lars/FYS-STK4155
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
930ffb34fa39c5bb6bae5283f1c3dc4f2ebf4e6c
FYS-STK4155/doc/pub/DecisionTrees/html/DecisionTrees.html
T
mhjensen 8bf7984604 Updating various chapters with codes
2018-05-30 23:00:43 -04:00

283 lines
19 KiB
HTML
Raw Blame History

<!--
Automatically generated HTML file from DocOnce source
(https://github.com/hplgit/doconce/)
-->
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
<meta name="description" content="Data Analysis and Machine Learning: Nearest Neighbors and Decision Trees">
<title>Data Analysis and Machine Learning: Nearest Neighbors and Decision Trees</title>
<style type="text/css">
/* bloodish style */
body {
font-family: Helvetica, Verdana, Arial, Sans-serif;
color: #404040;
background: #ffffff;
}
h1 { font-size: 1.8em; color: #8A0808; }
h2 { font-size: 1.6em; color: #8A0808; }
h3 { font-size: 1.4em; color: #8A0808; }
h4 { color: #8A0808; }
a { color: #8A0808; text-decoration:none; }
tt { font-family: "Courier New", Courier; }
/* pre style removed because it will interfer with pygments */
p { text-indent: 0px; }
hr { border: 0; width: 80%; border-bottom: 1px solid #aaa}
p.caption { width: 80%; font-style: normal; text-align: left; }
hr.figure { border: 0; width: 80%; border-bottom: 1px solid #aaa}
.alert-text-small { font-size: 80%; }
.alert-text-large { font-size: 130%; }
.alert-text-normal { font-size: 90%; }
.alert {
padding:8px 35px 8px 14px; margin-bottom:18px;
text-shadow:0 1px 0 rgba(255,255,255,0.5);
border:1px solid #bababa;
border-radius: 4px;
-webkit-border-radius: 4px;
-moz-border-radius: 4px;
color: #555;
background-color: #f8f8f8;
background-position: 10px 5px;
background-repeat: no-repeat;
background-size: 38px;
padding-left: 55px;
width: 75%;
}
.alert-block {padding-top:14px; padding-bottom:14px}
.alert-block > p, .alert-block > ul {margin-bottom:1em}
.alert li {margin-top: 1em}
.alert-block p+p {margin-top:5px}
.alert-notice { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_notice.png); }
.alert-summary { background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_summary.png); }
.alert-warning { background-image: url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_warning.png); }
.alert-question {background-image:url(https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_images/small_gray_question.png); }
div { text-align: justify; text-justify: inter-word; }
</style>
</head>
<!-- tocinfo
{'highest level': 2,
'sections': [('Decision trees, overarching aims', 2, None, '___sec0'),
('Nearest Neighbors', 2, None, '___sec1'),
('Decision trees and Regression', 2, None, '___sec2')]}
end of tocinfo -->
<body>
<!-- ------------------- main content ---------------------- -->
<center><h1>Data Analysis and Machine Learning: Nearest Neighbors and Decision Trees</h1></center> <!-- document title -->
<p>
<!-- author(s): Morten Hjorth-Jensen -->
<center>
<b>Morten Hjorth-Jensen</b> [1, 2]
</center>
<p>
<!-- institution(s) -->
<center>[1] <b>Department of Physics, University of Oslo</b></center>
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>May 30, 2018</h4></center> <!-- date -->
<br>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec0">Decision trees, overarching aims </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
</div>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec1">Nearest Neighbors </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<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">mglearn</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>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> linear_model
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression
<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>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> PolynomialFeatures
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.pipeline</span> <span style="color: #008000; font-weight: bold">import</span> Pipeline
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.neighbors</span> <span style="color: #008000; font-weight: bold">import</span> KNeighborsClassifier
<span style="color: #408080; font-style: italic"># Generate sample data</span>
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>)
y <span style="color: #666666">=</span> X<span style="color: #666666">**3</span>
y<span style="color: #666666">=</span>y<span style="color: #666666">.</span>ravel()
<span style="color: #408080; font-style: italic"># Add noise to targets</span>
X[::<span style="color: #666666">4</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">1</span>))
y[::<span style="color: #666666">5</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>))
a<span style="color: #666666">=</span>np<span style="color: #666666">.</span>array(X)
b<span style="color: #666666">=</span>np<span style="color: #666666">.</span>array(y)
X_train<span style="color: #666666">=</span>a[:<span style="color: #666666">19</span>]
X_test<span style="color: #666666">=</span>a[<span style="color: #666666">19</span>:]
