<!DOCTYPE html>
<html lang="en" data-content_root="../../" >
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<meta property="og:title" content="Kernel Approximation" />
<meta property="og:type" content="website" />
<meta property="og:url" content="https://scikit-learn/stable/auto_examples/kernel_approximation/index.html" />
<meta property="og:site_name" content="scikit-learn" />
<meta property="og:description" content="Examples concerning the sklearn.kernel_approximation module. Scalable learning with polynomial kernel approximation" />
<meta property="og:image" content="https://scikit-learn/stable/_images/sphx_glr_plot_scalable_poly_kernels_thumb.png" />
<meta property="og:image:alt" content="" />
<meta name="description" content="Examples concerning the sklearn.kernel_approximation module. Scalable learning with polynomial kernel approximation" />
<title>Kernel Approximation — scikit-learn 1.6.dev0 documentation</title>
<script data-cfasync="false">
document.documentElement.dataset.mode = localStorage.getItem("mode") || "";
document.documentElement.dataset.theme = localStorage.getItem("theme") || "";
</script>
<!-- Loaded before other Sphinx assets -->
<link href="../../_static/styles/theme.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="../../_static/styles/bootstrap.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="../../_static/styles/pydata-sphinx-theme.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link href="../../_static/vendor/fontawesome/6.5.2/css/all.min.css?digest=dfe6caa3a7d634c4db9b" rel="stylesheet" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.5.2/webfonts/fa-solid-900.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
<link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=a746c00c" />
<link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
<link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css" />
<link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Vibur" />
<link rel="stylesheet" type="text/css" href="../../_static/jupyterlite_sphinx.css?v=ca70e7f1" />
<link rel="stylesheet" type="text/css" href="../../_static/sg_gallery.css?v=d2d258e8" />
<link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-binder.css?v=f4aeca0c" />
<link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
<link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
<link rel="stylesheet" type="text/css" href="../../_static/sphinx-design.min.css?v=95c83b7e" />
<link rel="stylesheet" type="text/css" href="../../_static/styles/colors.css?v=cc94ab7d" />
<link rel="stylesheet" type="text/css" href="../../_static/styles/custom.css?v=e340c087" />
<!-- Pre-loaded scripts that we'll load fully later -->
<link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=dfe6caa3a7d634c4db9b" />
<link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=dfe6caa3a7d634c4db9b" />
<script src="../../_static/vendor/fontawesome/6.5.2/js/all.min.js?digest=dfe6caa3a7d634c4db9b"></script>
<script src="../../_static/documentation_options.js?v=d875d36e"></script>
<script src="../../_static/doctools.js?v=9a2dae69"></script>
<script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
<script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
<script src="../../_static/copybutton.js?v=97f0b27d"></script>
<script src="../../_static/jupyterlite_sphinx.js?v=d6bdf5f8"></script>
<script src="../../_static/design-tabs.js?v=f930bc37"></script>
<script data-domain="scikit-learn.org" defer="defer" src="https://views.scientific-python.org/js/script.js"></script>
<script>DOCUMENTATION_OPTIONS.pagename = 'auto_examples/kernel_approximation/index';</script>
<script>
DOCUMENTATION_OPTIONS.theme_version = '0.15.4';
DOCUMENTATION_OPTIONS.theme_switcher_json_url = 'https://scikit-learn.org/dev/_static/versions.json';
DOCUMENTATION_OPTIONS.theme_switcher_version_match = '1.6.dev0';
DOCUMENTATION_OPTIONS.show_version_warning_banner = true;
</script>
<script src="../../_static/scripts/dropdown.js?v=e2048168"></script>
<script src="../../_static/scripts/version-switcher.js?v=a6dd8357"></script>
<link rel="icon" href="../../_static/favicon.ico"/>
<link rel="author" title="About these documents" href="../../about.html" />
<link rel="search" title="Search" href="../../search.html" />
<link rel="next" title="Scalable learning with polynomial kernel approximation" href="plot_scalable_poly_kernels.html" />
<link rel="prev" title="Permutation Importance with Multicollinear or Correlated Features" href="../inspection/plot_permutation_importance_multicollinear.html" />
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
</head>
<body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="">
<div id="pst-skip-link" class="skip-link d-print-none"><a href="#main-content">Skip to main content</a></div>
<div id="pst-scroll-pixel-helper"></div>
<button type="button" class="btn rounded-pill" id="pst-back-to-top">
<i class="fa-solid fa-arrow-up"></i>Back to top</button>
<input type="checkbox"
class="sidebar-toggle"
id="pst-primary-sidebar-checkbox"/>
<label class="overlay overlay-primary" for="pst-primary-sidebar-checkbox"></label>
<input type="checkbox"
class="sidebar-toggle"
id="pst-secondary-sidebar-checkbox"/>
<label class="overlay overlay-secondary" for="pst-secondary-sidebar-checkbox"></label>
<div class="search-button__wrapper">
<div class="search-button__overlay"></div>
<div class="search-button__search-container">
<form class="bd-search d-flex align-items-center"
action="../../search.html"
method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search"
class="form-control"
name="q"
id="search-input"
placeholder="Search the docs ..."
aria-label="Search the docs ..."
autocomplete="off"
autocorrect="off"
autocapitalize="off"
spellcheck="false"/>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form></div>
</div>
<div class="pst-async-banner-revealer d-none">
<aside id="bd-header-version-warning" class="d-none d-print-none" aria-label="Version warning"></aside>
</div>
<header class="bd-header navbar navbar-expand-lg bd-navbar d-print-none">
<div class="bd-header__inner bd-page-width">
<button class="pst-navbar-icon sidebar-toggle primary-toggle" aria-label="Site navigation">
<span class="fa-solid fa-bars"></span>
</button>
<div class=" navbar-header-items__start">
<div class="navbar-item">
<a class="navbar-brand logo" href="../../index.html">
<img src="../../_static/scikit-learn-logo-small.png" class="logo__image only-light" alt="scikit-learn homepage"/>
<script>document.write(`<img src="../../_static/scikit-learn-logo-small.png" class="logo__image only-dark" alt="scikit-learn homepage"/>`);</script>
</a></div>
</div>
<div class=" navbar-header-items">
<div class="me-auto navbar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../install.html">
Install
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../user_guide.html">
User Guide
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../api/index.html">
API
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../index.html">
Examples
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://blog.scikit-learn.org/">
Community
</a>
</li>
<li class="nav-item dropdown">
<button class="btn dropdown-toggle nav-item" type="button" data-bs-toggle="dropdown" aria-expanded="false" aria-controls="pst-nav-more-links">
More
</button>
<ul id="pst-nav-more-links" class="dropdown-menu">
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../getting_started.html">
Getting Started
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../whats_new.html">
Release History
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../glossary.html">
Glossary
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../developers/index.html">
Development
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../faq.html">
FAQ
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../support.html">
Support
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../related_projects.html">
Related Projects
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../roadmap.html">
Roadmap
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../governance.html">
Governance
</a>
</li>
<li class=" ">
<a class="nav-link dropdown-item nav-internal" href="../../about.html">
About us
</a>
</li>
</ul>
</li>
</ul>
</nav></div>
</div>
<div class="navbar-header-items__end">
<div class="navbar-item navbar-persistent--container">
<script>
document.write(`
<button class="btn btn-sm pst-navbar-icon search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass fa-lg"></i>
</button>
`);
</script>
</div>
<div class="navbar-item">
<script>
document.write(`
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto"></i>
</button>
`);
</script></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://github.com/scikit-learn/scikit-learn" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitHub</span></a>
</li>
</ul></div>
<div class="navbar-item">
<script>
document.write(`
<div class="version-switcher__container dropdown">
<button id="pst-version-switcher-button-2"
type="button"
class="version-switcher__button btn btn-sm dropdown-toggle"
data-bs-toggle="dropdown"
aria-haspopup="listbox"
aria-controls="pst-version-switcher-list-2"
aria-label="Version switcher list"
>
Choose version <!-- this text may get changed later by javascript -->
<span class="caret"></span>
</button>
<div id="pst-version-switcher-list-2"
class="version-switcher__menu dropdown-menu list-group-flush py-0"
role="listbox" aria-labelledby="pst-version-switcher-button-2">
<!-- dropdown will be populated by javascript on page load -->
</div>
</div>
`);
</script></div>
</div>
</div>
<div class="navbar-persistent--mobile">
<script>
document.write(`
<button class="btn btn-sm pst-navbar-icon search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass fa-lg"></i>
</button>
`);
</script>
</div>
</div>
</header>
<div class="bd-container">
<div class="bd-container__inner bd-page-width">
<div class="bd-sidebar-primary bd-sidebar">
<div class="sidebar-header-items sidebar-primary__section">
<div class="sidebar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../install.html">
Install
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../user_guide.html">
User Guide
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../api/index.html">
API
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../index.html">
Examples
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://blog.scikit-learn.org/">
Community
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../getting_started.html">
Getting Started
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../whats_new.html">
Release History
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../glossary.html">
Glossary
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../developers/index.html">
Development
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../faq.html">
FAQ
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../support.html">
Support
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../related_projects.html">
Related Projects
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../roadmap.html">
Roadmap
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../governance.html">
Governance
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../about.html">
About us
</a>
</li>
</ul>
</nav></div>
</div>
<div class="sidebar-header-items__end">
<div class="navbar-item">
<script>
document.write(`
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto"></i>
</button>
`);
</script></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://github.com/scikit-learn/scikit-learn" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitHub</span></a>
</li>
</ul></div>
<div class="navbar-item">
<script>
document.write(`
<div class="version-switcher__container dropdown">
<button id="pst-version-switcher-button-3"
type="button"
class="version-switcher__button btn btn-sm dropdown-toggle"
data-bs-toggle="dropdown"
aria-haspopup="listbox"
aria-controls="pst-version-switcher-list-3"
aria-label="Version switcher list"
>
Choose version <!-- this text may get changed later by javascript -->
<span class="caret"></span>
</button>
<div id="pst-version-switcher-list-3"
class="version-switcher__menu dropdown-menu list-group-flush py-0"
role="listbox" aria-labelledby="pst-version-switcher-button-3">
<!-- dropdown will be populated by javascript on page load -->
</div>
</div>
`);
</script></div>
</div>
</div>
<div class="sidebar-primary-items__start sidebar-primary__section">
<div class="sidebar-primary-item">
<nav class="bd-docs-nav bd-links"
aria-label="Section Navigation">
<p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
