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<p class="first admonition-title">Note</p>
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<div class="sphx-glr-example-title section" id="two-class-adaboost">
<span id="sphx-glr-auto-examples-ensemble-plot-adaboost-twoclass-py"></span><h1>Two-class AdaBoost<a class="headerlink" href="#two-class-adaboost" title="Permalink to this headline">¶</a></h1>
<p>This example fits an AdaBoosted decision stump on a non-linearly separable
classification dataset composed of two “Gaussian quantiles” clusters
(see <a class="reference internal" href="../../modules/generated/sklearn.datasets.make_gaussian_quantiles.html#sklearn.datasets.make_gaussian_quantiles" title="sklearn.datasets.make_gaussian_quantiles"><code class="xref py py-func docutils literal"><span class="pre">sklearn.datasets.make_gaussian_quantiles</span></code></a>) and plots the decision
boundary and decision scores. The distributions of decision scores are shown
separately for samples of class A and B. The predicted class label for each
sample is determined by the sign of the decision score. Samples with decision
scores greater than zero are classified as B, and are otherwise classified
as A. The magnitude of a decision score determines the degree of likeness with
the predicted class label. Additionally, a new dataset could be constructed
containing a desired purity of class B, for example, by only selecting samples
with a decision score above some value.</p>
<img alt="../../_images/sphx_glr_plot_adaboost_twoclass_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_adaboost_twoclass_001.png" />
<p class="sphx-glr-script-out">Out:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="c1"># Author: Noel Dawe <[email protected]></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">sklearn.ensemble</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.ensemble.AdaBoostClassifier.html#sklearn.ensemble.AdaBoostClassifier" title="View documentation for sklearn.ensemble.AdaBoostClassifier"><span class="n">AdaBoostClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="View documentation for sklearn.tree.DecisionTreeClassifier"><span class="n">DecisionTreeClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.datasets.make_gaussian_quantiles.html#sklearn.datasets.make_gaussian_quantiles" title="View documentation for sklearn.datasets.make_gaussian_quantiles"><span class="n">make_gaussian_quantiles</span></a>
<span class="c1"># Construct dataset</span>
<span class="n">X1</span><span class="p">,</span> <span class="n">y1</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_gaussian_quantiles.html#sklearn.datasets.make_gaussian_quantiles" title="View documentation for sklearn.datasets.make_gaussian_quantiles"><span class="n">make_gaussian_quantiles</span></a><span class="p">(</span><span class="n">cov</span><span class="o">=</span><span class="mf">2.</span><span class="p">,</span>
<span class="n">n_samples</span><span class="o">=</span><span class="mi">200</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_classes</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">1</span><span class="p">)</span>
<span class="n">X2</span><span class="p">,</span> <span class="n">y2</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_gaussian_quantiles.html#sklearn.datasets.make_gaussian_quantiles" title="View documentation for sklearn.datasets.make_gaussian_quantiles"><span class="n">make_gaussian_quantiles</span></a><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="n">cov</span><span class="o">=</span><span class="mf">1.5</span><span class="p">,</span>
<span class="n">n_samples</span><span class="o">=</span><span class="mi">300</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_classes</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">1</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.html#numpy.concatenate" title="View documentation for numpy.concatenate"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span></a><span class="p">((</span><span class="n">X1</span><span class="p">,</span> <span class="n">X2</span><span class="p">))</span>
<span class="n">y</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.html#numpy.concatenate" title="View documentation for numpy.concatenate"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span></a><span class="p">((</span><span class="n">y1</span><span class="p">,</span> <span class="o">-</span> <span class="n">y2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
<span class="c1"># Create and fit an AdaBoosted decision tree</span>
<span class="n">bdt</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.AdaBoostClassifier.html#sklearn.ensemble.AdaBoostClassifier" title="View documentation for sklearn.ensemble.AdaBoostClassifier"><span class="n">AdaBoostClassifier</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="View documentation for sklearn.tree.DecisionTreeClassifier"><span class="n">DecisionTreeClassifier</span></a><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
<span class="n">algorithm</span><span class="o">=</span><span class="s2">"SAMME"</span><span class="p">,</span>
<span class="n">n_estimators</span><span class="o">=</span><span class="mi">200</span><span class="p">)</span>
<span class="n">bdt</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">plot_colors</span> <span class="o">=</span> <span class="s2">"br"</span>
<span class="n">plot_step</span> <span class="o">=</span> <span class="mf">0.02</span>
<span class="n">class_names</span> <span class="o">=</span> <span class="s2">"AB"</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="c1"># Plot the decision boundaries</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="View documentation for matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</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://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="View documentation for numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html#numpy.arange" title="View documentation for numpy.arange"><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://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html#numpy.arange" title="View documentation for numpy.arange"><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="n">Z</span> <span class="o">=</span> <span class="n">bdt</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><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/api/_as_gen/matplotlib.pyplot.contourf.html#matplotlib.pyplot.contourf" title="View documentation for matplotlib.pyplot.contourf"><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">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Paired</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<span class="c1"># Plot the training points</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span> <span class="n">class_names</span><span class="p">,</span> <span class="n">plot_colors</span><span class="p">):</span>
<span class="n">idx</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html#numpy.where" title="View documentation for numpy.where"><span class="n">np</span><span class="o">.</span><span class="n">where</span></a><span class="p">(</span><span class="n">y</span> <span class="o">==</span> <span class="n">i</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><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="n">idx</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="n">idx</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">c</span><span class="p">,</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">Paired</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Class </span><span class="si">%s</span><span class="s2">"</span> <span class="o">%</span> <span class="n">n</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlim.html#matplotlib.pyplot.xlim" title="View documentation for matplotlib.pyplot.xlim"><span class="n">plt</span><span class="o">.</span><span class="n">xlim</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>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylim.html#matplotlib.pyplot.ylim" title="View documentation for matplotlib.pyplot.ylim"><span class="n">plt</span><span class="o">.</span><span class="n">ylim</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>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'upper right'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'y'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Decision Boundary'</span><span class="p">)</span>
<span class="c1"># Plot the two-class decision scores</span>
<span class="n">twoclass_output</span> <span class="o">=</span> <span class="n">bdt</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">plot_range</span> <span class="o">=</span> <span class="p">(</span><span class="n">twoclass_output</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">twoclass_output</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="View documentation for matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span> <span class="n">class_names</span><span class="p">,</span> <span class="n">plot_colors</span><span class="p">):</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.hist.html#matplotlib.pyplot.hist" title="View documentation for matplotlib.pyplot.hist"><span class="n">plt</span><span class="o">.</span><span class="n">hist</span></a><span class="p">(</span><span class="n">twoclass_output</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="n">i</span><span class="p">],</span>
<span class="n">bins</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="nb">range</span><span class="o">=</span><span class="n">plot_range</span><span class="p">,</span>
<span class="n">facecolor</span><span class="o">=</span><span class="n">c</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'Class </span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="n">n</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
<span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">y2</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">()</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">((</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">y2</span> <span class="o">*</span> <span class="mf">1.2</span><span class="p">))</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'upper right'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'Samples'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'Score'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Decision Scores'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="View documentation for matplotlib.pyplot.tight_layout"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="View documentation for matplotlib.pyplot.subplots_adjust"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="n">wspace</span><span class="o">=</span><span class="mf">0.35</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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