mhjensen
332 lines
13 KiB
HTML
332 lines
13 KiB
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<title>Data Analysis and Machine Learning: Support Vector Machines</title>
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<section>
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<!-- ------------------- main content ---------------------- -->
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<center><h1 style="text-align: center;">Data Analysis and Machine Learning: Support Vector Machines</h1></center> <!-- document title -->
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<p>
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<p> <br>
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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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<p> <br>
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<center><h4>May 30, 2018</h4></center> <!-- date -->
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<br>
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<p>
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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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</section>
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<section>
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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 "perldoc" -->
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<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.svm</span> <span style="color: #8B008B; font-weight: bold">import</span> SVR
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
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<span style="color: #228B22"># Generate sample data</span>
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X = np.sort(<span style="color: #B452CD">5</span>*np.random.rand(<span style="color: #B452CD">40</span>,<span style="color: #B452CD">1</span>), axis=<span style="color: #B452CD">0</span>)
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y = X**<span style="color: #B452CD">3</span>
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y=y.ravel()
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<span style="color: #228B22"># Add noise to targets</span>
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X[::<span style="color: #B452CD">4</span>] +=<span style="color: #B452CD">3</span>*(<span style="color: #B452CD">0.5</span> - np.random.rand(<span style="color: #B452CD">1</span>))
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y[::<span style="color: #B452CD">5</span>] += <span style="color: #B452CD">50</span> * (<span style="color: #B452CD">0.5</span> - np.random.rand(<span style="color: #B452CD">8</span>))
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plt.plot(X,y, <span style="color: #CD5555">'g^'</span>)
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<span style="color: #228B22">#SVR Fit</span>
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svr_poly = SVR(kernel=<span style="color: #CD5555">'poly'</span>, C=<span style="color: #B452CD">1e3</span>, degree=<span style="color: #B452CD">3</span>)
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y_poly = svr_poly.fit(X, y).predict(X)
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<span style="color: #228B22"># Plots</span>
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z = np.arange(<span style="color: #B452CD">0</span>, <span style="color: #B452CD">5</span>, <span style="color: #B452CD">0.1</span>)
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t = z**<span style="color: #B452CD">3</span>
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fig = plt.figure()
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ax = fig.add_subplot(<span style="color: #B452CD">111</span>)
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plt.plot(z,z**<span style="color: #B452CD">3</span>, <span style="color: #CD5555">'r--'</span>, label=<span style="color: #CD5555">'Cubic Function with No Noise'</span>)
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lw = <span style="color: #B452CD">2</span>
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plt.scatter(X, y, color=<span style="color: #CD5555">'darkorange'</span>, label=<span style="color: #CD5555">'Gaussian Cubic Noise'</span>)
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plt.plot(X, y_poly, color=<span style="color: #CD5555">'green'</span>, lw=lw, label=<span style="color: #CD5555">'Polynomial model'</span>)
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plt.xlabel(<span style="color: #CD5555">'data'</span>)
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plt.ylabel(<span style="color: #CD5555">'target'</span>)
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plt.title(<span style="color: #CD5555">'Cubic Gaussian Distribution'</span>)
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plt.legend()
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plt.show()
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</pre></div>
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