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<ul>
<li><a class="reference internal" href="#">Precision-Recall</a><ul>
<li><a class="reference internal" href="#in-binary-classification-settings">In binary classification settings</a><ul>
<li><a class="reference internal" href="#create-simple-data">Create simple data</a></li>
<li><a class="reference internal" href="#compute-the-average-precision-score">Compute the average precision score</a></li>
<li><a class="reference internal" href="#plot-the-precision-recall-curve">Plot the Precision-Recall curve</a></li>
</ul>
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<li><a class="reference internal" href="#in-multi-label-settings">In multi-label settings</a><ul>
<li><a class="reference internal" href="#create-multi-label-data-fit-and-predict">Create multi-label data, fit, and predict</a></li>
<li><a class="reference internal" href="#the-average-precision-score-in-multi-label-settings">The average precision score in multi-label settings</a></li>
<li><a class="reference internal" href="#plot-the-micro-averaged-precision-recall-curve">Plot the micro-averaged Precision-Recall curve</a></li>
<li><a class="reference internal" href="#plot-precision-recall-curve-for-each-class-and-iso-f1-curves">Plot Precision-Recall curve for each class and iso-f1 curves</a></li>
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<div class="section" id="precision-recall">
<span id="sphx-glr-auto-examples-model-selection-plot-precision-recall-py"></span><h1>Precision-Recall<a class="headerlink" href="#precision-recall" title="Permalink to this headline">¶</a></h1>
<p>Example of Precision-Recall metric to evaluate classifier output quality.</p>
<p>Precision-Recall is a useful measure of success of prediction when the
classes are very imbalanced. In information retrieval, precision is a
measure of result relevancy, while recall is a measure of how many truly
relevant results are returned.</p>
<p>The precision-recall curve shows the tradeoff between precision and
recall for different threshold. A high area under the curve represents
both high recall and high precision, where high precision relates to a
low false positive rate, and high recall relates to a low false negative
rate. High scores for both show that the classifier is returning accurate
results (high precision), as well as returning a majority of all positive
results (high recall).</p>
<p>A system with high recall but low precision returns many results, but most of
its predicted labels are incorrect when compared to the training labels. A
system with high precision but low recall is just the opposite, returning very
few results, but most of its predicted labels are correct when compared to the
training labels. An ideal system with high precision and high recall will
return many results, with all results labeled correctly.</p>
<p>Precision (<img class="math" src="../../_images/math/9dcbbef8e0f76051d388013b90a95bec3069e484.png" alt="P"/>) is defined as the number of true positives (<img class="math" src="../../_images/math/d3aa1ff959d5695cfd37dc9e0bbe7da71b7b3bc4.png" alt="T_p"/>)
over the number of true positives plus the number of false positives
(<img class="math" src="../../_images/math/a45eb409815563f5496bf48ef224ce4cb923d210.png" alt="F_p"/>).</p>
<p><img class="math" src="../../_images/math/4427313bbf584ad5dc95320f3fe1f8356b3c5f9f.png" alt="P = \frac{T_p}{T_p+F_p}"/></p>
<p>Recall (<img class="math" src="../../_images/math/a00254b18ffa992f0ef19f6e6e095b83c8f85e94.png" alt="R"/>) is defined as the number of true positives (<img class="math" src="../../_images/math/d3aa1ff959d5695cfd37dc9e0bbe7da71b7b3bc4.png" alt="T_p"/>)
over the number of true positives plus the number of false negatives
(<img class="math" src="../../_images/math/afd71442aee38aca1189c1f9637bd1840ae9965e.png" alt="F_n"/>).</p>
<p><img class="math" src="../../_images/math/3bcc92cd7cbd26a3d6c6aa0b407cb9d7c89c6254.png" alt="R = \frac{T_p}{T_p + F_n}"/></p>
<p>These quantities are also related to the (<img class="math" src="../../_images/math/8c53fbe6ce6d32b88c70c65652fbd3592a4d9048.png" alt="F_1"/>) score, which is defined
as the harmonic mean of precision and recall.</p>
<p><img class="math" src="../../_images/math/6d03e9528e504c0801b231b90bdb480e01269ea1.png" alt="F1 = 2\frac{P \times R}{P+R}"/></p>
<p>Note that the precision may not decrease with recall. The
definition of precision (<img class="math" src="../../_images/math/f8691f3cf6ee6642cdf86c9512293b7adffe8f89.png" alt="\frac{T_p}{T_p + F_p}"/>) shows that lowering
the threshold of a classifier may increase the denominator, by increasing the
number of results returned. If the threshold was previously set too high, the
new results may all be true positives, which will increase precision. If the
previous threshold was about right or too low, further lowering the threshold
will introduce false positives, decreasing precision.</p>
<p>Recall is defined as <img class="math" src="../../_images/math/5ba03dfa4df80f4848c44aaac0ba10f8595e4f06.png" alt="\frac{T_p}{T_p+F_n}"/>, where <img class="math" src="../../_images/math/a69e1d587e3642647e53aecf4805d448bc1b9ed0.png" alt="T_p+F_n"/> does
not depend on the classifier threshold. This means that lowering the classifier
threshold may increase recall, by increasing the number of true positive
results. It is also possible that lowering the threshold may leave recall
unchanged, while the precision fluctuates.</p>
<p>The relationship between recall and precision can be observed in the
stairstep area of the plot - at the edges of these steps a small change
in the threshold considerably reduces precision, with only a minor gain in
recall.</p>
<p><strong>Average precision</strong> (AP) summarizes such a plot as the weighted mean of
