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<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="#dataset-and-model">Dataset and model</a></li>
<li><a class="reference internal" href="#plot-the-precision-recall-curve">Plot the Precision-Recall curve</a></li>
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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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<section class="sphx-glr-example-title" 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="Link to this heading">¶</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 (<span class="math notranslate nohighlight">\(P\)</span>) is defined as the number of true positives (<span class="math notranslate nohighlight">\(T_p\)</span>)
over the number of true positives plus the number of false positives
(<span class="math notranslate nohighlight">\(F_p\)</span>).</p>
<p><span class="math notranslate nohighlight">\(P = \frac{T_p}{T_p+F_p}\)</span></p>
<p>Recall (<span class="math notranslate nohighlight">\(R\)</span>) is defined as the number of true positives (<span class="math notranslate nohighlight">\(T_p\)</span>)
over the number of true positives plus the number of false negatives
(<span class="math notranslate nohighlight">\(F_n\)</span>).</p>
<p><span class="math notranslate nohighlight">\(R = \frac{T_p}{T_p + F_n}\)</span></p>
<p>These quantities are also related to the <span class="math notranslate nohighlight">\(F_1\)</span> score, which is the
harmonic mean of precision and recall. Thus, we can compute the <span class="math notranslate nohighlight">\(F_1\)</span>
using the following formula:</p>
<p><span class="math notranslate nohighlight">\(F_1 = \frac{2T_p}{2T_p + F_p + F_n}\)</span></p>
<p>Note that the precision may not decrease with recall. The
definition of precision (<span class="math notranslate nohighlight">\(\frac{T_p}{T_p + F_p}\)</span>) 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 <span class="math notranslate nohighlight">\(\frac{T_p}{T_p+F_n}\)</span>, where <span class="math notranslate nohighlight">\(T_p+F_n\)</span> 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><span class="math notranslate nohighlight">\(\text{AP} = \sum_n (R_n - R_{n-1}) P_n\)</span></p>
<p>where <span class="math notranslate nohighlight">\(P_n\)</span> and <span class="math notranslate nohighlight">\(R_n\)</span> are the precision and recall at the
nth threshold. A pair <span class="math notranslate nohighlight">\((R_k, P_k)\)</span> 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 notranslate"><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="admonition-title">Note</p>
<dl class="simple">
<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 notranslate"><span class="pre">sklearn.metrics.average_precision_score</span></code></a>,</dt><dd><p><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 notranslate"><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 notranslate"><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 notranslate"><span class="pre">sklearn.metrics.f1_score</span></code></a></p>
</dd>
</dl>
</div>
<section id="in-binary-classification-settings">
<h2>In binary classification settings<a class="headerlink" href="#in-binary-classification-settings" title="Link to this heading">¶</a></h2>
<section id="dataset-and-model">
<h3>Dataset and model<a class="headerlink" href="#dataset-and-model" title="Link to this heading">¶</a></h3>
<p>We will use a Linear SVC classifier to differentiate two types of irises.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a>
<span class="kn">from</span> <span class="nn">sklearn.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="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><span class="n">train_test_split</span></a>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_iris.html#sklearn.datasets.load_iris" title="sklearn.datasets.load_iris" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">load_iris</span></a><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Add noisy features</span>
<span class="n">random_state</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html#numpy.concatenate" title="numpy.concatenate" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</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="n">axis</span><span class="o">=</span><span class="mi">1</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="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><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="mf">0.5</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>
</pre></div>
</div>
<p>Linear SVC will expect each feature to have a similar range of values. Thus,
we will first scale the data using a
<a class="reference internal" href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler"><code class="xref py py-class docutils literal notranslate"><span class="pre">StandardScaler</span></code></a>.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="sklearn.svm.LinearSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearSVC</span></a>
<span class="n">classifier</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span> <a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="sklearn.svm.LinearSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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">dual</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">)</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>
</pre></div>
</div>
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</style><div id="sk-container-id-55" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>Pipeline(steps=[('standardscaler', StandardScaler()),
('linearsvc',
LinearSVC(dual='auto',
random_state=RandomState(MT19937) at 0x7FDEBF5D0140))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-231" type="checkbox" ><label for="sk-estimator-id-231" class="sk-toggleable__label fitted sk-toggleable__label-arrow fitted"> Pipeline<a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.4/modules/generated/sklearn.pipeline.Pipeline.html">?<span>Documentation for Pipeline</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></label><div class="sk-toggleable__content fitted"><pre>Pipeline(steps=[('standardscaler', StandardScaler()),
('linearsvc',
LinearSVC(dual='auto',
random_state=RandomState(MT19937) at 0x7FDEBF5D0140))])</pre></div> </div></div><div class="sk-serial"><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-232" type="checkbox" ><label for="sk-estimator-id-232" class="sk-toggleable__label fitted sk-toggleable__label-arrow fitted"> StandardScaler<a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.4/modules/generated/sklearn.preprocessing.StandardScaler.html">?<span>Documentation for StandardScaler</span></a></label><div class="sk-toggleable__content fitted"><pre>StandardScaler()</pre></div> </div></div><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-233" type="checkbox" ><label for="sk-estimator-id-233" class="sk-toggleable__label fitted sk-toggleable__label-arrow fitted"> LinearSVC<a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.4/modules/generated/sklearn.svm.LinearSVC.html">?<span>Documentation for LinearSVC</span></a></label><div class="sk-toggleable__content fitted"><pre>LinearSVC(dual='auto', random_state=RandomState(MT19937) at 0x7FDEBF5D0140)</pre></div> </div></div></div></div></div></div>
