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<li><a class="reference internal" href="#">Plot the decision surfaces of ensembles of trees on the iris dataset</a></li>
</ul>
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<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-ensemble-plot-forest-iris-py"><span class="std std-ref">here</span></a>
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="plot-the-decision-surfaces-of-ensembles-of-trees-on-the-iris-dataset">
<span id="sphx-glr-auto-examples-ensemble-plot-forest-iris-py"></span><h1>Plot the decision surfaces of ensembles of trees on the iris dataset<a class="headerlink" href="#plot-the-decision-surfaces-of-ensembles-of-trees-on-the-iris-dataset" title="Permalink to this heading">¶</a></h1>
<p>Plot the decision surfaces of forests of randomized trees trained on pairs of
features of the iris dataset.</p>
<p>This plot compares the decision surfaces learned by a decision tree classifier
(first column), by a random forest classifier (second column), by an extra-
trees classifier (third column) and by an AdaBoost classifier (fourth column).</p>
<p>In the first row, the classifiers are built using the sepal width and
the sepal length features only, on the second row using the petal length and
sepal length only, and on the third row using the petal width and the
petal length only.</p>
<p>In descending order of quality, when trained (outside of this example) on all
4 features using 30 estimators and scored using 10 fold cross validation,
we see:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><a href="../../modules/generated/sklearn.ensemble.ExtraTreesClassifier.html#sklearn.ensemble.ExtraTreesClassifier" title="sklearn.ensemble.ExtraTreesClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ExtraTreesClassifier</span></a><span class="p">()</span> <span class="c1"># 0.95 score</span>
<a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="sklearn.ensemble.RandomForestClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RandomForestClassifier</span></a><span class="p">()</span> <span class="c1"># 0.94 score</span>
<span class="n">AdaBoost</span><span class="p">(</span><span class="n">DecisionTree</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">3</span><span class="p">))</span> <span class="c1"># 0.94 score</span>
<span class="n">DecisionTree</span><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span> <span class="c1"># 0.94 score</span>
</pre></div>
</div>
<p>Increasing <code class="docutils literal notranslate"><span class="pre">max_depth</span></code> for AdaBoost lowers the standard deviation of
the scores (but the average score does not improve).</p>
<p>See the console’s output for further details about each model.</p>
<p>In this example you might try to:</p>
<ol class="arabic simple">
<li><p>vary the <code class="docutils literal notranslate"><span class="pre">max_depth</span></code> for the <code class="docutils literal notranslate"><span class="pre">DecisionTreeClassifier</span></code> and
<code class="docutils literal notranslate"><span class="pre">AdaBoostClassifier</span></code>, perhaps try <code class="docutils literal notranslate"><span class="pre">max_depth=3</span></code> for the
<code class="docutils literal notranslate"><span class="pre">DecisionTreeClassifier</span></code> or <code class="docutils literal notranslate"><span class="pre">max_depth=None</span></code> for <code class="docutils literal notranslate"><span class="pre">AdaBoostClassifier</span></code></p></li>
<li><p>vary <code class="docutils literal notranslate"><span class="pre">n_estimators</span></code></p></li>
</ol>
<p>It is worth noting that RandomForests and ExtraTrees can be fitted in parallel
on many cores as each tree is built independently of the others. AdaBoost’s
samples are built sequentially and so do not use multiple cores.</p>
<img src="../../_images/sphx_glr_plot_forest_iris_001.png" srcset="../../_images/sphx_glr_plot_forest_iris_001.png" alt="Classifiers on feature subsets of the Iris dataset, DecisionTree, RandomForest, ExtraTrees, AdaBoost" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>DecisionTree with features [0, 1] has a score of 0.9266666666666666
RandomForest with 30 estimators with features [0, 1] has a score of 0.9266666666666666
ExtraTrees with 30 estimators with features [0, 1] has a score of 0.9266666666666666
AdaBoost with 30 estimators with features [0, 1] has a score of 0.8666666666666667
DecisionTree with features [0, 2] has a score of 0.9933333333333333
RandomForest with 30 estimators with features [0, 2] has a score of 0.9933333333333333
ExtraTrees with 30 estimators with features [0, 2] has a score of 0.9933333333333333
AdaBoost with 30 estimators with features [0, 2] has a score of 0.9933333333333333
DecisionTree with features [2, 3] has a score of 0.9933333333333333
RandomForest with 30 estimators with features [2, 3] has a score of 0.9933333333333333
ExtraTrees with 30 estimators with features [2, 3] has a score of 0.9933333333333333
AdaBoost with 30 estimators with features [2, 3] has a score of 0.9933333333333333
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="p">(</span>
<a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="sklearn.ensemble.RandomForestClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RandomForestClassifier</span></a><span class="p">,</span>
<a href="../../modules/generated/sklearn.ensemble.ExtraTreesClassifier.html#sklearn.ensemble.ExtraTreesClassifier" title="sklearn.ensemble.ExtraTreesClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ExtraTreesClassifier</span></a><span class="p">,</span>
<a href="../../modules/generated/sklearn.ensemble.AdaBoostClassifier.html#sklearn.ensemble.AdaBoostClassifier" title="sklearn.ensemble.AdaBoostClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">AdaBoostClassifier</span></a><span class="p">,</span>