y_train<span style="color: #666666">=</span>b[:<span style="color: #666666">19</span>]
y_test<span style="color: #666666">=</span>b[<span style="color: #666666">19</span>:]
model<span style="color: #666666">=</span>Pipeline([(<span style="color: #BA2121">&#39;poly&#39;</span>, PolynomialFeatures(degree<span style="color: #666666">=3</span>)),(<span style="color: #BA2121">&#39;linear&#39;</span>, LinearRegression(fit_intercept<span style="color: #666666">=</span><span style="color: #008000">False</span>))])
model<span style="color: #666666">=</span>model<span style="color: #666666">.</span>fit(X_train, y_train)
pred<span style="color: #666666">=</span>model<span style="color: #666666">.</span>predict(X_test)
poly<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=3</span>)
poly<span style="color: #666666">.</span>fit_transform(X_train, y_train)
plt<span style="color: #666666">.</span>scatter(X_test, y_test)
plt<span style="color: #666666">.</span>plot(X_test, pred, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;green&#39;</span>)
plt<span style="color: #666666">.</span>show()
<span style="color: #008000; font-weight: bold">print</span> (model<span style="color: #666666">.</span>score(X_test,y_test))
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;---------K-Nearest Neighbors-------&quot;</span>)
<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;neighbors_settings=range(1,11)</span>
<span style="color: #BA2121; font-style: italic">for n_neighbors in neighbors_settings:</span>
<span style="color: #BA2121; font-style: italic"> clf=KNeighborsClassifier(n_neighbors=n_neighbors)</span>
<span style="color: #BA2121; font-style: italic"> clf.fit(X_train, y_train)</span>
<span style="color: #BA2121; font-style: italic"> training_accuracy.append(clf.score(X_train, y_train))</span>
<span style="color: #BA2121; font-style: italic"> test_accuracy.append(clf.score(X_test, y_test))</span>
<span style="color: #BA2121; font-style: italic">print (mglearn.plots.plot_knn_regression(n_neighbors=3))&quot;&quot;&quot;</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.neighbors</span> <span style="color: #008000; font-weight: bold">import</span> KNeighborsRegressor
X, y<span style="color: #666666">=</span>mglearn<span style="color: #666666">.</span>datasets<span style="color: #666666">.</span>make_wave(n_samples<span style="color: #666666">=40</span>)
reg <span style="color: #666666">=</span> KNeighborsRegressor(n_neighbors<span style="color: #666666">=3</span>)
reg<span style="color: #666666">.</span>fit(X_train, y_train)
</pre></div>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec2">Decision trees and Regression </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<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>
<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>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> PolynomialFeatures
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LinearRegression
steps<span style="color: #666666">=250</span>
distance<span style="color: #666666">=0</span>
x<span style="color: #666666">=0</span>
distance_list<span style="color: #666666">=</span>[]
steps_list<span style="color: #666666">=</span>[]
<span style="color: #008000; font-weight: bold">while</span> x<span style="color: #666666">&lt;</span>steps:
distance<span style="color: #666666">+=</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(<span style="color: #666666">-1</span>,<span style="color: #666666">2</span>)
distance_list<span style="color: #666666">.</span>append(distance)
x<span style="color: #666666">+=1</span>
steps_list<span style="color: #666666">.</span>append(x)
plt<span style="color: #666666">.</span>plot(steps_list,distance_list, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;green&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;Random Walk Data&quot;</span>)
steps_list<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(steps_list)
distance_list<span style="color: #666666">=</span>np<span style="color: #666666">.</span>asarray(distance_list)
X<span style="color: #666666">=</span>steps_list[:,np<span style="color: #666666">.</span>newaxis]
<span style="color: #408080; font-style: italic">#Polynomial fits</span>
<span style="color: #408080; font-style: italic">#Degree 2</span>
poly_features<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=2</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000">False</span>)
X_poly<span style="color: #666666">=</span>poly_features<span style="color: #666666">.</span>fit_transform(X)
lin_reg<span style="color: #666666">=</span>LinearRegression()
poly_fit<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly,distance_list)
b<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>coef_
c<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>intercept_
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;2nd degree coefficients:&quot;</span>)
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;zero power: &quot;</span>,c)
