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<li><a class="reference internal" href="#">Feature discretization</a></li>
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to download the full example code or to run this example in your browser via Binder</p>
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<section class="sphx-glr-example-title" id="feature-discretization">
<span id="sphx-glr-auto-examples-preprocessing-plot-discretization-classification-py"></span><h1>Feature discretization<a class="headerlink" href="#feature-discretization" title="Permalink to this heading">¶</a></h1>
<p>A demonstration of feature discretization on synthetic classification datasets.
Feature discretization decomposes each feature into a set of bins, here equally
distributed in width. The discrete values are then one-hot encoded, and given
to a linear classifier. This preprocessing enables a non-linear behavior even
though the classifier is linear.</p>
<p>On this example, the first two rows represent linearly non-separable datasets
(moons and concentric circles) while the third is approximately linearly
separable. On the two linearly non-separable datasets, feature discretization
largely increases the performance of linear classifiers. On the linearly
separable dataset, feature discretization decreases the performance of linear
classifiers. Two non-linear classifiers are also shown for comparison.</p>
<p>This example should be taken with a grain of salt, as the intuition conveyed
does not necessarily carry over to real datasets. Particularly in
high-dimensional spaces, data can more easily be separated linearly. Moreover,
using feature discretization and one-hot encoding increases the number of
features, which easily lead to overfitting when the number of samples is small.</p>
<p>The plots show training points in solid colors and testing points
semi-transparent. The lower right shows the classification accuracy on the test
set.</p>
<img src="../../_images/sphx_glr_plot_discretization_classification_001.png" srcset="../../_images/sphx_glr_plot_discretization_classification_001.png" alt="Input data, LogisticRegression, LinearSVC, KBinsDiscretizer LogisticRegression, KBinsDiscretizer LinearSVC, GradientBoostingClassifier, SVC" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>dataset 0
---------
LogisticRegression: 0.86
LinearSVC: 0.86
KBinsDiscretizer + LogisticRegression: 0.86
KBinsDiscretizer + LinearSVC: 0.94
GradientBoostingClassifier: 0.90
SVC: 0.94
dataset 1
---------
LogisticRegression: 0.40
LinearSVC: 0.40
KBinsDiscretizer + LogisticRegression: 0.78
KBinsDiscretizer + LinearSVC: 0.80
GradientBoostingClassifier: 0.84
SVC: 0.84
dataset 2
---------
LogisticRegression: 0.98
LinearSVC: 0.96
KBinsDiscretizer + LogisticRegression: 0.94
KBinsDiscretizer + LinearSVC: 0.94
GradientBoostingClassifier: 0.94
SVC: 0.98
</pre></div>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Code source: Tom Dupré la Tour</span>
<span class="c1"># Adapted from plot_classifier_comparison by Gaël Varoquaux and Andreas Müller</span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.colors</span> <span class="kn">import</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ListedColormap</span></a>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.make_moons.html#sklearn.datasets.make_moons" title="sklearn.datasets.make_moons" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_moons</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.datasets.make_circles.html#sklearn.datasets.make_circles" title="sklearn.datasets.make_circles" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_circles</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.datasets.make_classification.html#sklearn.datasets.make_classification" title="sklearn.datasets.make_classification" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_classification</span></a>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="sklearn.linear_model.LogisticRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LogisticRegression</span></a>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GridSearchCV</span></a>
<span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.KBinsDiscretizer.html#sklearn.preprocessing.KBinsDiscretizer" title="sklearn.preprocessing.KBinsDiscretizer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KBinsDiscretizer</span></a>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVC</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="sklearn.svm.LinearSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearSVC</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GradientBoostingClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.utils._testing</span> <span class="kn">import</span> <span class="n">ignore_warnings</span>
<span class="kn">from</span> <span class="nn">sklearn.exceptions</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.exceptions.ConvergenceWarning.html#sklearn.exceptions.ConvergenceWarning" title="sklearn.exceptions.ConvergenceWarning" class="sphx-glr-backref-module-sklearn-exceptions sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ConvergenceWarning</span></a>
<span class="n">h</span> <span class="o">=</span> <span class="mf">0.02</span> <span class="c1"># step size in the mesh</span>
<span class="k">def</span> <span class="nf">get_name</span><span class="p">(</span><span class="n">estimator</span><span class="p">):</span>
<span class="n">name</span> <span class="o">=</span> <span class="n">estimator</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span>
<span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">"Pipeline"</span><span class="p">:</span>
<span class="n">name</span> <span class="o">=</span> <span class="p">[</span><span class="n">get_name</span><span class="p">(</span><span class="n">est</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="k">for</span> <span class="n">est</span> <span class="ow">in</span> <span class="n">estimator</span><span class="o">.</span><span class="n">steps</span><span class="p">]</span>
<span class="n">name</span> <span class="o">=</span> <span class="s2">" + "</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
<span class="k">return</span> <span class="n">name</span>
<span class="c1"># list of (estimator, param_grid), where param_grid is used in GridSearchCV</span>
<span class="c1"># The parameter spaces in this example are limited to a narrow band to reduce</span>
<span class="c1"># its runtime. In a real use case, a broader search space for the algorithms</span>
<span class="c1"># should be used.</span>
<span class="n">classifiers</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">(</span>
<a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="sklearn.linear_model.LogisticRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LogisticRegression</span></a><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)),</span>
<span class="p">{</span><span class="s2">"logisticregression__C"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">)},</span>
<span class="p">),</span>
<span class="p">(</span>
<a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span> <a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="sklearn.svm.LinearSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearSVC</span></a><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)),</span>
<span class="p">{</span><span class="s2">"linearsvc__C"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">)},</span>
<span class="p">),</span>
<span class="p">(</span>
<a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span>
<a href="../../modules/generated/sklearn.preprocessing.KBinsDiscretizer.html#sklearn.preprocessing.KBinsDiscretizer" title="sklearn.preprocessing.KBinsDiscretizer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KBinsDiscretizer</span></a><span class="p">(</span><span class="n">encode</span><span class="o">=</span><span class="s2">"onehot"</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="sklearn.linear_model.LogisticRegression" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LogisticRegression</span></a><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span>
<span class="p">),</span>
<span class="p">{</span>
<span class="s2">"kbinsdiscretizer__n_bins"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">8</span><span class="p">),</span>
<span class="s2">"logisticregression__C"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>
<span class="p">},</span>
<span class="p">),</span>
<span class="p">(</span>
<a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span>
<a href="../../modules/generated/sklearn.preprocessing.KBinsDiscretizer.html#sklearn.preprocessing.KBinsDiscretizer" title="sklearn.preprocessing.KBinsDiscretizer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KBinsDiscretizer</span></a><span class="p">(</span><span class="n">encode</span><span class="o">=</span><span class="s2">"onehot"</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="sklearn.svm.LinearSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearSVC</span></a><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span>
<span class="p">),</span>
<span class="p">{</span>
<span class="s2">"kbinsdiscretizer__n_bins"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">8</span><span class="p">),</span>
<span class="s2">"linearsvc__C"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>
<span class="p">},</span>
<span class="p">),</span>
<span class="p">(</span>
<a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span> <a href="../../modules/generated/sklearn.ensemble.GradientBoostingClassifier.html#sklearn.ensemble.GradientBoostingClassifier" title="sklearn.ensemble.GradientBoostingClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GradientBoostingClassifier</span></a><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="p">),</span>
<span class="p">{</span><span class="s2">"gradientboostingclassifier__learning_rate"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">)},</span>
<span class="p">),</span>
<span class="p">(</span>
<a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="sklearn.svm.SVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SVC</span></a><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)),</span>
<span class="p">{</span><span class="s2">"svc__C"</span><span class="p">:</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.logspace.html#numpy.logspace" title="numpy.logspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">)},</span>
<span class="p">),</span>
<span class="p">]</span>
<span class="n">names</span> <span class="o">=</span> <span class="p">[</span><span class="n">get_name</span><span class="p">(</span><span class="n">e</span><span class="p">)</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s2">"StandardScaler + "</span><span class="p">,</span> <span class="s2">""</span><span class="p">)</span> <span class="k">for</span> <span class="n">e</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">classifiers</span><span class="p">]</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">datasets</span> <span class="o">=</span> <span class="p">[</span>
<a href="../../modules/generated/sklearn.datasets.make_moons.html#sklearn.datasets.make_moons" title="sklearn.datasets.make_moons" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_moons</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.datasets.make_circles.html#sklearn.datasets.make_circles" title="sklearn.datasets.make_circles" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_circles</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">factor</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.datasets.make_classification.html#sklearn.datasets.make_classification" title="sklearn.datasets.make_classification" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_classification</span></a><span class="p">(</span>
<span class="n">n_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span>
<span class="n">n_features</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">n_redundant</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
<span class="n">n_informative</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">n_clusters_per_class</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="p">),</span>
<span class="p">]</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span>
<span class="n">nrows</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">datasets</span><span class="p">),</span> <span class="n">ncols</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">classifiers</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">21</span><span class="p">,</span> <span class="mi">9</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">cm_piyg</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">PiYG</span>
<span class="n">cm_bright</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ListedColormap</span></a><span class="p">([</span><span class="s2">"#b30065"</span><span class="p">,</span> <span class="s2">"#178000"</span><span class="p">])</span>
<span class="c1"># iterate over datasets</span>
<span class="k">for</span> <span class="n">ds_cnt</span><span class="p">,</span> <span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">datasets</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="se">\n</span><span class="s2">dataset </span><span class="si">{</span><span class="n">ds_cnt</span><span class="si">}</span><span class="se">\n</span><span class="s2">---------"</span><span class="p">)</span>
<span class="c1"># split into training and test part</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a><span class="p">(</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span>
<span class="p">)</span>
<span class="c1"># create the grid for background colors</span>
<span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">-</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="mf">0.5</span>
<span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">-</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="mf">0.5</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span><span class="p">,</span> <span class="n">h</span><span class="p">),</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span><span class="p">,</span> <span class="n">h</span><span class="p">))</span>
<span class="c1"># plot the dataset first</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="n">ds_cnt</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="k">if</span> <span class="n">ds_cnt</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Input data"</span><span class="p">)</span>
<span class="c1"># plot the training points</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_train</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_train</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y_train</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cm_bright</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span><span class="p">)</span>
<span class="c1"># and testing points</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<span class="n">X_test</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_test</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y_test</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cm_bright</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span>
<span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">xx</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">yy</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<span class="c1"># iterate over classifiers</span>
<span class="k">for</span> <span class="n">est_idx</span><span class="p">,</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">(</span><span class="n">estimator</span><span class="p">,</span> <span class="n">param_grid</span><span class="p">))</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">names</span><span class="p">,</span> <span class="n">classifiers</span><span class="p">)):</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="n">ds_cnt</span><span class="p">,</span> <span class="n">est_idx</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV" title="sklearn.model_selection.GridSearchCV" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GridSearchCV</span></a><span class="p">(</span><span class="n">estimator</span><span class="o">=</span><span class="n">estimator</span><span class="p">,</span> <span class="n">param_grid</span><span class="o">=</span><span class="n">param_grid</span><span class="p">)</span>
<span class="k">with</span> <span class="n">ignore_warnings</span><span class="p">(</span><span class="n">category</span><span class="o">=</span><a href="../../modules/generated/sklearn.exceptions.ConvergenceWarning.html#sklearn.exceptions.ConvergenceWarning" title="sklearn.exceptions.ConvergenceWarning" class="sphx-glr-backref-module-sklearn-exceptions sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ConvergenceWarning</span></a><span class="p">):</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">score</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">score</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="c1"># plot the decision boundary. For that, we will assign a color to each</span>
<span class="c1"># point in the mesh [x_min, x_max]*[y_min, y_max].</span>
<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="s2">"decision_function"</span><span class="p">):</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.column_stack.html#numpy.column_stack" title="numpy.column_stack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">column_stack</span></a><span class="p">([</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()]))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.column_stack.html#numpy.column_stack" title="numpy.column_stack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">column_stack</span></a><span class="p">([</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()]))[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="c1"># put the result into a color plot</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">contourf</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cm_piyg</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
<span class="c1"># plot the training points</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<span class="n">X_train</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_train</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y_train</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cm_bright</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span>
<span class="p">)</span>
<span class="c1"># and testing points</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<span class="n">X_test</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">X_test</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">c</span><span class="o">=</span><span class="n">y_test</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">cm_bright</span><span class="p">,</span>
<span class="n">edgecolors</span><span class="o">=</span><span class="s2">"k"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">xx</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">yy</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<span class="k">if</span> <span class="n">ds_cnt</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">name</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s2">" + "</span><span class="p">,</span> <span class="s2">"</span><span class="se">\n</span><span class="s2">"</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span>
<span class="mf">0.95</span><span class="p">,</span>
<span class="mf">0.06</span><span class="p">,</span>
<span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">score</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="s2">"0"</span><span class="p">),</span>
<span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span>
<span class="n">bbox</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">boxstyle</span><span class="o">=</span><span class="s2">"round"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="s2">"white"</span><span class="p">),</span>
<span class="n">transform</span><span class="o">=</span><span class="n">ax</span><span class="o">.</span><span class="n">transAxes</span><span class="p">,</span>
<span class="n">horizontalalignment</span><span class="o">=</span><span class="s2">"right"</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<span class="c1"># Add suptitles above the figure</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="matplotlib.pyplot.subplots_adjust" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="n">top</span><span class="o">=</span><span class="mf">0.90</span><span class="p">)</span>
<span class="n">suptitles</span> <span class="o">=</span> <span class="p">[</span>
<span class="s2">"Linear classifiers"</span><span class="p">,</span>
<span class="s2">"Feature discretization and linear classifiers"</span><span class="p">,</span>
<span class="s2">"Non-linear classifiers"</span><span class="p">,</span>
<span class="p">]</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">suptitle</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">suptitles</span><span class="p">):</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span>
<span class="mf">1.05</span><span class="p">,</span>
<span class="mf">1.25</span><span class="p">,</span>
<span class="n">suptitle</span><span class="p">,</span>
<span class="n">transform</span><span class="o">=</span><span class="n">ax</span><span class="o">.</span><span class="n">transAxes</span><span class="p">,</span>
<span class="n">horizontalalignment</span><span class="o">=</span><span class="s2">"center"</span><span class="p">,</span>
<span class="n">size</span><span class="o">=</span><span class="s2">"x-large"</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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