precisions achieved at each threshold, with the increase in recall from the
previous threshold used as the weight:</p>
<p><img class="math" src="../../_images/math/55a3b96113273e4a25048306bff9411823131bff.png" alt="\text{AP} = \sum_n (R_n - R_{n-1}) P_n"/></p>
<p>where <img class="math" src="../../_images/math/1e5d2a8a15728214cc4ddf4013464458f398338a.png" alt="P_n"/> and <img class="math" src="../../_images/math/209d3b1de562f50026e49bca1cd2c42af83383f0.png" alt="R_n"/> are the precision and recall at the
nth threshold. A pair <img class="math" src="../../_images/math/b3bdafad878c30dafff7bbaed0e860a43e435f4a.png" alt="(R_k, P_k)"/> is referred to as an
<em>operating point</em>.</p>
<p>AP and the trapezoidal area under the operating points
(<a class="reference internal" href="../../modules/generated/sklearn.metrics.auc.html#sklearn.metrics.auc" title="sklearn.metrics.auc"><code class="xref py py-func docutils literal"><span class="pre">sklearn.metrics.auc</span></code></a>) are common ways to summarize a precision-recall
curve that lead to different results. Read more in the
<a class="reference internal" href="../../modules/model_evaluation.html#precision-recall-f-measure-metrics"><span class="std std-ref">User Guide</span></a>.</p>
<p>Precision-recall curves are typically used in binary classification to study
the output of a classifier. In order to extend the precision-recall curve and
average precision to multi-class or multi-label classification, it is necessary
to binarize the output. One curve can be drawn per label, but one can also draw
a precision-recall curve by considering each element of the label indicator
matrix as a binary prediction (micro-averaging).</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<dl class="last docutils">
<dt>See also <a class="reference internal" href="../../modules/generated/sklearn.metrics.average_precision_score.html#sklearn.metrics.average_precision_score" title="sklearn.metrics.average_precision_score"><code class="xref py py-func docutils literal"><span class="pre">sklearn.metrics.average_precision_score</span></code></a>,</dt>
<dd><a class="reference internal" href="../../modules/generated/sklearn.metrics.recall_score.html#sklearn.metrics.recall_score" title="sklearn.metrics.recall_score"><code class="xref py py-func docutils literal"><span class="pre">sklearn.metrics.recall_score</span></code></a>,
<a class="reference internal" href="../../modules/generated/sklearn.metrics.precision_score.html#sklearn.metrics.precision_score" title="sklearn.metrics.precision_score"><code class="xref py py-func docutils literal"><span class="pre">sklearn.metrics.precision_score</span></code></a>,
<a class="reference internal" href="../../modules/generated/sklearn.metrics.f1_score.html#sklearn.metrics.f1_score" title="sklearn.metrics.f1_score"><code class="xref py py-func docutils literal"><span class="pre">sklearn.metrics.f1_score</span></code></a></dd>
</dl>
</div>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span>
</pre></div>
</div>
<div class="section" id="in-binary-classification-settings">
<h2>In binary classification settings<a class="headerlink" href="#in-binary-classification-settings" title="Permalink to this headline">¶</a></h2>
<div class="section" id="create-simple-data">
<h3>Create simple data<a class="headerlink" href="#create-simple-data" title="Permalink to this headline">¶</a></h3>
<p>Try to differentiate the two first classes of the iris data</p>
<div class="highlight-python"><div class="highlight"><pre><span></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.model_selection</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</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="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">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="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"># Limit to the two first classes, and split into training and test</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">y</span> <span class="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">test_size</span><span class="o">=.</span><span class="mi">5</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">random_state</span><span class="p">)</span>
<span class="c1"># Create a simple classifier</span>
<span class="n">classifier</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="View documentation for sklearn.svm.LinearSVC"><span class="n">svm</span><span class="o">.</span><span class="n">LinearSVC</span></a><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">classifier</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">y_score</span> <span class="o">=</span> <span class="n">classifier</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="compute-the-average-precision-score">
<h3>Compute the average precision score<a class="headerlink" href="#compute-the-average-precision-score" title="Permalink to this headline">¶</a></h3>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.average_precision_score.html#sklearn.metrics.average_precision_score" title="View documentation for sklearn.metrics.average_precision_score"><span class="n">average_precision_score</span></a>
<span class="n">average_precision</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.average_precision_score.html#sklearn.metrics.average_precision_score" title="View documentation for sklearn.metrics.average_precision_score"><span class="n">average_precision_score</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_score</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s1">'Average precision-recall score: {0:0.2f}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
<span class="n">average_precision</span><span class="p">))</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-default"><div class="highlight"><pre><span></span><span class="n">Average</span> <span class="n">precision</span><span class="o">-</span><span class="n">recall</span> <span class="n">score</span><span class="p">:</span> <span class="mf">0.88</span>
</pre></div>
</div>
</div>
<div class="section" id="plot-the-precision-recall-curve">
<h3>Plot the Precision-Recall curve<a class="headerlink" href="#plot-the-precision-recall-curve" title="Permalink to this headline">¶</a></h3>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.precision_recall_curve.html#sklearn.metrics.precision_recall_curve" title="View documentation for sklearn.metrics.precision_recall_curve"><span class="n">precision_recall_curve</span></a>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="n">precision</span><span class="p">,</span> <span class="n">recall</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.precision_recall_curve.html#sklearn.metrics.precision_recall_curve" title="View documentation for sklearn.metrics.precision_recall_curve"><span class="n">precision_recall_curve</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_score</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.step.html#matplotlib.pyplot.step" title="View documentation for matplotlib.pyplot.step"><span class="n">plt</span><span class="o">.</span><span class="n">step</span></a><span class="p">(</span><span class="n">recall</span><span class="p">,</span> <span class="n">precision</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">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">where</span><span class="o">=</span><span class="s1">'post'</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">recall</span><span class="p">,</span> <span class="n">precision</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="s1">'post'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s1">'b'</span><span class="p">)</span>
<a href="http://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">'Recall'</span><span class="p">)</span>
<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">'Precision'</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="mf">0.0</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.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="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</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">'2-class Precision-Recall curve: AP={0:0.2f}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
<span class="n">average_precision</span><span class="p">))</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_precision_recall_001.png" class="align-center" src="../../_images/sphx_glr_plot_precision_recall_001.png" />
</div>
</div>
<div class="section" id="in-multi-label-settings">
<h2>In multi-label settings<a class="headerlink" href="#in-multi-label-settings" title="Permalink to this headline">¶</a></h2>
<div class="section" id="create-multi-label-data-fit-and-predict">
<h3>Create multi-label data, fit, and predict<a class="headerlink" href="#create-multi-label-data-fit-and-predict" title="Permalink to this headline">¶</a></h3>
<p>We create a multi-label dataset, to illustrate the precision-recall in
multi-label settings</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.label_binarize.html#sklearn.preprocessing.label_binarize" title="View documentation for sklearn.preprocessing.label_binarize"><span class="n">label_binarize</span></a>
<span class="c1"># Use label_binarize to be multi-label like settings</span>
<span class="n">Y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.label_binarize.html#sklearn.preprocessing.label_binarize" title="View documentation for sklearn.preprocessing.label_binarize"><span class="n">label_binarize</span></a><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">classes</span><span class="o">=</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="mi">2</span><span class="p">])</span>
<span class="n">n_classes</span> <span class="o">=</span> <span class="n">Y</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="c1"># Split into training and test</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">Y_train</span><span class="p">,</span> <span class="n">Y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=.</span><span class="mi">5</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="c1"># We use OneVsRestClassifier for multi-label prediction</span>
<span class="kn">from</span> <span class="nn">sklearn.multiclass</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.multiclass.OneVsRestClassifier.html#sklearn.multiclass.OneVsRestClassifier" title="View documentation for sklearn.multiclass.OneVsRestClassifier"><span class="n">OneVsRestClassifier</span></a>
<span class="c1"># Run classifier</span>
<span class="n">classifier</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.multiclass.OneVsRestClassifier.html#sklearn.multiclass.OneVsRestClassifier" title="View documentation for sklearn.multiclass.OneVsRestClassifier"><span class="n">OneVsRestClassifier</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="View documentation for sklearn.svm.LinearSVC"><span class="n">svm</span><span class="o">.</span><span class="n">LinearSVC</span></a><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">classifier</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train</span><span class="p">)</span>
<span class="n">y_score</span> <span class="o">=</span> <span class="n">classifier</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="the-average-precision-score-in-multi-label-settings">