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;first power: &quot;</span>, b[<span style="color: #666666">0</span>])
<span style="color: #008000; font-weight: bold">print</span> (<span style="color: #BA2121">&quot;second power: &quot;</span>,b[<span style="color: #666666">1</span>])
z <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0</span>, steps, <span style="color: #666666">.01</span>)
z_mod<span style="color: #666666">=</span>b[<span style="color: #666666">1</span>]<span style="color: #666666">*</span>z<span style="color: #666666">**2+</span>b[<span style="color: #666666">0</span>]<span style="color: #666666">*</span>z<span style="color: #666666">+</span>c
fit_mod<span style="color: #666666">=</span>b[<span style="color: #666666">1</span>]<span style="color: #666666">*</span>X<span style="color: #666666">**2+</span>b[<span style="color: #666666">0</span>]<span style="color: #666666">*</span>X<span style="color: #666666">+</span>c
plt<span style="color: #666666">.</span>plot(z, z_mod, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;r&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;2nd Degree Fit&quot;</span>)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Polynomial Regression&quot;</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&quot;Steps&quot;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&quot;Distance&quot;</span>)
<span style="color: #408080; font-style: italic">#Degree 10</span>
poly_features10<span style="color: #666666">=</span>PolynomialFeatures(degree<span style="color: #666666">=10</span>, include_bias<span style="color: #666666">=</span><span style="color: #008000">False</span>)
X_poly10<span style="color: #666666">=</span>poly_features10<span style="color: #666666">.</span>fit_transform(X)
poly_fit10<span style="color: #666666">=</span>lin_reg<span style="color: #666666">.</span>fit(X_poly10,distance_list)
y_plot<span style="color: #666666">=</span>poly_fit10<span style="color: #666666">.</span>predict(X_poly10)
plt<span style="color: #666666">.</span>plot(X, y_plot, color<span style="color: #666666">=</span><span style="color: #BA2121">&#39;black&#39;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;10th Degree Fit&quot;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
<span style="color: #408080; font-style: italic">#Decision Tree Regression</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.tree</span> <span style="color: #008000; font-weight: bold">import</span> DecisionTreeRegressor
regr_1<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=2</span>)
regr_2<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=5</span>)
regr_3<span style="color: #666666">=</span>DecisionTreeRegressor(max_depth<span style="color: #666666">=7</span>)
regr_1<span style="color: #666666">.</span>fit(X, distance_list)
regr_2<span style="color: #666666">.</span>fit(X, distance_list)
regr_3<span style="color: #666666">.</span>fit(X, distance_list)
X_test <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #666666">0.0</span>, steps, <span style="color: #666666">0.01</span>)[:, np<span style="color: #666666">.</span>newaxis]
y_1 <span style="color: #666666">=</span> regr_1<span style="color: #666666">.</span>predict(X_test)
y_2 <span style="color: #666666">=</span> regr_2<span style="color: #666666">.</span>predict(X_test)
y_3<span style="color: #666666">=</span>regr_3<span style="color: #666666">.</span>predict(X_test)
<span style="color: #408080; font-style: italic"># Plot the results</span>
plt<span style="color: #666666">.</span>figure()
plt<span style="color: #666666">.</span>scatter(X, distance_list, s<span style="color: #666666">=2.5</span>, c<span style="color: #666666">=</span><span style="color: #BA2121">&quot;black&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;data&quot;</span>)
plt<span style="color: #666666">.</span>plot(X_test, y_1, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;red&quot;</span>,
label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=2&quot;</span>, linewidth<span style="color: #666666">=2</span>)
plt<span style="color: #666666">.</span>plot(X_test, y_2, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;green&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=5&quot;</span>, linewidth<span style="color: #666666">=2</span>)
plt<span style="color: #666666">.</span>plot(X_test, y_3, color<span style="color: #666666">=</span><span style="color: #BA2121">&quot;m&quot;</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;max_depth=7&quot;</span>, linewidth<span style="color: #666666">=2</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&quot;Data&quot;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&quot;Darget&quot;</span>)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;Decision Tree Regression&quot;</span>)
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
</pre></div>
<p>
<!-- ------------------- end of main content --------------- -->
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
</center>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink