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<li><a class="reference internal" href="#">Sparsity Example: Fitting only features 1 and 2</a></li>
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<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-linear-model-plot-ols-3d-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
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<div class="sphx-glr-example-title section" id="sparsity-example-fitting-only-features-1-and-2">
<span id="sphx-glr-auto-examples-linear-model-plot-ols-3d-py"></span><h1>Sparsity Example: Fitting only features 1 and 2<a class="headerlink" href="#sparsity-example-fitting-only-features-1-and-2" title="Permalink to this headline">¶</a></h1>
<p>Features 1 and 2 of the diabetes-dataset are fitted and
plotted below. It illustrates that although feature 2
has a strong coefficient on the full model, it does not
give us much regarding <code class="docutils literal notranslate"><span class="pre">y</span></code> when compared to just feature 1</p>
<ul class="sphx-glr-horizontal">
<li><img alt="../../_images/sphx_glr_plot_ols_3d_001.png" class="sphx-glr-multi-img" src="../../_images/sphx_glr_plot_ols_3d_001.png" />
</li>
<li><img alt="../../_images/sphx_glr_plot_ols_3d_002.png" class="sphx-glr-multi-img" src="../../_images/sphx_glr_plot_ols_3d_002.png" />
</li>
<li><img alt="../../_images/sphx_glr_plot_ols_3d_003.png" class="sphx-glr-multi-img" src="../../_images/sphx_glr_plot_ols_3d_003.png" />
</li>
</ul>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="c1"># Code source: Gaël Varoquaux</span>
<span class="c1"># Modified for documentation by Jaques Grobler</span>
<span class="c1"># License: BSD 3 clause</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">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">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">linear_model</span>
<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_diabetes.html#sklearn.datasets.load_diabetes" title="View documentation for sklearn.datasets.load_diabetes"><span class="n">datasets</span><span class="o">.</span><span class="n">load_diabetes</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="n">indices</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="n">X_train</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span> <span class="n">indices</span><span class="p">]</span>
<span class="n">X_test</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="o">-</span><span class="mi">20</span><span class="p">:,</span> <span class="n">indices</span><span class="p">]</span>
<span class="n">y_train</span> <span class="o">=</span> <span class="n">y</span><span class="p">[:</span><span class="o">-</span><span class="mi">20</span><span class="p">]</span>
<span class="n">y_test</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="o">-</span><span class="mi">20</span><span class="p">:]</span>
<span class="n">ols</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression" title="View documentation for sklearn.linear_model.LinearRegression"><span class="n">linear_model</span><span class="o">.</span><span class="n">LinearRegression</span></a><span class="p">()</span>
<span class="n">ols</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="c1"># #############################################################################</span>
<span class="c1"># Plot the figure</span>
<span class="k">def</span> <span class="nf">plot_figs</span><span class="p">(</span><span class="n">fig_num</span><span class="p">,</span> <span class="n">elev</span><span class="p">,</span> <span class="n">azim</span><span class="p">,</span> <span class="n">X_train</span><span class="p">,</span> <span class="n">clf</span><span class="p">):</span>
<span class="n">fig</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.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">fig_num</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.clf.html#matplotlib.pyplot.clf" title="View documentation for matplotlib.pyplot.clf"><span class="n">plt</span><span class="o">.</span><span class="n">clf</span></a><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">Axes3D</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">elev</span><span class="o">=</span><span class="n">elev</span><span class="p">,</span> <span class="n">azim</span><span class="o">=</span><span class="n">azim</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_train</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_train</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">'+'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([[</span><span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">-.</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">.</span><span class="mi">15</span><span class="p">,</span> <span class="o">.</span><span class="mi">15</span><span class="p">]]),</span>
<a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([[</span><span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">15</span><span class="p">],</span> <span class="p">[</span><span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">15</span><span class="p">]]),</span>
<span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([[</span><span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">15</span><span class="p">,</span> <span class="o">.</span><span class="mi">15</span><span class="p">],</span>
<span class="p">[</span><span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">15</span><span class="p">,</span> <span class="o">-.</span><span class="mi">1</span><span class="p">,</span> <span class="o">.</span><span class="mi">15</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span>
<span class="p">)</span><span class="o">.</span><span class="n">reshape</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">alpha</span><span class="o">=.</span><span class="mi">5</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">'X_1'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'X_2'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_zlabel</span><span class="p">(</span><span class="s1">'Y'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">w_xaxis</span><span class="o">.</span><span class="n">set_ticklabels</span><span class="p">([])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">w_yaxis</span><span class="o">.</span><span class="n">set_ticklabels</span><span class="p">([])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">w_zaxis</span><span class="o">.</span><span class="n">set_ticklabels</span><span class="p">([])</span>
<span class="c1"># Generate the three different figures from different views</span>
<span class="n">elev</span> <span class="o">=</span> <span class="mf">43.5</span>
<span class="n">azim</span> <span class="o">=</span> <span class="o">-</span><span class="mi">110</span>
<span class="n">plot_figs</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">elev</span><span class="p">,</span> <span class="n">azim</span><span class="p">,</span> <span class="n">X_train</span><span class="p">,</span> <span class="n">ols</span><span class="p">)</span>
<span class="n">elev</span> <span class="o">=</span> <span class="o">-.</span><span class="mi">5</span>
<span class="n">azim</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">plot_figs</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">elev</span><span class="p">,</span> <span class="n">azim</span><span class="p">,</span> <span class="n">X_train</span><span class="p">,</span> <span class="n">ols</span><span class="p">)</span>
<span class="n">elev</span> <span class="o">=</span> <span class="o">-.</span><span class="mi">5</span>
<span class="n">azim</span> <span class="o">=</span> <span class="mi">90</span>
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