<div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
<li class="toctree-l1 has-children"><a class="reference internal" href="../release_highlights/index.html">Release Highlights</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_5_0.html">Release Highlights for scikit-learn 1.5</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_4_0.html">Release Highlights for scikit-learn 1.4</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_3_0.html">Release Highlights for scikit-learn 1.3</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_2_0.html">Release Highlights for scikit-learn 1.2</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_1_0.html">Release Highlights for scikit-learn 1.1</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_1_0_0.html">Release Highlights for scikit-learn 1.0</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_0_24_0.html">Release Highlights for scikit-learn 0.24</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_0_23_0.html">Release Highlights for scikit-learn 0.23</a></li>
<li class="toctree-l2"><a class="reference internal" href="../release_highlights/plot_release_highlights_0_22_0.html">Release Highlights for scikit-learn 0.22</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../bicluster/index.html">Biclustering</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../bicluster/plot_spectral_biclustering.html">A demo of the Spectral Biclustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../bicluster/plot_spectral_coclustering.html">A demo of the Spectral Co-Clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../bicluster/plot_bicluster_newsgroups.html">Biclustering documents with the Spectral Co-clustering algorithm</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../calibration/index.html">Calibration</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_compare_calibration.html">Comparison of Calibration of Classifiers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_calibration_curve.html">Probability Calibration curves</a></li>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_calibration_multiclass.html">Probability Calibration for 3-class classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../calibration/plot_calibration.html">Probability calibration of classifiers</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../classification/index.html">Classification</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_classifier_comparison.html">Classifier comparison</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_lda_qda.html">Linear and Quadratic Discriminant Analysis with covariance ellipsoid</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_lda.html">Normal, Ledoit-Wolf and OAS Linear Discriminant Analysis for classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_classification_probability.html">Plot classification probability</a></li>
<li class="toctree-l2"><a class="reference internal" href="../classification/plot_digits_classification.html">Recognizing hand-written digits</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../cluster/index.html">Clustering</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_digits.html">A demo of K-Means clustering on the handwritten digits data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_coin_ward_segmentation.html">A demo of structured Ward hierarchical clustering on an image of coins</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_mean_shift.html">A demo of the mean-shift clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_adjusted_for_chance_measures.html">Adjustment for chance in clustering performance evaluation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_clustering.html">Agglomerative clustering with and without structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_clustering_metrics.html">Agglomerative clustering with different metrics</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_plusplus.html">An example of K-Means++ initialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_bisect_kmeans.html">Bisecting K-Means and Regular K-Means Performance Comparison</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_birch_vs_minibatchkmeans.html">Compare BIRCH and MiniBatchKMeans</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_cluster_comparison.html">Comparing different clustering algorithms on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_linkage_comparison.html">Comparing different hierarchical linkage methods on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_mini_batch_kmeans.html">Comparison of the K-Means and MiniBatchKMeans clustering algorithms</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_dbscan.html">Demo of DBSCAN clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_hdbscan.html">Demo of HDBSCAN clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_optics.html">Demo of OPTICS clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_affinity_propagation.html">Demo of affinity propagation clustering algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_assumptions.html">Demonstration of k-means assumptions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_stability_low_dim_dense.html">Empirical evaluation of the impact of k-means initialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_digits_agglomeration.html">Feature agglomeration</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_feature_agglomeration_vs_univariate_selection.html">Feature agglomeration vs. univariate selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_ward_structured_vs_unstructured.html">Hierarchical clustering: structured vs unstructured ward</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_inductive_clustering.html">Inductive Clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_dict_face_patches.html">Online learning of a dictionary of parts of faces</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_agglomerative_dendrogram.html">Plot Hierarchical Clustering Dendrogram</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_coin_segmentation.html">Segmenting the picture of greek coins in regions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_kmeans_silhouette_analysis.html">Selecting the number of clusters with silhouette analysis on KMeans clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_segmentation_toy.html">Spectral clustering for image segmentation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_digits_linkage.html">Various Agglomerative Clustering on a 2D embedding of digits</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cluster/plot_face_compress.html">Vector Quantization Example</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../covariance/index.html">Covariance estimation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_lw_vs_oas.html">Ledoit-Wolf vs OAS estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_mahalanobis_distances.html">Robust covariance estimation and Mahalanobis distances