<span class="p">)</span>
<span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier" class="sphx-glr-backref-module-sklearn-tree sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">DecisionTreeClassifier</span></a>
<span class="c1"># Parameters</span>
<span class="n">n_classes</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">n_estimators</span> <span class="o">=</span> <span class="mi">30</span>
<span class="n">cmap</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">RdYlBu</span>
<span class="n">plot_step</span> <span class="o">=</span> <span class="mf">0.02</span> <span class="c1"># fine step width for decision surface contours</span>
<span class="n">plot_step_coarser</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="c1"># step widths for coarse classifier guesses</span>
<span class="n">RANDOM_SEED</span> <span class="o">=</span> <span class="mi">13</span> <span class="c1"># fix the seed on each iteration</span>
<span class="c1"># Load data</span>
<span class="n">iris</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a><span class="p">()</span>
<span class="n">plot_idx</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">models</span> <span class="o">=</span> <span class="p">[</span>
<a href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier" class="sphx-glr-backref-module-sklearn-tree sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">DecisionTreeClassifier</span></a><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="kc">None</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier" title="sklearn.ensemble.RandomForestClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">RandomForestClassifier</span></a><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="n">n_estimators</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.ensemble.ExtraTreesClassifier.html#sklearn.ensemble.ExtraTreesClassifier" title="sklearn.ensemble.ExtraTreesClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ExtraTreesClassifier</span></a><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="n">n_estimators</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.ensemble.AdaBoostClassifier.html#sklearn.ensemble.AdaBoostClassifier" title="sklearn.ensemble.AdaBoostClassifier" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">AdaBoostClassifier</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier" class="sphx-glr-backref-module-sklearn-tree sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">DecisionTreeClassifier</span></a><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">3</span><span class="p">),</span> <span class="n">n_estimators</span><span class="o">=</span><span class="n">n_estimators</span><span class="p">),</span>
<span class="p">]</span>
<span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]):</span>
<span class="k">for</span> <span class="n">model</span> <span class="ow">in</span> <span class="n">models</span><span class="p">:</span>
<span class="c1"># We only take the two corresponding features</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">[:,</span> <span class="n">pair</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="c1"># Shuffle</span>
<span class="n">idx</span> <span class="o">=</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</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html#numpy.random.seed" title="numpy.random.seed" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span></a><span class="p">(</span><span class="n">RANDOM_SEED</span><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.shuffle.html#numpy.random.shuffle" title="numpy.random.shuffle" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">shuffle</span></a><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="c1"># Standardize</span>
<span class="n">mean</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">std</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="p">(</span><span class="n">X</span> <span class="o">-</span> <span class="n">mean</span><span class="p">)</span> <span class="o">/</span> <span class="n">std</span>
<span class="c1"># Train</span>
<span class="n">model</span><span class="o">.</span><span class="n">fit</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="n">scores</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">score</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="c1"># Create a title for each column and the console by using str() and</span>
<span class="c1"># slicing away useless parts of the string</span>
<span class="n">model_title</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">model</span><span class="p">))</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s2">"."</span><span class="p">)[</span><span class="o">-</span><span class="mi">1</span><span class="p">][:</span><span class="o">-</span><span class="mi">2</span><span class="p">][:</span> <span class="o">-</span><span class="nb">len</span><span class="p">(</span><span class="s2">"Classifier"</span><span class="p">)]</span>
<span class="n">model_details</span> <span class="o">=</span> <span class="n">model_title</span>
<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="s2">"estimators_"</span><span class="p">):</span>
<span class="n">model_details</span> <span class="o">+=</span> <span class="s2">" with </span><span class="si">{}</span><span class="s2"> estimators"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">estimators_</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">model_details</span> <span class="o">+</span> <span class="s2">" with features"</span><span class="p">,</span> <span class="n">pair</span><span class="p">,</span> <span class="s2">"has a score of"</span><span class="p">,</span> <span class="n">scores</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" 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">subplot</span></a><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">plot_idx</span><span class="p">)</span>
