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<p class="first admonition-title">Note</p>
<p class="last">Click <a class="reference internal" href="#sphx-glr-download-auto-examples-classification-plot-classification-probability-py"><span class="std std-ref">here</span></a> to download the full example code or run this example in your browser via Binder</p>
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<div class="sphx-glr-example-title section" id="plot-classification-probability">
<span id="sphx-glr-auto-examples-classification-plot-classification-probability-py"></span><h1>Plot classification probability<a class="headerlink" href="#plot-classification-probability" title="Permalink to this headline">¶</a></h1>
<p>Plot the classification probability for different classifiers. We use a 3
class dataset, and we classify it with a Support Vector classifier, L1
and L2 penalized logistic regression with either a One-Vs-Rest or multinomial
setting, and Gaussian process classification.</p>
<p>The logistic regression is not a multiclass classifier out of the box. As
a result it can identify only the first class.</p>
<img alt="../../_images/sphx_glr_plot_classification_probability_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_classification_probability_001.png" />
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none"><div class="highlight"><pre><span></span>classif_rate for L1 logistic : 79.333333
classif_rate for L2 logistic (OvR) : 76.666667
classif_rate for Linear SVC : 82.000000
classif_rate for L2 logistic (Multinomial) : 82.000000
classif_rate for GPC : 82.666667
</pre></div>
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<div class="highlight-python"><div class="highlight"><pre><span></span><span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="c1"># Author: Alexandre Gramfort <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<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="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</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="View documentation for sklearn.svm.SVC"><span class="n">SVC</span></a>
<span class="kn">from</span> <span class="nn">sklearn.gaussian_process</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.gaussian_process.GaussianProcessClassifier.html#sklearn.gaussian_process.GaussianProcessClassifier" title="View documentation for sklearn.gaussian_process.GaussianProcessClassifier"><span class="n">GaussianProcessClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.gaussian_process.kernels</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.gaussian_process.kernels.RBF.html#sklearn.gaussian_process.kernels.RBF" title="View documentation for sklearn.gaussian_process.kernels.RBF"><span class="n">RBF</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="n">iris</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="View documentation for sklearn.datasets.load_iris"><span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span></a><span class="p">()</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="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span> <span class="c1"># we only take the first two features for visualization</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="n">n_features</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</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="mf">1.0</span>
<span class="n">kernel</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">*</span> <a href="../../modules/generated/sklearn.gaussian_process.kernels.RBF.html#sklearn.gaussian_process.kernels.RBF" title="View documentation for sklearn.gaussian_process.kernels.RBF"><span class="n">RBF</span></a><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">])</span> <span class="c1"># for GPC</span>
<span class="c1"># Create different classifiers. The logistic regression cannot do</span>
<span class="c1"># multiclass out of the box.</span>
<span class="n">classifiers</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'L1 logistic'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</span></a><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">penalty</span><span class="o">=</span><span class="s1">'l1'</span><span class="p">),</span>
<span class="s1">'L2 logistic (OvR)'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</span></a><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">penalty</span><span class="o">=</span><span class="s1">'l2'</span><span class="p">),</span>
<span class="s1">'Linear SVC'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="View documentation for sklearn.svm.SVC"><span class="n">SVC</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'linear'</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">probability</span><span class="o">=</span><span class="bp">True</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="s1">'L2 logistic (Multinomial)'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression" title="View documentation for sklearn.linear_model.LogisticRegression"><span class="n">LogisticRegression</span></a><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">solver</span><span class="o">=</span><span class="s1">'lbfgs'</span><span class="p">,</span> <span class="n">multi_class</span><span class="o">=</span><span class="s1">'multinomial'</span><span class="p">),</span>
<span class="s1">'GPC'</span><span class="p">:</span> <a href="../../modules/generated/sklearn.gaussian_process.GaussianProcessClassifier.html#sklearn.gaussian_process.GaussianProcessClassifier" title="View documentation for sklearn.gaussian_process.GaussianProcessClassifier"><span class="n">GaussianProcessClassifier</span></a><span class="p">(</span><span class="n">kernel</span><span class="p">)</span>
<span class="p">}</span>
<span class="n">n_classifiers</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">classifiers</span><span class="p">)</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">3</span> <span class="o">*</span> <span class="mi">2</span><span class="p">,</span> <span class="n">n_classifiers</span> <span class="o">*</span> <span class="mi">2</span><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">bottom</span><span class="o">=.</span><span class="mi">2</span><span class="p">,</span> <span class="n">top</span><span class="o">=.</span><span class="mi">95</span><span class="p">)</span>
<span class="n">xx</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">100</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.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span><span class="o">.</span><span class="n">T</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><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
<span class="n">Xfull</span> <span class="o">=</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="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">classifier</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">classifiers</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="n">classifier</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">y_pred</span> <span class="o">=</span> <span class="n">classifier</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">classif_rate</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html#numpy.mean" title="View documentation for numpy.mean"><span class="n">np</span><span class="o">.</span><span class="n">mean</span></a><span class="p">(</span><span class="n">y_pred</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span> <span class="o">==</span> <span class="n">y</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <span class="o">*</span> <span class="mi">100</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"classif_rate for </span><span class="si">%s</span><span class="s2"> : </span><span class="si">%f</span><span class="s2"> "</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">classif_rate</span><span class="p">))</span>
<span class="c1"># View probabilities=</span>
<span class="n">probas</span> <span class="o">=</span> <span class="n">classifier</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">Xfull</span><span class="p">)</span>
<span class="n">n_classes</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.unique.html#numpy.unique" title="View documentation for numpy.unique"><span class="n">np</span><span class="o">.</span><span class="n">unique</span></a><span class="p">(</span><span class="n">y_pred</span><span class="p">)</span><span class="o">.</span><span class="n">size</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_classes</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="n">n_classifiers</span><span class="p">,</span> <span class="n">n_classes</span><span class="p">,</span> <span class="n">index</span> <span class="o">*</span> <span class="n">n_classes</span> <span class="o">+</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</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="s2">"Class </span><span class="si">%d</span><span class="s2">"</span> <span class="o">%</span> <span class="n">k</span><span class="p">)</span>
<span class="k">if</span> <span class="n">k</span> <span class="o">==</span> <span class="mi">0</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="n">name</span><span class="p">)</span>
<span class="n">imshow_handle</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="View documentation for matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">probas</span><span class="p">[:,</span> <span class="n">k</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">)),</span>
<span class="n">extent</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">origin</span><span class="o">=</span><span class="s1">'lower'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="View documentation for matplotlib.pyplot.xticks"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="View documentation for matplotlib.pyplot.yticks"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<span class="n">idx</span> <span class="o">=</span> <span class="p">(</span><span class="n">y_pred</span> <span class="o">==</span> <span class="n">k</span><span class="p">)</span>
<span class="k">if</span> <span class="n">idx</span><span class="o">.</span><span class="n">any</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">marker</span><span class="o">=</span><span class="s1">'o'</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axes.html#matplotlib.pyplot.axes" title="View documentation for matplotlib.pyplot.axes"><span class="n">plt</span><span class="o">.</span><span class="n">axes</span></a><span class="p">([</span><span class="mf">0.15</span><span class="p">,</span> <span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.05</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="s2">"Probability"</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="View documentation for matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">imshow_handle</span><span class="p">,</span> <span class="n">cax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s1">'horizontal'</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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