</div>
<br />
<br /></section>
<section id="plot-the-precision-recall-curve">
<h3>Plot the Precision-Recall curve<a class="headerlink" href="#plot-the-precision-recall-curve" title="Link to this heading">¶</a></h3>
<p>To plot the precision-recall curve, you should use
<a class="reference internal" href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay" title="sklearn.metrics.PrecisionRecallDisplay"><code class="xref py py-class docutils literal notranslate"><span class="pre">PrecisionRecallDisplay</span></code></a>. Indeed, there is two
methods available depending if you already computed the predictions of the
classifier or not.</p>
<p>Let’s first plot the precision-recall curve without the classifier
predictions. We use
<a class="reference internal" href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay.from_estimator" title="sklearn.metrics.PrecisionRecallDisplay.from_estimator"><code class="xref py py-func docutils literal notranslate"><span class="pre">from_estimator</span></code></a> that
computes the predictions for us before plotting the curve.</p>
<div class="highlight-Python notranslate"><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.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay" title="sklearn.metrics.PrecisionRecallDisplay" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">PrecisionRecallDisplay</span></a>
<span class="n">display</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay.from_estimator" title="sklearn.metrics.PrecisionRecallDisplay.from_estimator" class="sphx-glr-backref-module-sklearn-metrics-PrecisionRecallDisplay sphx-glr-backref-type-py-method"><span class="n">PrecisionRecallDisplay</span><span class="o">.</span><span class="n">from_estimator</span></a><span class="p">(</span>
<span class="n">classifier</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s2">"LinearSVC"</span><span class="p">,</span> <span class="n">plot_chance_level</span><span class="o">=</span><span class="kc">True</span>
<span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">display</span><span class="o">.</span><span class="n">ax_</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"2-class Precision-Recall curve"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_precision_recall_001.png" srcset="../../_images/sphx_glr_plot_precision_recall_001.png" alt="2-class Precision-Recall curve" class = "sphx-glr-single-img"/><p>If we already got the estimated probabilities or scores for
our model, then we can use
<a class="reference internal" href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay.from_predictions" title="sklearn.metrics.PrecisionRecallDisplay.from_predictions"><code class="xref py py-func docutils literal notranslate"><span class="pre">from_predictions</span></code></a>.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></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>
<span class="n">display</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay.from_predictions" title="sklearn.metrics.PrecisionRecallDisplay.from_predictions" class="sphx-glr-backref-module-sklearn-metrics-PrecisionRecallDisplay sphx-glr-backref-type-py-method"><span class="n">PrecisionRecallDisplay</span><span class="o">.</span><span class="n">from_predictions</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">name</span><span class="o">=</span><span class="s2">"LinearSVC"</span><span class="p">,</span> <span class="n">plot_chance_level</span><span class="o">=</span><span class="kc">True</span>
<span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">display</span><span class="o">.</span><span class="n">ax_</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"2-class Precision-Recall curve"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_precision_recall_002.png" srcset="../../_images/sphx_glr_plot_precision_recall_002.png" alt="2-class Precision-Recall curve" class = "sphx-glr-single-img"/></section>
</section>
<section id="in-multi-label-settings">
<h2>In multi-label settings<a class="headerlink" href="#in-multi-label-settings" title="Link to this heading">¶</a></h2>
<p>The precision-recall curve does not support the multilabel setting. However,
one can decide how to handle this case. We show such an example below.</p>
<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="Link to this heading">¶</a></h3>
<p>We create a multi-label dataset, to illustrate the precision-recall in
multi-label settings.</p>
<div class="highlight-Python notranslate"><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="sklearn.preprocessing.label_binarize" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-function"><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="sklearn.preprocessing.label_binarize" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-function"><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="sklearn.model_selection.train_test_split" class="sphx-glr-backref-module-sklearn-model_selection sphx-glr-backref-type-py-function"><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="mf">0.5</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>
</pre></div>
</div>
<p>We use <a class="reference internal" href="../../modules/generated/sklearn.multiclass.OneVsRestClassifier.html#sklearn.multiclass.OneVsRestClassifier" title="sklearn.multiclass.OneVsRestClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">OneVsRestClassifier</span></code></a> for multi-label
prediction.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></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="sklearn.multiclass.OneVsRestClassifier" class="sphx-glr-backref-module-sklearn-multiclass sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">OneVsRestClassifier</span></a>
<span class="n">classifier</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.multiclass.OneVsRestClassifier.html#sklearn.multiclass.OneVsRestClassifier" title="sklearn.multiclass.OneVsRestClassifier" class="sphx-glr-backref-module-sklearn-multiclass sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">OneVsRestClassifier</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">StandardScaler</span></a><span class="p">(),</span> <a href="../../modules/generated/sklearn.svm.LinearSVC.html#sklearn.svm.LinearSVC" title="sklearn.svm.LinearSVC" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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">dual</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">))</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>
</section>
<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="Link to this heading">¶</a></h3>
<div class="highlight-Python notranslate"><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="sklearn.metrics.average_precision_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">average_precision_score</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.metrics.precision_recall_curve.html#sklearn.metrics.precision_recall_curve" title="sklearn.metrics.precision_recall_curve" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">precision_recall_curve</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="sklearn.metrics.precision_recall_curve" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><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="sklearn.metrics.average_precision_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><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="sklearn.metrics.precision_recall_curve" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><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="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="sklearn.metrics.average_precision_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><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>
