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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-02-28T11:28:09","documenter_version":"1.2.1"}}
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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-03-02T10:34:26","documenter_version":"1.2.1"}}

previews/PR11/basics/index.html

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previews/PR11/docs_custom_oracle/index.html

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# transformation obtained through OAVI by using your custom oracle
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X_transformed, sets = fit_oavi(X; oracle=custom_oracle)</code></pre><p>You can also pass further kwargs used by your oracle and we will pass them through to your oracle call. This is done by the <code>oracle_kwargs</code> argument. Let&#39;s say we want to pass the keyword arguments <code>epsilon=1.0e-5</code> and <code>max_iteration=5000</code> along to our custom oracle.</p><pre><code class="language-julia hljs">kwargs = [(:epsilon, 1.0e-5), (:max_iteration, 5000)]
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X_transformed, sets = fit_oavi(X; oracle=custom_oracle, oracle_kwargs=kwargs)</code></pre><p>The above code will call <code>custom_oracle</code> with the keyword arguments <code>epsilon</code> and <code>max_iteration</code> exchanged for <code>1.0e-5</code> and <code>5000</code>, respectively, that is, <code>custom_oracle(data, labels; epsilon=1.0e-5, max_iteration=5000)</code> and ultimately when calling the algorithm in our example <code>blended_conditional_gradient(f, grad!, region, x0; epsilon=1.0e-5, max_iteration=5000)</code>.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../docs_oavi_transformation/">« Transforming data using <span>$\; \texttt{OAVI}$</span></a><a class="docs-footer-nextpage" href="../docs_vca_transformation/">Transforming data using <span>$\; \texttt{VCA}$</span> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 28 February 2024 11:28">Wednesday 28 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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X_transformed, sets = fit_oavi(X; oracle=custom_oracle, oracle_kwargs=kwargs)</code></pre><p>The above code will call <code>custom_oracle</code> with the keyword arguments <code>epsilon</code> and <code>max_iteration</code> exchanged for <code>1.0e-5</code> and <code>5000</code>, respectively, that is, <code>custom_oracle(data, labels; epsilon=1.0e-5, max_iteration=5000)</code> and ultimately when calling the algorithm in our example <code>blended_conditional_gradient(f, grad!, region, x0; epsilon=1.0e-5, max_iteration=5000)</code>.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../docs_oavi_transformation/">« Transforming data using <span>$\; \texttt{OAVI}$</span></a><a class="docs-footer-nextpage" href="../docs_vca_transformation/">Transforming data using <span>$\; \texttt{VCA}$</span> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Saturday 2 March 2024 10:34">Saturday 2 March 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR11/docs_oavi_transformation/index.html

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# apply transformation to test set
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X_test_transformed, sets_test = apply_G_transformation(best_sets, X_test)</code></pre><p>Note that <code>X_test</code> has to have the same second dimension as <code>X_train</code>, that is <code>size(X_train, 2) == size(X_test, 2)</code>, so be careful when applying the transformation to other data.</p><p>Lastly, to be safe, we check that the dimensions of the transformations indeed match the number of vanishing polynomials constructed by the algorithm.</p><pre><code class="language-julia hljs">println(&quot;Number of vanishing polynomials: &quot;, size(best_sets.leading_terms, 2))
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size(best_transform, 2) == size(X_test_transformed, 2) == size(best_sets.leading_terms, 2)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../how_to_run/">« Obtaining a transformation</a><a class="docs-footer-nextpage" href="../docs_custom_oracle/">Custom Oracles »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 28 February 2024 11:28">Wednesday 28 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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size(best_transform, 2) == size(X_test_transformed, 2) == size(best_sets.leading_terms, 2)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../how_to_run/">« Obtaining a transformation</a><a class="docs-footer-nextpage" href="../docs_custom_oracle/">Custom Oracles »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Saturday 2 March 2024 10:34">Saturday 2 March 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR11/docs_vca_transformation/index.html

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polys = ApproximateVanishingIdeals.V_to_matrix(best_sets_vca)
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println(&quot;Number of vanishing polynomials: &quot;, size(polys, 2))
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size(best_transform_vca, 2) == size(X_test_transformed_vca, 2) == size(polys, 2)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../docs_custom_oracle/">« Custom Oracles</a><a class="docs-footer-nextpage" href="../print_polynomials/">Printing polynomials »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 28 February 2024 11:28">Wednesday 28 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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size(best_transform_vca, 2) == size(X_test_transformed_vca, 2) == size(polys, 2)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../docs_custom_oracle/">« Custom Oracles</a><a class="docs-footer-nextpage" href="../print_polynomials/">Printing polynomials »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Saturday 2 March 2024 10:34">Saturday 2 March 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR11/how_to_run/index.html

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fit_oavi(X; oracle=&quot;ABM&quot;)</code></pre><h2 id="\\texttt{VCA}-transformation"><a class="docs-heading-anchor" href="#\\texttt{VCA}-transformation"><span>$\texttt{VCA}$</span> transformation</a><a id="\\texttt{VCA}-transformation-1"></a><a class="docs-heading-anchor-permalink" href="#\\texttt{VCA}-transformation" title="Permalink"></a></h2><p>Apart from <span>$\texttt{OAVI}$</span> with its multiple different possibilities of running, we also provide an implementation of the <span>$\texttt{VCA}$</span> algorithm introduced in <a href="https://proceedings.mlr.press/v28/livni13.html">Livni et al. (2013)</a>. The algorithm is implemented in <a href="../reference/1_algorithms/#ApproximateVanishingIdeals.fit_vca"><code>fit_vca</code></a> and a feature transformation based on <span>$\texttt{VCA}$</span> can be obtained by calling</p><pre><code class="language-julia hljs">using ApproximateVanishingIdeals
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X = your_data_set
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X_transformed_vca, sets_vca = fit_vca(X)</code></pre><p>Similar to <span>$\texttt{OAVI}$</span>, the vanishing parameter <span>$\psi$</span> is adjustable for <span>$\texttt{VCA}$</span> through the keyword <code>psi</code>. To the best of our knowledge, there is currently no similar guarantee on the degree of constructed polynomials for <span>$\texttt{VCA}$</span> as there is for <span>$\texttt{OAVI}$</span>, but adjusting <code>psi</code> and comparing results is nonetheless recommended.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../basics/">« How does it work?</a><a class="docs-footer-nextpage" href="../docs_oavi_transformation/">Transforming data using <span>$\; \texttt{OAVI}$</span> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 28 February 2024 11:28">Wednesday 28 February 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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X_transformed_vca, sets_vca = fit_vca(X)</code></pre><p>Similar to <span>$\texttt{OAVI}$</span>, the vanishing parameter <span>$\psi$</span> is adjustable for <span>$\texttt{VCA}$</span> through the keyword <code>psi</code>. To the best of our knowledge, there is currently no similar guarantee on the degree of constructed polynomials for <span>$\texttt{VCA}$</span> as there is for <span>$\texttt{OAVI}$</span>, but adjusting <code>psi</code> and comparing results is nonetheless recommended.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../basics/">« How does it work?</a><a class="docs-footer-nextpage" href="../docs_oavi_transformation/">Transforming data using <span>$\; \texttt{OAVI}$</span> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Saturday 2 March 2024 10:34">Saturday 2 March 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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