mhjensen
459 lines
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HTML
459 lines
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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: Nearest Neighbors and Decision Trees</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">Decision trees, overarching aims </h2>
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<div class="alert alert-block alert-block alert-text-normal">
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<b></b>
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<p>
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</div>
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</section>
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<section>
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<h2 id="___sec1">Nearest Neighbors </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">mglearn</span>
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<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</span> <span style="color: #8B008B; font-weight: bold">import</span> linear_model
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
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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: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> PolynomialFeatures
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.pipeline</span> <span style="color: #8B008B; font-weight: bold">import</span> Pipeline
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.neighbors</span> <span style="color: #8B008B; font-weight: bold">import</span> KNeighborsClassifier
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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">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">0.5</span> - np.random.rand(<span style="color: #B452CD">8</span>))
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a=np.array(X)
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b=np.array(y)
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X_train=a[:<span style="color: #B452CD">19</span>]
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X_test=a[<span style="color: #B452CD">19</span>:]
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y_train=b[:<span style="color: #B452CD">19</span>]
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y_test=b[<span style="color: #B452CD">19</span>:]
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model=Pipeline([(<span style="color: #CD5555">'poly'</span>, PolynomialFeatures(degree=<span style="color: #B452CD">3</span>)),(<span style="color: #CD5555">'linear'</span>, LinearRegression(fit_intercept=<span style="color: #658b00">False</span>))])
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model=model.fit(X_train, y_train)
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pred=model.predict(X_test)
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poly=PolynomialFeatures(degree=<span style="color: #B452CD">3</span>)
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poly.fit_transform(X_train, y_train)
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plt.scatter(X_test, y_test)
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plt.plot(X_test, pred, color=<span style="color: #CD5555">'green'</span>)
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plt.show()
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<span style="color: #8B008B; font-weight: bold">print</span> (model.score(X_test,y_test))
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<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">"---------K-Nearest Neighbors-------"</span>)
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<span style="color: #CD5555">"""neighbors_settings=range(1,11)</span>
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<span style="color: #CD5555">for n_neighbors in neighbors_settings:</span>
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<span style="color: #CD5555"> clf=KNeighborsClassifier(n_neighbors=n_neighbors)</span>
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<span style="color: #CD5555"> clf.fit(X_train, y_train)</span>
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<span style="color: #CD5555"> training_accuracy.append(clf.score(X_train, y_train))</span>
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<span style="color: #CD5555"> test_accuracy.append(clf.score(X_test, y_test))</span>
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<span style="color: #CD5555">print (mglearn.plots.plot_knn_regression(n_neighbors=3))"""</span>
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.neighbors</span> <span style="color: #8B008B; font-weight: bold">import</span> KNeighborsRegressor
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X, y=mglearn.datasets.make_wave(n_samples=<span style="color: #B452CD">40</span>)
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reg = KNeighborsRegressor(n_neighbors=<span style="color: #B452CD">3</span>)
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reg.fit(X_train, y_train)
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</pre></div>
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</section>
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<section>
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<h2 id="___sec2">Decision trees and Regression </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">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: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> PolynomialFeatures
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
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steps=<span style="color: #B452CD">250</span>
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distance=<span style="color: #B452CD">0</span>
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x=<span style="color: #B452CD">0</span>
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distance_list=[]
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steps_list=[]
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<span style="color: #8B008B; font-weight: bold">while</span> x<steps:
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distance+=np.random.randint(-<span style="color: #B452CD">1</span>,<span style="color: #B452CD">2</span>)
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distance_list.append(distance)
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x+=<span style="color: #B452CD">1</span>
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steps_list.append(x)
