporal scales with the default parameters (embedding dimension = 2, time delay = 1, histogram binning method = ‘sturges’, normalisation with respect to number of histogram bins = true)

>> X = ExampleData(‘uniform2’);

>> Mobj = MSobject(‘XDistEn’);

>> XMSEn(X, Mobj)

0. 95735 0. 86769 0. 83544 0. 80433 0. 82617 0. 77619 0. 78893

As expected, the normalised multiscale cross-distribution entropy values remain relatively constant over multiple time scales as no information can be gained about one sequence from the other at any time scale

Discussion

The growing number of entropy methods reported in the scientific literature for time series and image analysis warrants new software tools that enable researchers to apply such methods [, , ]. Currently, there is a dearth of validated, open-source tools that implement a comprehensive array of entropy methods at the command-line with options to modify multiple parameter values. EntropyHub is the first toolkit to provide this functionality in a package that is available in three programming languages (MATLAB, Python, and Julia) with consistent syntax, and is supported by extensive documentation ( Table 3 ). To the best of the Authors knowledge, EntropyHub is also the first toolkit to provide multiple functions for bidimensional entropy [–], multiscale entropy [, , , , ] and multiscale cross-entropy analyses [, , ] all in one package. Specific programming language editions of the EntropyHub toolkit are hosted on the native package repositories for MATLAB, Python and Julia ( Table 3 ), facilitating straightforward installation and version updates. EntropyHub is compatible with both Windows, Mac and Linux operating systems, and is open for use under the Apache License (Version 2. 0) on condition that the present manuscript be cited in any outputs achieved through the use of the toolkit.

Table 3

List of resources for the EntropyHub toolkit

Online ResourcesEntropyHub Websitewww. EntropyHub. xyzMattWillFlood. github. io/EntropyHubGitHub Repositorywww. github. com/MattWillFlood/EntropyHubwww. github. com/MattWillFlood/EntropyHub. jl (Julia only repository)MATLAB Packagewww. mathworks. com/matlabcentral/fileexchange/94185-entropyhubPython Packagepypi. org/project/EntropyHub/Julia Packagejuliahub. com/ui/Packages/EntropyHub/npy5E/0. 1. 0Contact DetailsGeneral Inquirieszyx. buhyportne@ofniHelp and Supportzyx. buhyportne@plehReporting Bugszyx. buhyportne@xif

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All information about the toolkit, including installations instructions, documentation, and release updates can be found on the main EntropyHub website. Users can get in touch directly with the package developers by contacting the email addresses provided

The application of entropy in the study of time series data is becoming more common in all manner of research fields such as engineering [, ], medicine [–] and finance [–]. The broad range of entropy functions provided by EntropyHub in multiple programming languages can serve to support researchers in these fields by characterising the uncertainty and complexity of time series data with various stochastic, time-frequency and chaotic properties. Additionally, this is the first toolkit to provide several functions for performing bidimensional (2D) entropy analysis, which can enable users to estimate the entropy of images and matrix data

The goal of EntropyHub is to continually integrate newly developed entropy methods and serve as a cohesive computing resource for all entropy-based analysis, independent of the application or research field. To achieve this goal, suggestions for new features and contributions from other researchers are welcomed

Supporting information

S1 Fig

(TIF)

Click here for additional data file. (6. 5M, tif)

S2 Fig

(TIF)

Click here for additional data file. (3. 1M, tif)

S3 Fig

(TIF)

Click here for additional data file. (2. 7M, tif)

Acknowledgments

The Authors wish to thank Dr Lara McManus and Ben O’Callaghan for generously donating their time to test the toolkit and provide constructive feedback which substantially improved the end result. The Authors would also like to acknowledge the work of the scientific community in deriving the entropy methods that motivated the development of EntropyHub

Funding Statement

Penelitian ini didanai oleh Luxembourg Institute of Health (https. //www. lih. lu). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Data Availability

Tidak ada data yang terkait dengan naskah ini

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