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<div class="section" id="receiver-operating-characteristic-roc-with-cross-validation">
<span id="sphx-glr-auto-examples-model-selection-plot-roc-crossval-py"></span><h1>Receiver Operating Characteristic (ROC) with cross validation<a class="headerlink" href="#receiver-operating-characteristic-roc-with-cross-validation" title="Permalink to this headline">¶</a></h1>
<p>Example of Receiver Operating Characteristic (ROC) metric to evaluate
classifier output quality using cross-validation.</p>
<p>ROC curves typically feature true positive rate on the Y axis, and false
positive rate on the X axis. This means that the top left corner of the plot is
the “ideal” point - a false positive rate of zero, and a true positive rate of
one. This is not very realistic, but it does mean that a larger area under the
curve (AUC) is usually better.</p>
<p>The “steepness” of ROC curves is also important, since it is ideal to maximize
the true positive rate while minimizing the false positive rate.</p>
<p>This example shows the ROC response of different datasets, created from K-fold
cross-validation. Taking all of these curves, it is possible to calculate the
mean area under curve, and see the variance of the curve when the
training set is split into different subsets. This roughly shows how the
classifier output is affected by changes in the training data, and how
different the splits generated by K-fold cross-validation are from one another.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<dl class="last docutils">
<dt>See also <code class="xref py py-func docutils literal"><span class="pre">sklearn.metrics.auc_score</span></code>,</dt>
<dd><a class="reference internal" href="../../modules/generated/sklearn.model_selection.cross_val_score.html#sklearn.model_selection.cross_val_score" title="sklearn.model_selection.cross_val_score"><code class="xref py py-func docutils literal"><span class="pre">sklearn.model_selection.cross_val_score</span></code></a>,
<a class="reference internal" href="plot_roc.html#sphx-glr-auto-examples-model-selection-plot-roc-py"><span class="std std-ref">Receiver Operating Characteristic (ROC)</span></a>,</dd>
</dl>
</div>
<img alt="../../_images/sphx_glr_plot_roc_crossval_001.png" class="align-center" src="../../_images/sphx_glr_plot_roc_crossval_001.png" />
<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="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">scipy</span> <span class="kn">import</span> <span class="n">interp</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">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">cycle</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">svm</span><span class="p">,</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.metrics.auc.html#sklearn.metrics.auc" title="View documentation for sklearn.metrics.auc"><span class="n">auc</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.StratifiedKFold.html#sklearn.model_selection.StratifiedKFold" title="View documentation for sklearn.model_selection.StratifiedKFold"><span class="n">StratifiedKFold</span></a>
<span class="c1"># #############################################################################</span>
<span class="c1"># Data IO and generation</span>
<span class="c1"># Import some data to play with</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="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">y</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">y</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">]</span>
<span class="n">n_samples</span><span class="p">,</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="c1"># Add noisy features</span>
<span class="n">random_state</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.RandomState.wald.html#numpy.random.RandomState" title="View documentation for numpy.random.RandomState"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/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">X</span><span class="p">,</span> <span class="n">random_state</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="mi">200</span> <span class="o">*</span> <span class="n">n_features</span><span class="p">)]</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Classification and ROC analysis</span>
<span class="c1"># Run classifier with cross-validation and plot ROC curves</span>
<span class="n">cv</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.StratifiedKFold.html#sklearn.model_selection.StratifiedKFold" title="View documentation for sklearn.model_selection.StratifiedKFold"><span class="n">StratifiedKFold</span></a><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>
<span class="n">classifier</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC" title="View documentation for sklearn.svm.SVC"><span class="n">svm</span><span class="o">.</span><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">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="n">random_state</span><span class="p">)</span>
<span class="n">tprs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">aucs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">mean_fpr</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/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">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">train</span><span class="p">,</span> <span class="n">test</span> <span class="ow">in</span> <span class="n">cv</span><span class="o">.</span><span class="n">split</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">probas_</span> <span class="o">=</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">train</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">train</span><span class="p">])</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">test</span><span class="p">])</span>
<span class="c1"># Compute ROC curve and area the curve</span>
<span class="n">fpr</span><span class="p">,</span> <span class="n">tpr</span><span class="p">,</span> <span class="n">thresholds</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.roc_curve.html#sklearn.metrics.roc_curve" title="View documentation for sklearn.metrics.roc_curve"><span class="n">roc_curve</span></a><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">test</span><span class="p">],</span> <span class="n">probas_</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">tprs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">interp</span><span class="p">(</span><span class="n">mean_fpr</span><span class="p">,</span> <span class="n">fpr</span><span class="p">,</span> <span class="n">tpr</span><span class="p">))</span>
<span class="n">tprs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="n">roc_auc</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.auc.html#sklearn.metrics.auc" title="View documentation for sklearn.metrics.auc"><span class="n">auc</span></a><span class="p">(</span><span class="n">fpr</span><span class="p">,</span> <span class="n">tpr</span><span class="p">)</span>
<span class="n">aucs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">roc_auc</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">fpr</span><span class="p">,</span> <span class="n">tpr</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'ROC fold </span><span class="si">%d</span><span class="s1"> (AUC = </span><span class="si">%0.2f</span><span class="s1">)'</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">roc_auc</span><span class="p">))</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><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">1</span><span class="p">],</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">'--'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'r'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'Luck'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=.</span><span class="mi">8</span><span class="p">)</span>
<span class="n">mean_tpr</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/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">tprs</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">mean_tpr</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span>
<span class="n">mean_auc</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.auc.html#sklearn.metrics.auc" title="View documentation for sklearn.metrics.auc"><span class="n">auc</span></a><span class="p">(</span><span class="n">mean_fpr</span><span class="p">,</span> <span class="n">mean_tpr</span><span class="p">)</span>
<span class="n">std_auc</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.std.html#numpy.std" title="View documentation for numpy.std"><span class="n">np</span><span class="o">.</span><span class="n">std</span></a><span class="p">(</span><span class="n">aucs</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">mean_fpr</span><span class="p">,</span> <span class="n">mean_tpr</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'b'</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s1">'Mean ROC (AUC = </span><span class="si">%0.2f</span><span class="s1"> $\pm$ </span><span class="si">%0.2f</span><span class="s1">)'</span> <span class="o">%</span> <span class="p">(</span><span class="n">mean_auc</span><span class="p">,</span> <span class="n">std_auc</span><span class="p">),</span>
<span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=.</span><span class="mi">8</span><span class="p">)</span>
<span class="n">std_tpr</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.std.html#numpy.std" title="View documentation for numpy.std"><span class="n">np</span><span class="o">.</span><span class="n">std</span></a><span class="p">(</span><span class="n">tprs</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">tprs_upper</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.minimum.html#numpy.minimum" title="View documentation for numpy.minimum"><span class="n">np</span><span class="o">.</span><span class="n">minimum</span></a><span class="p">(</span><span class="n">mean_tpr</span> <span class="o">+</span> <span class="n">std_tpr</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">tprs_lower</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.maximum.html#numpy.maximum" title="View documentation for numpy.maximum"><span class="n">np</span><span class="o">.</span><span class="n">maximum</span></a><span class="p">(</span><span class="n">mean_tpr</span> <span class="o">-</span> <span class="n">std_tpr</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.fill_between.html#matplotlib.pyplot.fill_between" title="View documentation for matplotlib.pyplot.fill_between"><span class="n">plt</span><span class="o">.</span><span class="n">fill_between</span></a><span class="p">(</span><span class="n">mean_fpr</span><span class="p">,</span> <span class="n">tprs_lower</span><span class="p">,</span> <span class="n">tprs_upper</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'grey'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=.</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s1">'$\pm$ 1 std. dev.'</span><span class="p">)</span>
<a href="http://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="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">])</span>
<a href="http://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="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">])</span>
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<a href="http://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">'True Positive Rate'</span><span class="p">)</span>
<a href="http://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">'Receiver operating characteristic example'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/legend_api.html#matplotlib.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="s2">"lower right"</span><span class="p">)</span>
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