relevance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_robust_vs_empirical_covariance.html">Robust vs Empirical covariance estimate</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_covariance_estimation.html">Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covariance/plot_sparse_cov.html">Sparse inverse covariance estimation</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../cross_decomposition/index.html">Cross decomposition</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../cross_decomposition/plot_compare_cross_decomposition.html">Compare cross decomposition methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cross_decomposition/plot_pcr_vs_pls.html">Principal Component Regression vs Partial Least Squares Regression</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../datasets/index.html">Dataset examples</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../datasets/plot_random_multilabel_dataset.html">Plot randomly generated multilabel dataset</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../tree/index.html">Decision Trees</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_tree_regression.html">Decision Tree Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_iris_dtc.html">Plot the decision surface of decision trees trained on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_cost_complexity_pruning.html">Post pruning decision trees with cost complexity pruning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree/plot_unveil_tree_structure.html">Understanding the decision tree structure</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../decomposition/index.html">Decomposition</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_ica_blind_source_separation.html">Blind source separation using FastICA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_vs_lda.html">Comparison of LDA and PCA 2D projection of Iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_faces_decomposition.html">Faces dataset decompositions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_varimax_fa.html">Factor Analysis (with rotation) to visualize patterns</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_ica_vs_pca.html">FastICA on 2D point clouds</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_image_denoising.html">Image denoising using dictionary learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_incremental_pca.html">Incremental PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_kernel_pca.html">Kernel PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_vs_fa_model_selection.html">Model selection with Probabilistic PCA and Factor Analysis (FA)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_pca_iris.html">Principal Component Analysis (PCA) on Iris Dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../decomposition/plot_sparse_coding.html">Sparse coding with a precomputed dictionary</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../developing_estimators/index.html">Developing Estimators</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../developing_estimators/sklearn_is_fitted.html"><code class="docutils literal notranslate"><span class="pre">__sklearn_is_fitted__</span></code> as Developer API</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../ensemble/index.html">Ensemble methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_categorical.html">Categorical Feature Support in Gradient Boosting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_stack_predictors.html">Combine predictors using stacking</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_hist_grad_boosting_comparison.html">Comparing Random Forests and Histogram Gradient Boosting models</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_random_forest_regression_multioutput.html">Comparing random forests and the multi-output meta estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_regression.html">Decision Tree Regression with AdaBoost</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_early_stopping.html">Early stopping in Gradient Boosting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_importances.html">Feature importances with a forest of trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_feature_transformation.html">Feature transformations with ensembles of trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_hgbt_regression.html">Features in Histogram Gradient Boosting Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_oob.html">Gradient Boosting Out-of-Bag estimates</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_regression.html">Gradient Boosting regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_regularization.html">Gradient Boosting regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_random_forest_embedding.html">Hashing feature transformation using Totally Random Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_isolation_forest.html">IsolationForest example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_monotonic_constraints.html">Monotonic Constraints</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_multiclass.html">Multi-class AdaBoosted Decision Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_ensemble_oob.html">OOB Errors for Random Forests</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_probas.html">Plot class probabilities calculated by the VotingClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_regressor.html">Plot individual and voting regression predictions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_voting_decision_regions.html">Plot the decision boundaries of a VotingClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_forest_iris.html">Plot the decision surfaces of ensembles of trees on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_gradient_boosting_quantile.html">Prediction Intervals for Gradient Boosting Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_bias_variance.html">Single estimator versus bagging: bias-variance decomposition</a></li>