<h3>The average precision score in multi-label settings<a class="headerlink" href="#the-average-precision-score-in-multi-label-settings" title="Permalink to this headline">¶</a></h3>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.precision_recall_curve.html#sklearn.metrics.precision_recall_curve" title="View documentation for sklearn.metrics.precision_recall_curve"><span class="n">precision_recall_curve</span></a>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.metrics.average_precision_score.html#sklearn.metrics.average_precision_score" title="View documentation for sklearn.metrics.average_precision_score"><span class="n">average_precision_score</span></a>
<span class="c1"># For each class</span>
<span class="n">precision</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="n">recall</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="n">average_precision</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
<span class="k">for</span> <span class="n">i</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>
<span class="n">precision</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">recall</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.precision_recall_curve.html#sklearn.metrics.precision_recall_curve" title="View documentation for sklearn.metrics.precision_recall_curve"><span class="n">precision_recall_curve</span></a><span class="p">(</span><span class="n">Y_test</span><span class="p">[:,</span> <span class="n">i</span><span class="p">],</span>
<span class="n">y_score</span><span class="p">[:,</span> <span class="n">i</span><span class="p">])</span>
<span class="n">average_precision</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.average_precision_score.html#sklearn.metrics.average_precision_score" title="View documentation for sklearn.metrics.average_precision_score"><span class="n">average_precision_score</span></a><span class="p">(</span><span class="n">Y_test</span><span class="p">[:,</span> <span class="n">i</span><span class="p">],</span> <span class="n">y_score</span><span class="p">[:,</span> <span class="n">i</span><span class="p">])</span>
<span class="c1"># A "micro-average": quantifying score on all classes jointly</span>
<span class="n">precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span> <span class="n">recall</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span> <span class="n">_</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.precision_recall_curve.html#sklearn.metrics.precision_recall_curve" title="View documentation for sklearn.metrics.precision_recall_curve"><span class="n">precision_recall_curve</span></a><span class="p">(</span><span class="n">Y_test</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span>
<span class="n">y_score</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
<span class="n">average_precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">]</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.average_precision_score.html#sklearn.metrics.average_precision_score" title="View documentation for sklearn.metrics.average_precision_score"><span class="n">average_precision_score</span></a><span class="p">(</span><span class="n">Y_test</span><span class="p">,</span> <span class="n">y_score</span><span class="p">,</span>
<span class="n">average</span><span class="o">=</span><span class="s2">"micro"</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s1">'Average precision score, micro-averaged over all classes: {0:0.2f}'</span>
<span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">average_precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">]))</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-default"><div class="highlight"><pre><span></span><span class="n">Average</span> <span class="n">precision</span> <span class="n">score</span><span class="p">,</span> <span class="n">micro</span><span class="o">-</span><span class="n">averaged</span> <span class="n">over</span> <span class="nb">all</span> <span class="n">classes</span><span class="p">:</span> <span class="mf">0.43</span>
</pre></div>
</div>
</div>
<div class="section" id="plot-the-micro-averaged-precision-recall-curve">
<h3>Plot the micro-averaged Precision-Recall curve<a class="headerlink" href="#plot-the-micro-averaged-precision-recall-curve" title="Permalink to this headline">¶</a></h3>
<div class="highlight-python"><div class="highlight"><pre><span></span><a href="http://matplotlib.org/api/_as_gen/matplotlib.figure.AxesStack.html#matplotlib.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>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.step.html#matplotlib.pyplot.step" title="View documentation for matplotlib.pyplot.step"><span class="n">plt</span><span class="o">.</span><span class="n">step</span></a><span class="p">(</span><span class="n">recall</span><span class="p">[</span><span class="s1">'micro'</span><span class="p">],</span> <span class="n">precision</span><span class="p">[</span><span class="s1">'micro'</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">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">where</span><span class="o">=</span><span class="s1">'post'</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">recall</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span> <span class="n">precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span> <span class="n">step</span><span class="o">=</span><span class="s1">'post'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="s1">'b'</span><span class="p">)</span>
<a href="http://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">'Recall'</span><span class="p">)</span>
<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">'Precision'</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="mf">0.0</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.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="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</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">'Average precision score, micro-averaged over all classes: AP={0:0.2f}'</span>