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plt.plot(steps_list,distance_list, color=<span style="color: #CD5555">'green'</span>, label=<span style="color: #CD5555">"Random Walk Data"</span>)
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steps_list=np.asarray(steps_list)
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distance_list=np.asarray(distance_list)
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X=steps_list[:,np.newaxis]
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<span style="color: #228B22">#Polynomial fits</span>
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<span style="color: #228B22">#Degree 2</span>
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poly_features=PolynomialFeatures(degree=<span style="color: #B452CD">2</span>, include_bias=<span style="color: #658b00">False</span>)
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X_poly=poly_features.fit_transform(X)
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lin_reg=LinearRegression()
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poly_fit=lin_reg.fit(X_poly,distance_list)
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b=lin_reg.coef_
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c=lin_reg.intercept_
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<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">"2nd degree coefficients:"</span>)
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<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">"zero power: "</span>,c)
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<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">"first power: "</span>, b[<span style="color: #B452CD">0</span>])
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<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">"second power: "</span>,b[<span style="color: #B452CD">1</span>])
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z = np.arange(<span style="color: #B452CD">0</span>, steps, .<span style="color: #B452CD">01</span>)
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z_mod=b[<span style="color: #B452CD">1</span>]*z**<span style="color: #B452CD">2</span>+b[<span style="color: #B452CD">0</span>]*z+c
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fit_mod=b[<span style="color: #B452CD">1</span>]*X**<span style="color: #B452CD">2</span>+b[<span style="color: #B452CD">0</span>]*X+c
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plt.plot(z, z_mod, color=<span style="color: #CD5555">'r'</span>, label=<span style="color: #CD5555">"2nd Degree Fit"</span>)
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plt.title(<span style="color: #CD5555">"Polynomial Regression"</span>)
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plt.xlabel(<span style="color: #CD5555">"Steps"</span>)
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plt.ylabel(<span style="color: #CD5555">"Distance"</span>)
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<span style="color: #228B22">#Degree 10</span>
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poly_features10=PolynomialFeatures(degree=<span style="color: #B452CD">10</span>, include_bias=<span style="color: #658b00">False</span>)
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X_poly10=poly_features10.fit_transform(X)
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poly_fit10=lin_reg.fit(X_poly10,distance_list)
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y_plot=poly_fit10.predict(X_poly10)
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plt.plot(X, y_plot, color=<span style="color: #CD5555">'black'</span>, label=<span style="color: #CD5555">"10th Degree Fit"</span>)
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plt.legend()
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plt.show()
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<span style="color: #228B22">#Decision Tree Regression</span>
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.tree</span> <span style="color: #8B008B; font-weight: bold">import</span> DecisionTreeRegressor
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regr_1=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">2</span>)
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regr_2=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">5</span>)
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regr_3=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">7</span>)
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regr_1.fit(X, distance_list)
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regr_2.fit(X, distance_list)
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regr_3.fit(X, distance_list)
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X_test = np.arange(<span style="color: #B452CD">0.0</span>, steps, <span style="color: #B452CD">0.01</span>)[:, np.newaxis]
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y_1 = regr_1.predict(X_test)
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y_2 = regr_2.predict(X_test)
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y_3=regr_3.predict(X_test)
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<span style="color: #228B22"># Plot the results</span>
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plt.figure()
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plt.scatter(X, distance_list, s=<span style="color: #B452CD">2.5</span>, c=<span style="color: #CD5555">"black"</span>, label=<span style="color: #CD5555">"data"</span>)
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plt.plot(X_test, y_1, color=<span style="color: #CD5555">"red"</span>,
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label=<span style="color: #CD5555">"max_depth=2"</span>, linewidth=<span style="color: #B452CD">2</span>)
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plt.plot(X_test, y_2, color=<span style="color: #CD5555">"green"</span>, label=<span style="color: #CD5555">"max_depth=5"</span>, linewidth=<span style="color: #B452CD">2</span>)
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plt.plot(X_test, y_3, color=<span style="color: #CD5555">"m"</span>, label=<span style="color: #CD5555">"max_depth=7"</span>, linewidth=<span style="color: #B452CD">2</span>)
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plt.xlabel(<span style="color: #CD5555">"Data"</span>)
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plt.ylabel(<span style="color: #CD5555">"Darget"</span>)
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plt.title(<span style="color: #CD5555">"Decision Tree Regression"</span>)