<li class="toctree-l2"><a class="reference internal" href="../ensemble/plot_adaboost_twoclass.html">Two-class AdaBoost</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../applications/index.html">Examples based on real world datasets</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_tomography_l1_reconstruction.html">Compressive sensing: tomography reconstruction with L1 prior (Lasso)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_face_recognition.html">Faces recognition example using eigenfaces and SVMs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_digits_denoising.html">Image denoising using kernel PCA</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_time_series_lagged_features.html">Lagged features for time series forecasting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_model_complexity_influence.html">Model Complexity Influence</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_out_of_core_classification.html">Out-of-core classification of text documents</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_outlier_detection_wine.html">Outlier detection on a real data set</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_prediction_latency.html">Prediction Latency</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_species_distribution_modeling.html">Species distribution modeling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_cyclical_feature_engineering.html">Time-related feature engineering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_topics_extraction_with_nmf_lda.html">Topic extraction with Non-negative Matrix Factorization and Latent Dirichlet Allocation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/plot_stock_market.html">Visualizing the stock market structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../applications/wikipedia_principal_eigenvector.html">Wikipedia principal eigenvector</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../feature_selection/index.html">Feature Selection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_f_test_vs_mi.html">Comparison of F-test and mutual information</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_select_from_model_diabetes.html">Model-based and sequential feature selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_feature_selection_pipeline.html">Pipeline ANOVA SVM</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_rfe_digits.html">Recursive feature elimination</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_rfe_with_cross_validation.html">Recursive feature elimination with cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../feature_selection/plot_feature_selection.html">Univariate Feature Selection</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../mixture/index.html">Gaussian Mixture Models</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_concentration_prior.html">Concentration Prior Type Analysis of Variation Bayesian Gaussian Mixture</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_pdf.html">Density Estimation for a Gaussian mixture</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_init.html">GMM Initialization Methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_covariances.html">GMM covariances</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm.html">Gaussian Mixture Model Ellipsoids</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_selection.html">Gaussian Mixture Model Selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mixture/plot_gmm_sin.html">Gaussian Mixture Model Sine Curve</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../gaussian_process/index.html">Gaussian Process for Machine Learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_noisy.html">Ability of Gaussian process regression (GPR) to estimate data noise-level</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_compare_gpr_krr.html">Comparison of kernel ridge and Gaussian process regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_co2.html">Forecasting of CO2 level on Mona Loa dataset using Gaussian process regression (GPR)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_noisy_targets.html">Gaussian Processes regression: basic introductory example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_iris.html">Gaussian process classification (GPC) on iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_on_structured_data.html">Gaussian processes on discrete data structures</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_xor.html">Illustration of Gaussian process classification (GPC) on the XOR dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpr_prior_posterior.html">Illustration of prior and posterior Gaussian process for different kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc_isoprobability.html">Iso-probability lines for Gaussian Processes classification (GPC)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../gaussian_process/plot_gpc.html">Probabilistic predictions with Gaussian process classification (GPC)</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../linear_model/index.html">Generalized Linear Models</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ard.html">Comparing Linear Bayesian Regressors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_comparison.html">Comparing various online solvers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_bayesian_ridge_curvefit.html">Curve Fitting with Bayesian Ridge Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_multinomial.html">Decision Boundaries of Multinomial and One-vs-Rest Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_early_stopping.html">Early stopping of Stochastic Gradient Descent</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_elastic_net_precomputed_gram_matrix_with_weighted_samples.html">Fitting an Elastic Net with a precomputed Gram Matrix and Weighted Samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_huber_vs_ridge.html">HuberRegressor vs Ridge on dataset with strong outliers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_multi_task_lasso_support.html">Joint feature selection with multi-task Lasso</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_l1_l2_sparsity.html">L1 Penalty and Sparsity in Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_and_elasticnet.html">L1-based models for Sparse Signals</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_lars_ic.html">Lasso model selection via information criteria</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_model_selection.html">Lasso model selection: AIC-BIC / cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_dense_vs_sparse_data.html">Lasso on dense and sparse data</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_lasso_lasso_lars_elasticnet_path.html">Lasso, Lasso-LARS, and Elastic Net paths</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic.html">Logistic function</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sparse_logistic_regression_mnist.html">MNIST classification using multinomial logistic + L1</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sparse_logistic_regression_20newsgroups.html">Multiclass sparse logistic regression on 20newgroups</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_nnls.html">Non-negative least squares</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgdocsvm_vs_ocsvm.html">One-Class SVM versus One-Class SVM using Stochastic Gradient Descent</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ols.html">Ordinary Least Squares Example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ols_ridge_variance.html">Ordinary Least Squares and Ridge Regression Variance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_omp.html">Orthogonal Matching Pursuit</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ridge_path.html">Plot Ridge coefficients as a function of the regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_iris.html">Plot multi-class SGD on