mhjensen
129 lines
6.8 KiB
HTML
129 lines
6.8 KiB
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<meta name="description" content="Data Analysis and Machine Learning: Support Vector Machines">
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<title>Data Analysis and Machine Learning: Support Vector Machines</title>
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{'highest level': 2,
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'sections': [('Support Vector Machines, overarching aims',
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2,
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'___sec0')]}
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<!-- ------------------- main content ---------------------- -->
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<center><h1>Data Analysis and Machine Learning: Support Vector Machines</h1></center> <!-- document title -->
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<!-- author(s): Morten Hjorth-Jensen -->
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<b>Morten Hjorth-Jensen</b> [1, 2]
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<!-- institution(s) -->
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<center><h4>May 30, 2018</h4></center> <!-- date -->
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<br>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec0">Support Vector Machines, overarching aims </h2>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVR
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
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<span style="color: #408080; font-style: italic"># Generate sample data</span>
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X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>sort(<span style="color: #666666">5*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">40</span>,<span style="color: #666666">1</span>), axis<span style="color: #666666">=0</span>)
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y <span style="color: #666666">=</span> X<span style="color: #666666">**3</span>
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y<span style="color: #666666">=</span>y<span style="color: #666666">.</span>ravel()
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<span style="color: #408080; font-style: italic"># Add noise to targets</span>
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X[::<span style="color: #666666">4</span>] <span style="color: #666666">+=3*</span>(<span style="color: #666666">0.5</span> <span style="color: #666666">-</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">1</span>))
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y[::<span style="color: #666666">5</span>] <span style="color: #666666">+=</span> <span style="color: #666666">50</span> <span style="color: #666666">*</span> (<span style="color: #666666">0.5</span> <span style="color: #666666">-</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">8</span>))
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plt<span style="color: #666666">.</span>plot(X,y, <span style="color: #BA2121">'g^'</span>)
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<span style="color: #408080; font-style: italic">#SVR Fit</span>
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svr_poly <span style="color: #666666">=</span> SVR(kernel<span style="color: #666666">=</span><span style="color: #BA2121">'poly'</span>, C<span style="color: #666666">=1e3</span>, degree<span style="color: #666666">=3</span>)
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y_poly <span style="color: #666666">=</span> svr_poly<span style="color: #666666">.</span>fit(X, y)<span style="color: #666666">.</span>predict(X)
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<span style="color: #408080; font-style: italic"># Plots</span>
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z <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0</span>, <span style="color: #666666">5</span>, <span style="color: #666666">0.1</span>)
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t <span style="color: #666666">=</span> z<span style="color: #666666">**3</span>
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fig <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>figure()
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ax <span style="color: #666666">=</span> fig<span style="color: #666666">.</span>add_subplot(<span style="color: #666666">111</span>)
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plt<span style="color: #666666">.</span>plot(z,z<span style="color: #666666">**3</span>, <span style="color: #BA2121">'r--'</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">'Cubic Function with No Noise'</span>)
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lw <span style="color: #666666">=</span> <span style="color: #666666">2</span>
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plt<span style="color: #666666">.</span>scatter(X, y, color<span style="color: #666666">=</span><span style="color: #BA2121">'darkorange'</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">'Gaussian Cubic Noise'</span>)
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plt<span style="color: #666666">.</span>plot(X, y_poly, color<span style="color: #666666">=</span><span style="color: #BA2121">'green'</span>, lw<span style="color: #666666">=</span>lw, label<span style="color: #666666">=</span><span style="color: #BA2121">'Polynomial model'</span>)
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plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">'data'</span>)
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plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">'target'</span>)
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plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">'Cubic Gaussian Distribution'</span>)
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plt<span style="color: #666666">.</span>legend()
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plt<span style="color: #666666">.</span>show()
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</pre></div>
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<p>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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</body>
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