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<div class="section" id="linear-discriminant-analysis-quadratic-discriminant-analysis">
<span id="example-plot-lda-qda-py"></span><h1>Linear Discriminant Analysis & Quadratic Discriminant Analysis<a class="headerlink" href="#linear-discriminant-analysis-quadratic-discriminant-analysis" title="Permalink to this headline">ΒΆ</a></h1>
<p>Plot the confidence ellipsoids of each class and decision boundary</p>
<img alt="auto_examples/images/plot_lda_qda.png" class="align-center" src="auto_examples/images/plot_lda_qda.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/plot_lda_qda.py"><tt class="xref download docutils literal"><span class="pre">plot_lda_qda.py</span></tt></a></p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">print</span> <span class="n">__doc__</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">linalg</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pylab</span> <span class="kn">as</span> <span class="nn">pl</span>
<span class="kn">import</span> <span class="nn">matplotlib</span> <span class="kn">as</span> <span class="nn">mpl</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
<span class="kn">from</span> <span class="nn">scikits.learn.lda</span> <span class="kn">import</span> <span class="n">LDA</span>
<span class="kn">from</span> <span class="nn">scikits.learn.qda</span> <span class="kn">import</span> <span class="n">QDA</span>
<span class="c">###############################################################################</span>
<span class="c"># colormap</span>
<span class="n">cmap</span> <span class="o">=</span> <span class="n">colors</span><span class="o">.</span><span class="n">LinearSegmentedColormap</span><span class="p">(</span><span class="s">'red_blue_classes'</span><span class="p">,</span>
<span class="p">{</span><span class="s">'red'</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">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">)],</span>
<span class="s">'green'</span> <span class="p">:</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">)],</span>
<span class="s">'blue'</span> <span class="p">:</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span>
<span class="p">})</span>
<span class="n">pl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">register_cmap</span><span class="p">(</span><span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">)</span>
<span class="c">###############################################################################</span>
<span class="c"># generate datasets</span>
<span class="k">def</span> <span class="nf">dataset_fixed_cov</span><span class="p">():</span>
<span class="sd">'''Generate 2 Gaussians samples with the same covariance matrix'''</span>
<span class="n">n</span><span class="p">,</span> <span class="n">dim</span> <span class="o">=</span> <span class="mi">300</span><span class="p">,</span> <span class="mi">2</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">C</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.23</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.83</span><span class="p">,</span> <span class="o">.</span><span class="mi">23</span><span class="p">]])</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">dim</span><span class="p">),</span> <span class="n">C</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">dim</span><span class="p">),</span> <span class="n">C</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</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">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">n</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span>
<span class="k">def</span> <span class="nf">dataset_cov</span><span class="p">():</span>
<span class="sd">'''Generate 2 Gaussians samples with different covariance matrices'''</span>
<span class="n">n</span><span class="p">,</span> <span class="n">dim</span> <span class="o">=</span> <span class="mi">300</span><span class="p">,</span> <span class="mi">2</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">C</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.5</span><span class="p">,</span> <span class="o">.</span><span class="mi">7</span><span class="p">]])</span> <span class="o">*</span> <span class="mf">2.</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">dim</span><span class="p">),</span> <span class="n">C</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">dim</span><span class="p">),</span> <span class="n">C</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">])]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">n</span><span class="p">)))</span>
<span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span>
<span class="c">###############################################################################</span>
<span class="c"># plot functions</span>
<span class="k">def</span> <span class="nf">plot_data</span><span class="p">(</span><span class="n">lda</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">fig_index</span><span class="p">):</span>
<span class="n">splot</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">fig_index</span><span class="p">)</span>
<span class="k">if</span> <span class="n">fig_index</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'Linear Discriminant Analysis'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'Fixed covariance'</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">fig_index</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'Quadratic Discriminant Analysis'</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">fig_index</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'Different covariances'</span><span class="p">)</span>
<span class="n">tp</span> <span class="o">=</span> <span class="p">(</span><span class="n">y</span> <span class="o">==</span> <span class="n">y_pred</span><span class="p">)</span> <span class="c"># True Positive</span>
<span class="n">tp0</span><span class="p">,</span> <span class="n">tp1</span> <span class="o">=</span> <span class="n">tp</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">tp</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">X0</span><span class="p">,</span> <span class="n">X1</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="mi">0</span><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">1</span><span class="p">]</span>
<span class="n">X0_tp</span><span class="p">,</span> <span class="n">X0_fp</span> <span class="o">=</span> <span class="n">X0</span><span class="p">[</span><span class="n">tp0</span><span class="p">],</span> <span class="n">X0</span><span class="p">[</span><span class="n">tp0</span> <span class="o">!=</span> <span class="bp">True</span><span class="p">]</span>
<span class="n">X1_tp</span><span class="p">,</span> <span class="n">X1_fp</span> <span class="o">=</span> <span class="n">X1</span><span class="p">[</span><span class="n">tp1</span><span class="p">],</span> <span class="n">X1</span><span class="p">[</span><span class="n">tp1</span> <span class="o">!=</span> <span class="bp">True</span><span class="p">]</span>
<span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="c"># class 0: dots</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X0_tp</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X0_tp</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'red'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X0_fp</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X0_fp</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s">'.'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'#990000'</span><span class="p">)</span> <span class="c"># dark red</span>
<span class="c"># class 1: dots</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X1_tp</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X1_tp</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'blue'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X1_fp</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X1_fp</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s">'.'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'#000099'</span><span class="p">)</span> <span class="c"># dark blue</span>