the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_poisson_regression_non_normal_loss.html">Poisson regression and non-normal loss</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_polynomial_interpolation.html">Polynomial and Spline interpolation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_quantile_regression.html">Quantile regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_logistic_path.html">Regularization path of L1- Logistic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ridge_coeffs.html">Ridge coefficients as a function of the L2 Regularization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_robust_fit.html">Robust linear estimator fitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_ransac.html">Robust linear model estimation using RANSAC</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_separating_hyperplane.html">SGD: Maximum margin separating hyperplane</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_penalties.html">SGD: Penalties</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_weighted_samples.html">SGD: Weighted samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_sgd_loss_functions.html">SGD: convex loss functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_theilsen.html">Theil-Sen Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../linear_model/plot_tweedie_regression_insurance_claims.html">Tweedie regression on insurance claims</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../inspection/index.html">Inspection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_linear_model_coefficient_interpretation.html">Common pitfalls in the interpretation of coefficients of linear models</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_causal_interpretation.html">Failure of Machine Learning to infer causal effects</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_partial_dependence.html">Partial Dependence and Individual Conditional Expectation Plots</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_permutation_importance.html">Permutation Importance vs Random Forest Feature Importance (MDI)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../inspection/plot_permutation_importance_multicollinear.html">Permutation Importance with Multicollinear or Correlated Features</a></li>
</ul>
</details></li>
<li class="toctree-l1 current active has-children"><a class="current reference internal" href="#">Kernel Approximation</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="plot_scalable_poly_kernels.html">Scalable learning with polynomial kernel approximation</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../manifold/index.html">Manifold learning</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_compare_methods.html">Comparison of Manifold Learning methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_manifold_sphere.html">Manifold Learning methods on a severed sphere</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_lle_digits.html">Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_mds.html">Multi-dimensional scaling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_swissroll.html">Swiss Roll And Swiss-Hole Reduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manifold/plot_t_sne_perplexity.html">t-SNE: The effect of various perplexity values on the shape</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../miscellaneous/index.html">Miscellaneous</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_partial_dependence_visualization_api.html">Advanced Plotting With Partial Dependence</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_anomaly_comparison.html">Comparing anomaly detection algorithms for outlier detection on toy datasets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_kernel_ridge_regression.html">Comparison of kernel ridge regression and SVR</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_pipeline_display.html">Displaying Pipelines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_estimator_representation.html">Displaying estimators and complex pipelines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_outlier_detection_bench.html">Evaluation of outlier detection estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_kernel_approximation.html">Explicit feature map approximation for RBF kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_multioutput_face_completion.html">Face completion with a multi-output estimators</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_set_output.html">Introducing the <code class="docutils literal notranslate"><span class="pre">set_output</span></code> API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_isotonic_regression.html">Isotonic Regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_metadata_routing.html">Metadata Routing</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_multilabel.html">Multilabel classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_roc_curve_visualization_api.html">ROC Curve with Visualization API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_johnson_lindenstrauss_bound.html">The Johnson-Lindenstrauss bound for embedding with random projections</a></li>
<li class="toctree-l2"><a class="reference internal" href="../miscellaneous/plot_display_object_visualization.html">Visualizations with Display Objects</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../impute/index.html">Missing Value Imputation</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../impute/plot_missing_values.html">Imputing missing values before building an estimator</a></li>
<li class="toctree-l2"><a class="reference internal" href="../impute/plot_iterative_imputer_variants_comparison.html">Imputing missing values with variants of IterativeImputer</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../model_selection/index.html">Model Selection</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_refit_callable.html">Balance model complexity and cross-validated score</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_likelihood_ratios.html">Class Likelihood Ratios to measure classification performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_randomized_search.html">Comparing randomized search and grid search for hyperparameter estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_successive_halving_heatmap.html">Comparison between grid search and successive halving</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_confusion_matrix.html">Confusion matrix</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_digits.html">Custom refit strategy of a grid search with cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_multi_metric_evaluation.html">Demonstration of multi-metric evaluation on cross_val_score and GridSearchCV</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_det.html">Detection error tradeoff (DET) curve</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_train_error_vs_test_error.html">Effect of model regularization on training and test