<span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">average_precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">]))</span>
</pre></div>
</div>
<img alt="../../_images/sphx_glr_plot_precision_recall_002.png" class="align-center" src="../../_images/sphx_glr_plot_precision_recall_002.png" />
</div>
<div class="section" id="plot-precision-recall-curve-for-each-class-and-iso-f1-curves">
<h3>Plot Precision-Recall curve for each class and iso-f1 curves<a class="headerlink" href="#plot-precision-recall-curve-for-each-class-and-iso-f1-curves" title="Permalink to this headline">¶</a></h3>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">cycle</span>
<span class="c1"># setup plot details</span>
<span class="n">colors</span> <span class="o">=</span> <span class="n">cycle</span><span class="p">([</span><span class="s1">'navy'</span><span class="p">,</span> <span class="s1">'turquoise'</span><span class="p">,</span> <span class="s1">'darkorange'</span><span class="p">,</span> <span class="s1">'cornflowerblue'</span><span class="p">,</span> <span class="s1">'teal'</span><span class="p">])</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.figure.AxesStack.html#matplotlib.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">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="n">f_scores</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="mf">0.2</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
<span class="n">lines</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">f_score</span> <span class="ow">in</span> <span class="n">f_scores</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.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="mf">0.01</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">f_score</span> <span class="o">*</span> <span class="n">x</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">x</span> <span class="o">-</span> <span class="n">f_score</span><span class="p">)</span>
<span class="n">l</span><span class="p">,</span> <span class="o">=</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">x</span><span class="p">[</span><span class="n">y</span> <span class="o">>=</span> <span class="mi">0</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">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.annotate.html#matplotlib.pyplot.annotate" title="View documentation for matplotlib.pyplot.annotate"><span class="n">plt</span><span class="o">.</span><span class="n">annotate</span></a><span class="p">(</span><span class="s1">'f1={0:0.1f}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">f_score</span><span class="p">),</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.9</span><span class="p">,</span> <span class="n">y</span><span class="p">[</span><span class="mi">45</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.02</span><span class="p">))</span>
<span class="n">lines</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s1">'iso-f1 curves'</span><span class="p">)</span>
<span class="n">l</span><span class="p">,</span> <span class="o">=</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">recall</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span> <span class="n">precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s1">'gold'</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">lines</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s1">'micro-average Precision-recall (area = {0:0.2f})'</span>
<span class="s1">''</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">average_precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">]))</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">color</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="n">n_classes</span><span class="p">),</span> <span class="n">colors</span><span class="p">):</span>
<span class="n">l</span><span class="p">,</span> <span class="o">=</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">recall</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">precision</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="n">color</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">lines</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s1">'Precision-recall for class {0} (area = {1:0.2f})'</span>
<span class="s1">''</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">average_precision</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
<span class="n">fig</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.gcf.html#matplotlib.pyplot.gcf" title="View documentation for matplotlib.pyplot.gcf"><span class="n">plt</span><span class="o">.</span><span class="n">gcf</span></a><span class="p">()</span>
<span class="n">fig</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">bottom</span><span class="o">=</span><span class="mf">0.25</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="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</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="mf">0.0</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.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">'Recall'</span><span class="p">)</span>
<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">'Precision'</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">'Extension of Precision-Recall curve to multi-class'</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">lines</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="o">-.</span><span class="mi">38</span><span class="p">),</span> <span class="n">prop</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="mi">14</span><span class="p">))</span>
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