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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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<div class="section" 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="Permalink to this headline">¶</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><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_pca_vs_lda_001.png"><img alt="../../_images/sphx_glr_plot_pca_vs_lda_001.png" src="../../_images/sphx_glr_plot_pca_vs_lda_001.png" style="width: 300.79999999999995px; height: 225.6px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_pca_vs_lda_002.png"><img alt="../../_images/sphx_glr_plot_pca_vs_lda_002.png" src="../../_images/sphx_glr_plot_pca_vs_lda_002.png" style="width: 300.79999999999995px; height: 225.6px;" /></a>
</li>
</ul>
<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">explained</span> <span class="n">variance</span> <span class="n">ratio</span> <span class="p">(</span><span class="n">first</span> <span class="n">two</span> <span class="n">components</span><span class="p">):</span> <span class="p">[</span><span class="mf">0.92461621</span> <span class="mf">0.05301557</span><span class="p">]</span>
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">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="View documentation for sklearn.decomposition.PCA"><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="View documentation for sklearn.discriminant_analysis.LinearDiscriminantAnalysis"><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="View documentation for sklearn.datasets.load_iris"><span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span></a><span class="p">()</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="n">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="View documentation for sklearn.decomposition.PCA"><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="View documentation for sklearn.discriminant_analysis.LinearDiscriminantAnalysis"><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="k">print</span><span class="p">(</span><span class="s1">'explained variance ratio (first two components): </span><span class="si">%s</span><span class="s1">'</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>
<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">colors</span> <span class="o">=</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="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="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">X_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="mi">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="http://matplotlib.org/api/legend_api.html#matplotlib.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'best'</span><span class="p">,</span> <span class="n">shadow</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span> <span class="n">scatterpoints</span><span class="o">=</span><span class="mi">1</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">'PCA of IRIS dataset'</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="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="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">X_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="mi">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>
<a href="http://matplotlib.org/api/legend_api.html#matplotlib.legend" title="View documentation for matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'best'</span><span class="p">,</span> <span class="n">shadow</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span> <span class="n">scatterpoints</span><span class="o">=</span><span class="mi">1</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">'LDA of IRIS dataset'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
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