error</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_roc.html">Multiclass Receiver Operating Characteristic (ROC)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_nested_cross_validation_iris.html">Nested versus non-nested cross-validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_cv_predict.html">Plotting Cross-Validated Predictions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_learning_curve.html">Plotting Learning Curves and Checking Models’ Scalability</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_tuned_decision_threshold.html">Post-hoc tuning the cut-off point of decision function</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_cost_sensitive_learning.html">Post-tuning the decision threshold for cost-sensitive learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_precision_recall.html">Precision-Recall</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_roc_crossval.html">Receiver Operating Characteristic (ROC) with cross validation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_text_feature_extraction.html">Sample pipeline for text feature extraction and evaluation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_grid_search_stats.html">Statistical comparison of models using grid search</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_successive_halving_iterations.html">Successive Halving Iterations</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_permutation_tests_for_classification.html">Test with permutations the significance of a classification score</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_underfitting_overfitting.html">Underfitting vs. Overfitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../model_selection/plot_cv_indices.html">Visualizing cross-validation behavior in scikit-learn</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../multiclass/index.html">Multiclass methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../multiclass/plot_multiclass_overview.html">Overview of multiclass training meta-estimators</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../multioutput/index.html">Multioutput methods</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../multioutput/plot_classifier_chain_yeast.html">Multilabel classification using a classifier chain</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../neighbors/index.html">Nearest Neighbors</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/approximate_nearest_neighbors.html">Approximate nearest neighbors in TSNE</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_caching_nearest_neighbors.html">Caching nearest neighbors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_classification.html">Comparing Nearest Neighbors with and without Neighborhood Components Analysis</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_dim_reduction.html">Dimensionality Reduction with Neighborhood Components Analysis</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_species_kde.html">Kernel Density Estimate of Species Distributions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_digits_kde_sampling.html">Kernel Density Estimation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nearest_centroid.html">Nearest Centroid Classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_classification.html">Nearest Neighbors Classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_regression.html">Nearest Neighbors regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_nca_illustration.html">Neighborhood Components Analysis Illustration</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_lof_novelty_detection.html">Novelty detection with Local Outlier Factor (LOF)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_lof_outlier_detection.html">Outlier detection with Local Outlier Factor (LOF)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neighbors/plot_kde_1d.html">Simple 1D Kernel Density Estimation</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../neural_networks/index.html">Neural Networks</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mlp_training_curves.html">Compare Stochastic learning strategies for MLPClassifier</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_rbm_logistic_classification.html">Restricted Boltzmann Machine features for digit classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mlp_alpha.html">Varying regularization in Multi-layer Perceptron</a></li>
<li class="toctree-l2"><a class="reference internal" href="../neural_networks/plot_mnist_filters.html">Visualization of MLP weights on MNIST</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../compose/index.html">Pipelines and composite estimators</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_column_transformer.html">Column Transformer with Heterogeneous Data Sources</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_column_transformer_mixed_types.html">Column Transformer with Mixed Types</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_feature_union.html">Concatenating multiple feature extraction methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_transformed_target.html">Effect of transforming the targets in regression model</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_digits_pipe.html">Pipelining: chaining a PCA and a logistic regression</a></li>
<li class="toctree-l2"><a class="reference internal" href="../compose/plot_compare_reduction.html">Selecting dimensionality reduction with Pipeline and GridSearchCV</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../preprocessing/index.html">Preprocessing</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_all_scaling.html">Compare the effect of different scalers on data with outliers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_target_encoder.html">Comparing Target Encoder with Other Encoders</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization_strategies.html">Demonstrating the different strategies of KBinsDiscretizer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization_classification.html">Feature discretization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_scaling_importance.html">Importance of Feature Scaling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_map_data_to_normal.html">Map data to a normal distribution</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_target_encoder_cross_val.html">Target Encoder’s Internal Cross fitting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../preprocessing/plot_discretization.html">Using KBinsDiscretizer to discretize continuous features</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../semi_supervised/index.html">Semi Supervised Classification</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_semi_supervised_versus_svm_iris.html">Decision boundary of semi-supervised classifiers versus SVM on the Iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_self_training_varying_threshold.html">Effect of varying threshold for