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plt.legend()
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plt.show()
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</pre></div>
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</section>
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// Enable keyboard shortcuts for navigation
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keyboard: true,
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// Enable the slide overview mode
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overview: true,
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// Vertical centering of slides
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//center: true,
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center: false,
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// Enables touch navigation on devices with touch input
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touch: true,
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// Loop the presentation
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loop: false,
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// Change the presentation direction to be RTL
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rtl: false,
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// Turns fragments on and off globally
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fragments: true,
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// Flags if the presentation is running in an embedded mode,
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// i.e. contained within a limited portion of the screen
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embedded: false,
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// Number of milliseconds between automatically proceeding to the
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// next slide, disabled when set to 0, this value can be overwritten
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// by using a data-autoslide attribute on your slides
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autoSlide: 0,
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// Stop auto-sliding after user input
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autoSlideStoppable: true,
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|
|
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// Enable slide navigation via mouse wheel
|
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mouseWheel: false,
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|
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// Hides the address bar on mobile devices
|
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hideAddressBar: true,
|
|
|
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// Opens links in an iframe preview overlay
|
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previewLinks: false,
|
|
|
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// Transition style
|
|
transition: 'default', // default/cube/page/concave/zoom/linear/fade/none
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|
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// Transition speed
|
|
transitionSpeed: 'default', // default/fast/slow
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|
|
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// Transition style for full page slide backgrounds
|
|
backgroundTransition: 'default', // default/none/slide/concave/convex/zoom
|
|
|
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// Number of slides away from the current that are visible
|
|
viewDistance: 3,
|
|
|
|
// Parallax background image
|
|
//parallaxBackgroundImage: '', // e.g. "'https://s3.amazonaws.com/hakim-static/reveal-js/reveal-parallax-1.jpg'"
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|
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// Parallax background size
|
|
//parallaxBackgroundSize: '' // CSS syntax, e.g. "2100px 900px"
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|
|
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theme: Reveal.getQueryHash().theme, // available themes are in reveal.js/css/theme
|
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transition: Reveal.getQueryHash().transition || 'default', // default/cube/page/concave/zoom/linear/none
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|
|
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});
|
|
|
|
Reveal.initialize({
|
|
dependencies: [
|
|
// Cross-browser shim that fully implements classList - https://github.com/eligrey/classList.js/
|
|
{ src: 'reveal.js/lib/js/classList.js', condition: function() { return !document.body.classList; } },
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|
|
|
// Interpret Markdown in <section> elements
|
|
{ src: 'reveal.js/plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
|
|
{ src: 'reveal.js/plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
|
|
|
|
// Syntax highlight for <code> elements
|
|
{ src: 'reveal.js/plugin/highlight/highlight.js', async: true, callback: function() { hljs.initHighlightingOnLoad(); } },
|
|
|
|
// Zoom in and out with Alt+click
|
|
{ src: 'reveal.js/plugin/zoom-js/zoom.js', async: true, condition: function() { return !!document.body.classList; } },
|
|
|
|
// Speaker notes
|
|
{ src: 'reveal.js/plugin/notes/notes.js', async: true, condition: function() { return !!document.body.classList; } },
|
|
|
|
// Remote control your reveal.js presentation using a touch device
|
|
//{ src: 'reveal.js/plugin/remotes/remotes.js', async: true, condition: function() { return !!document.body.classList; } },
|
|
|
|
// MathJax
|
|
//{ src: 'reveal.js/plugin/math/math.js', async: true }
|
|
]
|
|
});
|
|
|
|
Reveal.initialize({
|
|
|
|
// The "normal" size of the presentation, aspect ratio will be preserved
|
|
// when the presentation is scaled to fit different resolutions. Can be
|
|
// specified using percentage units.
|
|
width: 1170, // original: 960,
|
|
height: 700,
|
|
|
|
// Factor of the display size that should remain empty around the content
|
|
margin: 0.1,
|
|
|
|
// Bounds for smallest/largest possible scale to apply to content
|
|
minScale: 0.2,
|
|
maxScale: 1.0
|
|
|
|
});
|
|
</script>
|
|
|
|
<!-- begin footer logo
|
|
<div style="position: absolute; bottom: 0px; left: 0; margin-left: 0px">
|
|
<img src="somelogo.png">
|
|
</div>
|
|
end footer logo -->
|
|
|
|
|
|
|
|
</body>
|
|
</html>
|