<span class="c"># class 0 and 1 : areas</span>
<span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">=</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">100</span>
<span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">xlim</span><span class="p">()</span>
<span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">ylim</span><span class="p">()</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span><span class="p">,</span> <span class="n">nx</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span><span class="p">,</span> <span class="n">ny</span><span class="p">))</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">lda</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s">'red_blue_classes'</span><span class="p">,</span>
<span class="n">norm</span><span class="o">=</span><span class="n">colors</span><span class="o">.</span><span class="n">Normalize</span><span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">],</span> <span class="n">linewidths</span><span class="o">=</span><span class="mf">2.</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="s">'k'</span><span class="p">)</span>
<span class="c"># means</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">lda</span><span class="o">.</span><span class="n">means_</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">],</span> <span class="n">lda</span><span class="o">.</span><span class="n">means_</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="s">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">lda</span><span class="o">.</span><span class="n">means_</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">],</span> <span class="n">lda</span><span class="o">.</span><span class="n">means_</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span>
<span class="s">'o'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<span class="k">return</span> <span class="n">splot</span>
<span class="k">def</span> <span class="nf">plot_ellipse</span><span class="p">(</span><span class="n">splot</span><span class="p">,</span> <span class="n">mean</span><span class="p">,</span> <span class="n">cov</span><span class="p">,</span> <span class="n">color</span><span class="p">):</span>
<span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">linalg</span><span class="o">.</span><span class="n">eigh</span><span class="p">(</span><span class="n">cov</span><span class="p">)</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">angle</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">/</span><span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">angle</span> <span class="o">=</span> <span class="mi">180</span> <span class="o">*</span> <span class="n">angle</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="c"># convert to degrees</span>
<span class="c"># filled gaussian at 2 standard deviation</span>
<span class="n">ell</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">patches</span><span class="o">.</span><span class="n">Ellipse</span><span class="p">(</span><span class="n">mean</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">**</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">**</span> <span class="mf">0.5</span><span class="p">,</span>
<span class="mi">180</span> <span class="o">+</span> <span class="n">angle</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">ell</span><span class="o">.</span><span class="n">set_clip_box</span><span class="p">(</span><span class="n">splot</span><span class="o">.</span><span class="n">bbox</span><span class="p">)</span>
<span class="n">ell</span><span class="o">.</span><span class="n">set_alpha</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">splot</span><span class="o">.</span><span class="n">add_artist</span><span class="p">(</span><span class="n">ell</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_lda_cov</span><span class="p">(</span><span class="n">lda</span><span class="p">,</span> <span class="n">splot</span><span class="p">):</span>
<span class="n">plot_ellipse</span><span class="p">(</span><span class="n">splot</span><span class="p">,</span> <span class="n">lda</span><span class="o">.</span><span class="n">means_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">lda</span><span class="o">.</span><span class="n">covariance_</span><span class="p">,</span> <span class="s">'red'</span><span class="p">)</span>
<span class="n">plot_ellipse</span><span class="p">(</span><span class="n">splot</span><span class="p">,</span> <span class="n">lda</span><span class="o">.</span><span class="n">means_</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">lda</span><span class="o">.</span><span class="n">covariance_</span><span class="p">,</span> <span class="s">'blue'</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">plot_qda_cov</span><span class="p">(</span><span class="n">qda</span><span class="p">,</span> <span class="n">splot</span><span class="p">):</span>
<span class="n">plot_ellipse</span><span class="p">(</span><span class="n">splot</span><span class="p">,</span> <span class="n">qda</span><span class="o">.</span><span class="n">means_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">qda</span><span class="o">.</span><span class="n">covariances_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s">'red'</span><span class="p">)</span>
<span class="n">plot_ellipse</span><span class="p">(</span><span class="n">splot</span><span class="p">,</span> <span class="n">qda</span><span class="o">.</span><span class="n">means_</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">qda</span><span class="o">.</span><span class="n">covariances_</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s">'blue'</span><span class="p">)</span>
<span class="c">###############################################################################</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</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="ow">in</span> <span class="nb">enumerate</span><span class="p">([</span><span class="n">dataset_fixed_cov</span><span class="p">(),</span> <span class="n">dataset_cov</span><span class="p">()]):</span>
<span class="c"># LDA</span>
<span class="n">lda</span> <span class="o">=</span> <span class="n">LDA</span><span class="p">()</span>
<span class="n">y_pred</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="n">store_covariance</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">splot</span> <span class="o">=</span> <span class="n">plot_data</span><span class="p">(</span><span class="n">lda</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">fig_index</span><span class="o">=</span><span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">plot_lda_cov</span><span class="p">(</span><span class="n">lda</span><span class="p">,</span> <span class="n">splot</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s">'tight'</span><span class="p">)</span>
<span class="c"># QDA</span>
<span class="n">qda</span> <span class="o">=</span> <span class="n">QDA</span><span class="p">()</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">qda</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="n">store_covariances</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">splot</span> <span class="o">=</span> <span class="n">plot_data</span><span class="p">(</span><span class="n">qda</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">fig_index</span><span class="o">=</span><span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">plot_qda_cov</span><span class="p">(</span><span class="n">qda</span><span class="p">,</span> <span class="n">splot</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s">'tight'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s">'LDA vs QDA'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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