self-training</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_label_propagation_digits_active_learning.html">Label Propagation digits active learning</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_label_propagation_digits.html">Label Propagation digits: Demonstrating performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_label_propagation_structure.html">Label Propagation learning a complex structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="../semi_supervised/plot_semi_supervised_newsgroups.html">Semi-supervised Classification on a Text Dataset</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../svm/index.html">Support Vector Machines</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_oneclass.html">One-class SVM with non-linear kernel (RBF)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_svm_kernels.html">Plot classification boundaries with different SVM Kernels</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_iris_svc.html">Plot different SVM classifiers in the iris dataset</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_linearsvc_support_vectors.html">Plot the support vectors in LinearSVC</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_rbf_parameters.html">RBF SVM parameters</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_svm_margin.html">SVM Margins Example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_svm_tie_breaking.html">SVM Tie Breaking Example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_custom_kernel.html">SVM with custom kernel</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_svm_anova.html">SVM-Anova: SVM with univariate feature selection</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_separating_hyperplane.html">SVM: Maximum margin separating hyperplane</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_separating_hyperplane_unbalanced.html">SVM: Separating hyperplane for unbalanced classes</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_weighted_samples.html">SVM: Weighted samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_svm_scale_c.html">Scaling the regularization parameter for SVCs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../svm/plot_svm_regression.html">Support Vector Regression (SVR) using linear and non-linear kernels</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../exercises/index.html">Tutorial exercises</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../exercises/plot_cv_diabetes.html">Cross-validation on diabetes Dataset Exercise</a></li>
<li class="toctree-l2"><a class="reference internal" href="../exercises/plot_digits_classification_exercise.html">Digits Classification Exercise</a></li>
<li class="toctree-l2"><a class="reference internal" href="../exercises/plot_iris_exercise.html">SVM Exercise</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../text/index.html">Working with text documents</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="../text/plot_document_classification_20newsgroups.html">Classification of text documents using sparse features</a></li>
<li class="toctree-l2"><a class="reference internal" href="../text/plot_document_clustering.html">Clustering text documents using k-means</a></li>
<li class="toctree-l2"><a class="reference internal" href="../text/plot_hashing_vs_dict_vectorizer.html">FeatureHasher and DictVectorizer Comparison</a></li>
</ul>
</details></li>
</ul>
</div>
</nav></div>
</div>
<div class="sidebar-primary-items__end sidebar-primary__section">
</div>
<div id="rtd-footer-container"></div>
</div>
<main id="main-content" class="bd-main" role="main">
<div class="bd-content">
<div class="bd-article-container">
<div class="bd-header-article d-print-none">
<div class="header-article-items header-article__inner">
<div class="header-article-items__start">
<div class="header-article-item">
<nav aria-label="Breadcrumb" class="d-print-none">
<ul class="bd-breadcrumbs">
<li class="breadcrumb-item breadcrumb-home">
<a href="../../index.html" class="nav-link" aria-label="Home">
<i class="fa-solid fa-home"></i>
</a>
</li>
<li class="breadcrumb-item"><a href="../index.html" class="nav-link">Examples</a></li>
<li class="breadcrumb-item active" aria-current="page">Kernel Approximation</li>
</ul>
</nav>
</div>
</div>
</div>
</div>
<div id="searchbox"></div>
<article class="bd-article">
<section id="kernel-approximation">
<span id="kernel-approximation-examples"></span><span id="sphx-glr-auto-examples-kernel-approximation"></span><h1>Kernel Approximation<a class="headerlink" href="#kernel-approximation" title="Link to this heading">#</a></h1>
<p>Examples concerning the <a class="reference internal" href="../../api/sklearn.kernel_approximation.html#module-sklearn.kernel_approximation" title="sklearn.kernel_approximation"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.kernel_approximation</span></code></a> module.</p>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the use of PolynomialCountSketch to efficiently generate polynomial kernel feature-space approximations. This is used to train linear classifiers that approximate the accuracy of kernelized ones."><img alt="" src="../../_images/sphx_glr_plot_scalable_poly_kernels_thumb.png" />
<p><a class="reference internal" href="plot_scalable_poly_kernels.html#sphx-glr-auto-examples-kernel-approximation-plot-scalable-poly-kernels-py"><span class="std std-ref">Scalable learning with polynomial kernel approximation</span></a></p>
<div class="sphx-glr-thumbnail-title">Scalable learning with polynomial kernel approximation</div>
</div></div><div class="toctree-wrapper compound">
</div>
</section>
</article>
<footer class="bd-footer-article">
<div class="footer-article-items footer-article__inner">
<div class="footer-article-item">
<div class="prev-next-area">
<a class="left-prev"
href="../inspection/plot_permutation_importance_multicollinear.html"
title="previous page">
<i class="fa-solid fa-angle-left"></i>
<div class="prev-next-info">
<p class="prev-next-subtitle">previous</p>
<p class="prev-next-title">Permutation Importance with Multicollinear or Correlated Features</p>
</div>
</a>
<a class="right-next"
href="plot_scalable_poly_kernels.html"
title="next page">
<div class="prev-next-info">
<p class="prev-next-subtitle">next</p>
<p class="prev-next-title">Scalable learning with polynomial kernel approximation</p>
</div>
<i class="fa-solid fa-angle-right"></i>
</a>
</div></div>
</div>
</footer>
</div>
</div>
<footer class="bd-footer-content">
</footer>
</main>
</div>
</div>
<!-- Scripts loaded after <body> so the DOM is not blocked -->
<script src="../../_static/scripts/bootstrap.js?digest=dfe6caa3a7d634c4db9b"></script>
<script src="../../_static/scripts/pydata-sphinx-theme.js?digest=dfe6caa3a7d634c4db9b"></script>
<footer class="bd-footer">
<div class="bd-footer__inner bd-page-width">
<div class="footer-items__start">
<div class="footer-item">
<p class="copyright">
© Copyright 2007 - 2024, scikit-learn developers (BSD License).
<br/>
</p>
</div>
</div>
</div>
</footer>
</body>
</html>