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<div class="section" id="support-vector-regression-svr-using-linear-and-non-linear-kernels">
<span id="sphx-glr-auto-examples-svm-plot-svm-regression-py"></span><h1>Support Vector Regression (SVR) using linear and non-linear kernels<a class="headerlink" href="#support-vector-regression-svr-using-linear-and-non-linear-kernels" title="Permalink to this headline">¶</a></h1>
<p>Toy example of 1D regression using linear, polynomial and RBF kernels.</p>
<img alt="../../_images/sphx_glr_plot_svm_regression_001.png" class="align-center" src="../../_images/sphx_glr_plot_svm_regression_001.png" />
<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">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Generate sample data</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.sort.html#numpy.sort" title="View documentation for numpy.sort"><span class="n">np</span><span class="o">.</span><span class="n">sort</span></a><span class="p">(</span><span class="mi">5</span> <span class="o">*</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.rand.html#numpy.random.rand" title="View documentation for numpy.random.rand"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span></a><span class="p">(</span><span class="mi">40</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.sin.html#numpy.sin" title="View documentation for numpy.sin"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Add noise to targets</span>
<span class="n">y</span><span class="p">[::</span><span class="mi">5</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">3</span> <span class="o">*</span> <span class="p">(</span><span class="mf">0.5</span> <span class="o">-</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.rand.html#numpy.random.rand" title="View documentation for numpy.random.rand"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span></a><span class="p">(</span><span class="mi">8</span><span class="p">))</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Fit regression model</span>
<span class="n">svr_rbf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'rbf'</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mf">1e3</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">svr_lin</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'linear'</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mf">1e3</span><span class="p">)</span>
<span class="n">svr_poly</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.svm.SVR.html#sklearn.svm.SVR" title="View documentation for sklearn.svm.SVR"><span class="n">SVR</span></a><span class="p">(</span><span class="n">kernel</span><span class="o">=</span><span class="s1">'poly'</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mf">1e3</span><span class="p">,</span> <span class="n">degree</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">y_rbf</span> <span class="o">=</span> <span class="n">svr_rbf</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">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">y_lin</span> <span class="o">=</span> <span class="n">svr_lin</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">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">y_poly</span> <span class="o">=</span> <span class="n">svr_poly</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">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="c1"># #############################################################################</span>
<span class="c1"># Look at the results</span>
<span class="n">lw</span> <span class="o">=</span> <span class="mi">2</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</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'darkorange'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'data'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><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_rbf</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'navy'</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="s1">'RBF model'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><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_lin</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'c'</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="s1">'Linear model'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><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_poly</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'cornflowerblue'</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="s1">'Polynomial model'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'data'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'target'</span><span class="p">)</span>
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<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>
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