</pre></div>
</div>
</section>
<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="Link to this heading">¶</a></h3>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/collections.html#collections.Counter" title="collections.Counter" class="sphx-glr-backref-module-collections sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Counter</span></a>
<span class="n">display</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay" title="sklearn.metrics.PrecisionRecallDisplay" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">PrecisionRecallDisplay</span></a><span class="p">(</span>
<span class="n">recall</span><span class="o">=</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="o">=</span><span class="n">precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span>
<span class="n">average_precision</span><span class="o">=</span><span class="n">average_precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span>
<span class="n">prevalence_pos_label</span><span class="o">=</span><a href="https://docs.python.org/3/library/collections.html#collections.Counter" title="collections.Counter" class="sphx-glr-backref-module-collections sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Counter</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="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="n">Y_test</span><span class="o">.</span><span class="n">size</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">display</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">plot_chance_level</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">_</span> <span class="o">=</span> <span class="n">display</span><span class="o">.</span><span class="n">ax_</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Micro-averaged over all classes"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_precision_recall_003.png" srcset="../../_images/sphx_glr_plot_precision_recall_003.png" alt="Micro-averaged over all classes" class = "sphx-glr-single-img"/></section>
<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="Link to this heading">¶</a></h3>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/itertools.html#itertools.cycle" title="itertools.cycle" class="sphx-glr-backref-module-itertools sphx-glr-backref-type-py-function"><span class="n">cycle</span></a>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="c1"># setup plot details</span>
<span class="n">colors</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/itertools.html#itertools.cycle" title="itertools.cycle" class="sphx-glr-backref-module-itertools sphx-glr-backref-type-py-function"><span class="n">cycle</span></a><span class="p">([</span><span class="s2">"navy"</span><span class="p">,</span> <span class="s2">"turquoise"</span><span class="p">,</span> <span class="s2">"darkorange"</span><span class="p">,</span> <span class="s2">"cornflowerblue"</span><span class="p">,</span> <span class="s2">"teal"</span><span class="p">])</span>
<span class="n">_</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</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="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><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="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="p">[],</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="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><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="p">(</span><span class="n">l</span><span class="p">,)</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">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="s2">"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="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.annotate.html#matplotlib.pyplot.annotate" title="matplotlib.pyplot.annotate" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">annotate</span></a><span class="p">(</span><span class="s2">"f1=</span><span class="si">{0:0.1f}</span><span class="s2">"</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">display</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay" title="sklearn.metrics.PrecisionRecallDisplay" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">PrecisionRecallDisplay</span></a><span class="p">(</span>
<span class="n">recall</span><span class="o">=</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="o">=</span><span class="n">precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span>
<span class="n">average_precision</span><span class="o">=</span><span class="n">average_precision</span><span class="p">[</span><span class="s2">"micro"</span><span class="p">],</span>
<span class="p">)</span>
<span class="n">display</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s2">"Micro-average precision-recall"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"gold"</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">display</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.metrics.PrecisionRecallDisplay.html#sklearn.metrics.PrecisionRecallDisplay" title="sklearn.metrics.PrecisionRecallDisplay" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">PrecisionRecallDisplay</span></a><span class="p">(</span>
<span class="n">recall</span><span class="o">=</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="o">=</span><span class="n">precision</span><span class="p">[</span><span class="n">i</span><span class="p">],</span>
<span class="n">average_precision</span><span class="o">=</span><span class="n">average_precision</span><span class="p">[</span><span class="n">i</span><span class="p">],</span>
<span class="p">)</span>
<span class="n">display</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="sa">f</span><span class="s2">"Precision-recall for class </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">"</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="c1"># add the legend for the iso-f1 curves</span>
<span class="n">handles</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">display</span><span class="o">.</span><span class="n">ax_</span><span class="o">.</span><span class="n">get_legend_handles_labels</span><span class="p">()</span>
<span class="n">handles</span><span class="o">.</span><span class="n">extend</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">extend</span><span class="p">([</span><span class="s2">"iso-f1 curves"</span><span class="p">])</span>
<span class="c1"># set the legend and the axes</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">handles</span><span class="o">=</span><span class="n">handles</span><span class="p">,</span> <span class="n">labels</span><span class="o">=</span><span class="n">labels</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">"best"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Extension of Precision-Recall curve to multi-class"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
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