<span class="k">if</span> <span class="n">plot_idx</span> <span class="o"><=</span> <span class="nb">len</span><span class="p">(</span><span class="n">models</span><span class="p">):</span>
<span class="c1"># Add a title at the top of each column</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" 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">title</span></a><span class="p">(</span><span class="n">model_title</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">9</span><span class="p">)</span>
<span class="c1"># Now plot the decision boundary using a fine mesh as input to a</span>
<span class="c1"># filled contour plot</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="mi">1</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="mi">1</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="mi">1</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="mi">1</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">plot_step</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">plot_step</span><span class="p">)</span>
<span class="p">)</span>
<span class="c1"># Plot either a single DecisionTreeClassifier or alpha blend the</span>
<span class="c1"># decision surfaces of the ensemble of classifiers</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <a href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier" class="sphx-glr-backref-module-sklearn-tree sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">DecisionTreeClassifier</span></a><span class="p">):</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.c_.html#numpy.c_" title="numpy.c_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">c_</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="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">cs</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contourf.html#matplotlib.pyplot.contourf" title="matplotlib.pyplot.contourf" 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">contourf</span></a><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">cmap</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># Choose alpha blend level with respect to the number</span>
<span class="c1"># of estimators</span>
<span class="c1"># that are in use (noting that AdaBoost can use fewer estimators</span>
<span class="c1"># than its maximum if it achieves a good enough fit early on)</span>
<span class="n">estimator_alpha</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">estimators_</span><span class="p">)</span>
<span class="k">for</span> <span class="n">tree</span> <span class="ow">in</span> <span class="n">model</span><span class="o">.</span><span class="n">estimators_</span><span class="p">:</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">tree</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.c_.html#numpy.c_" title="numpy.c_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">c_</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="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">cs</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contourf.html#matplotlib.pyplot.contourf" title="matplotlib.pyplot.contourf" 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">contourf</span></a><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">alpha</span><span class="o">=</span><span class="n">estimator_alpha</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">)</span>
<span class="c1"># Build a coarser grid to plot a set of ensemble classifications</span>
<span class="c1"># to show how these are different to what we see in the decision</span>
<span class="c1"># surfaces. These points are regularly space and do not have a</span>
<span class="c1"># black outline</span>
<span class="n">xx_coarser</span><span class="p">,</span> <span class="n">yy_coarser</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">plot_step_coarser</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">plot_step_coarser</span><span class="p">),</span>
<span class="p">)</span>
<span class="n">Z_points_coarser</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.c_.html#numpy.c_" title="numpy.c_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><span class="p">[</span><span class="n">xx_coarser</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy_coarser</span><span class="o">.</span><span class="n">ravel</span><span class="p">()]</span>
<span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx_coarser</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">cs_points</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" 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">scatter</span></a><span class="p">(</span>
<span class="n">xx_coarser</span><span class="p">,</span>
<span class="n">yy_coarser</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span>
<span class="n">c</span><span class="o">=</span><span class="n">Z_points_coarser</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span>
<span class="n">edgecolors</span><span class="o">=</span><span class="s2">"none"</span><span class="p">,</span>
<span class="p">)</span>
<span class="c1"># Plot the training points, these are clustered together and have a</span>
<span class="c1"># black outline</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" 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">scatter</span></a><span class="p">(</span>
<span class="n">X</span><span class="p">[:,</span> <span class="mi">0</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="n">c</span><span class="o">=</span><span class="n">y</span><span class="p">,</span>
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