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<title>Binary classification as a phase separation process - a short tutorial</title>
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<li><a href="./">Binary classification as a phase separation process</a></li>
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<li class="chapter" data-level="1" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i><b>1</b> Introduction</a></li>
<li class="chapter" data-level="2" data-path="a-few-examples.html"><a href="a-few-examples.html"><i class="fa fa-check"></i><b>2</b> Nonlinear diffusion equations: a numerical example</a><ul>
<li class="chapter" data-level="2.1" data-path="a-few-examples.html"><a href="a-few-examples.html#propagation-with-randomly-generated-coefficients"><i class="fa fa-check"></i><b>2.1</b> Propagation with randomly generated coefficients</a></li>
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<li class="chapter" data-level="3" data-path="sec-PSBC.html"><a href="sec-PSBC.html"><i class="fa fa-check"></i><b>3</b> A glimpse at the PSBC model</a></li>
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<li class="chapter" data-level="4.1" data-path="sec-mnist.html"><a href="sec-mnist.html#multiclass-classification-using-the-psbc"><i class="fa fa-check"></i><b>4.1</b> Multiclass classification using the PSBC</a><ul>
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<i class="fa fa-circle-o-notch fa-spin"></i><a href="./">Binary classification as a phase separation process - a short tutorial</a>
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<h1 class="title">Binary classification as a phase separation process - a short tutorial</h1>
<p class="author"><em>Rafael Monteiro</em></p>
<address class="author_afil">
Mathematics for Advanced Materials - Open Innovation Laboratory/Tohoku University (AIST), Sendai, Japan<br><a class="author_email" href="mailto:#"><a href="mailto:monteirodasilva-rafael@aist.jp" class="email">monteirodasilva-rafael@aist.jp</a>, <a href="mailto:rafael.a.monteiro.math@gmail.com" class="email">rafael.a.monteiro.math@gmail.com</a></a>
</address>
<p class="date"><em>2021-09-27</em></p>
</div>
<div id="intro" class="section level1">
<h1><span class="header-section-number"> 1</span> Introduction</h1>
<p>This is a short companion tutorial to the github <span class="citation">(Monteiro <a href="#ref-Bin_phase_github" role="doc-biblioref">2020</a><a href="#ref-Bin_phase_github" role="doc-biblioref">a</a>)</span>. We give here a glimpse of the Phase Separation Binary Classifier (in short, PSBC), proposed in the article <strong>Binary Classification as a Phase Separation Process</strong>, by <a href="https://sites.google.com/view/rafaelmonteiro-math/home">Rafael Monteiro</a>; a <a href="https://arxiv.org/abs/2009.02467">preprint</a> is available on arXiv.</p>
<p>This is a new type of Recurrent Neural Network whose architecture is inspired on how (binary) fluids phase separate.</p>
<p>An implementation of the model can be found in the module <strong>binary_phase_separation.py</strong>. Part of this tutorial can also be found in <a href="https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation/blob/master/README_v2.pdf">README_v2.pdf</a>.</p>
<p><strong>…but, before we start…</strong></p>
<p>This project can be downloaded in tarballs. The first 3 of them are thos enecessary to replicate the numerical tests we did:</p>
<ul>
<li><a href="https://zenodo.org/record/5525794/files/PSBC_dataset.tar.gz?download=1">PSBC_dataset.tar.gz</a>;</li>
<li><a href="https://zenodo.org/record/5525794/files/PSBC_libs_grids_statistics.tar.gz?download=1">PSBC_libs_grids_statistics.tar.gz</a>;</li>
<li><a href="https://zenodo.org/record/5525794/files/PSBC_notebooks.tar.gz?download=1">PSBC_notebooks.tar.gz</a>,</li>
</ul>
<p>while the last 2 can be used to reproduce the figures shown in the paper:</p>
<ul>
<li><a href="https://zenodo.org/record/5525794/files/PSBC_BCs.tar.gz?download=1">PSBC_BCs.tar.gz</a>;</li>
<li><a href="https://zenodo.org/record/5525794/files/PSBC_classifier_PCA.tar.gz?download=1">PSBC_classifier_PCA.tar.gz</a>;</li>
</ul>
<p>All these files are available at <span class="citation">(Monteiro <a href="#ref-Bin_phase_data" role="doc-biblioref">2020</a><a href="#ref-Bin_phase_data" role="doc-biblioref">b</a>)</span>. All of them but <a href="https://zenodo.org/record/5525794/files/PSBC_dataset.tar.gz?download=1">PSBC_dataset.tar.gz</a> can also be downloaded from Github “<span class="citation">(Monteiro <a href="#ref-Bin_phase_github" role="doc-biblioref">2020</a><a href="#ref-Bin_phase_github" role="doc-biblioref">a</a>)</span>”.
* The main module for this project are in the folder <a href="https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation/tree/master/MOTHER_PSBC">MOTHER_PSBC</a>. The main module, <a href="https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation/blob/master/MOTHER_PSBC/"><strong>tfversion_binary_phase_separation.py</strong></a> does not depend on the folder-tree structure described in the README_v2 file on “<span class="citation">(Monteiro <a href="#ref-Bin_phase_github" role="doc-biblioref">2020</a><a href="#ref-Bin_phase_github" role="doc-biblioref">a</a>)</span>”.
* If you want to reproduce this notebook you should download the file - <a href="https://zenodo.org/record/5525794/files/PSBC_notebooks.tar.gz?download=1">PSBC_notebooks.tar.gz</a>.
* It is always recommended to download big using <a href="https://www.gnu.org/software/wget/">wget</a>), but you can use your browser.</p>
<ul>
<li><p>To decompress the tarballs, look online (like <a href="https://askubuntu.com/questions/25347/what-command-do-i-need-to-unzip-extract-a-tar-gz-file">here</a>) or check the <a href="https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation/blob/master/README_v2.pdf">README_v2.pdf</a> guide.</p></li>
<li><p>This website is partially based on <a href="https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation/blob/master/PSBC_Examples.ipynb">this jupyter-notebook</a>. For simplicity, I shall refrain from posting the whole oputput of some cases, marking then with a symbol <span class="math inline">\(>>>\)</span>.</p></li>
<li><p>We will summarize some of the outputs, adding a “…” to them. If you would like to see the whole output, please see <a href="https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation/blob/master/PSBC_Examples.ipynb">PSBC_Examples.ipynb</a>.</p></li>
</ul>
<p>As we said, this discussion is short but we want to offer a bit more than just a manual, so we will point out references along the way.</p>
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<h3>References</h3>
<div id="refs" class="references">
<div id="ref-Bin_phase_github">
<p>Monteiro, Rafael. 2020a. “Source Code for the Paper ‘Binary Classification as a Phase Separation Process’.” <em>GitHub Repository</em>. <a href="https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation">https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation</a>; GitHub.</p>
</div>
<div id="ref-Bin_phase_data">
<p>Monteiro, Rafael. 2020b. “Binary Classification as a Phase Separation Process (data repository).” Zenodo. <a href="https://doi.org/10.5281/zenodo.5525794">https://doi.org/10.5281/zenodo.5525794</a>.</p>
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