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<li><a class="reference internal" href="#">Comparison of LDA and PCA 2D projection of Iris dataset</a></li>
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<p><a class="reference internal" href="#sphx-glr-download-auto-examples-decomposition-plot-pca-vs-lda-py"><span class="std std-ref">Go to the end</span></a>
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<section class="sphx-glr-example-title" id="comparison-of-lda-and-pca-2d-projection-of-iris-dataset">
<span id="sphx-glr-auto-examples-decomposition-plot-pca-vs-lda-py"></span><h1>Comparison of LDA and PCA 2D projection of Iris dataset<a class="headerlink" href="#comparison-of-lda-and-pca-2d-projection-of-iris-dataset" title="Link to this heading">¶</a></h1>
<p>The Iris dataset represents 3 kind of Iris flowers (Setosa, Versicolour
and Virginica) with 4 attributes: sepal length, sepal width, petal length
and petal width.</p>
<p>Principal Component Analysis (PCA) applied to this data identifies the
combination of attributes (principal components, or directions in the
feature space) that account for the most variance in the data. Here we
plot the different samples on the 2 first principal components.</p>
<p>Linear Discriminant Analysis (LDA) tries to identify attributes that
account for the most variance <em>between classes</em>. In particular,
LDA, in contrast to PCA, is a supervised method, using known class labels.</p>
<ul class="sphx-glr-horizontal">
<li><img src="../../_images/sphx_glr_plot_pca_vs_lda_001.png" srcset="../../_images/sphx_glr_plot_pca_vs_lda_001.png" alt="PCA of IRIS dataset" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_pca_vs_lda_002.png" srcset="../../_images/sphx_glr_plot_pca_vs_lda_002.png" alt="LDA of IRIS dataset" class = "sphx-glr-multi-img"/></li>
</ul>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>explained variance ratio (first two components): [0.92461872 0.05306648]
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
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<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.decomposition</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="sklearn.decomposition.PCA" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">PCA</span></a>
<span class="kn">from</span> <span class="nn">sklearn.discriminant_analysis</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html#sklearn.discriminant_analysis.LinearDiscriminantAnalysis" title="sklearn.discriminant_analysis.LinearDiscriminantAnalysis" class="sphx-glr-backref-module-sklearn-discriminant_analysis sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearDiscriminantAnalysis</span></a>
<span class="n">iris</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">datasets</span><span class="o">.</span><span class="n">load_iris</span></a><span class="p">()</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="n">target_names</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target_names</span>
<span class="n">pca</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="sklearn.decomposition.PCA" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">PCA</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">X_r</span> <span class="o">=</span> <span class="n">pca</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">lda</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html#sklearn.discriminant_analysis.LinearDiscriminantAnalysis" title="sklearn.discriminant_analysis.LinearDiscriminantAnalysis" class="sphx-glr-backref-module-sklearn-discriminant_analysis sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LinearDiscriminantAnalysis</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">X_r2</span> <span class="o">=</span> <span class="n">lda</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="c1"># Percentage of variance explained for each components</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">"explained variance ratio (first two components): </span><span class="si">%s</span><span class="s2">"</span>
<span class="o">%</span> <span class="nb">str</span><span class="p">(</span><span class="n">pca</span><span class="o">.</span><span class="n">explained_variance_ratio_</span><span class="p">)</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" 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">figure</span></a><span class="p">()</span>
<span class="n">colors</span> <span class="o">=</span> <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="n">lw</span> <span class="o">=</span> <span class="mi">2</span>
<span class="k">for</span> <span class="n">color</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">target_name</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">colors</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">target_names</span><span class="p">):</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" 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">scatter</span></a><span class="p">(</span>
<span class="n">X_r</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_r</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="n">i</span><span class="p">,</span> <span class="mi">1</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">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="n">lw</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">target_name</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend" 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">legend</span></a><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">shadow</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">scatterpoints</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
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<span class="k">for</span> <span class="n">color</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">target_name</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">colors</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">target_names</span><span class="p">):</span>
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<span class="n">X_r2</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_r2</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</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">label</span><span class="o">=</span><span class="n">target_name</span>
<span class="p">)</span>
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<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" 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">title</span></a><span class="p">(</span><span class="s2">"LDA of IRIS dataset"</span><span class="p">)</span>
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<p class="rubric">Related examples</p>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="The rows being the samples and the columns being: Sepal Length, Sepal Width, Petal Length and P..."><img alt="" src="../../_images/sphx_glr_plot_iris_dataset_thumb.png" />
<p><a class="reference internal" href="../datasets/plot_iris_dataset.html#sphx-glr-auto-examples-datasets-plot-iris-dataset-py"><span class="std std-ref">The Iris Dataset</span></a></p>
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