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<div class="section" id="isolationforest-example">
<span id="sphx-glr-auto-examples-ensemble-plot-isolation-forest-py"></span><h1>IsolationForest example<a class="headerlink" href="#isolationforest-example" title="Permalink to this headline">¶</a></h1>
<p>An example using IsolationForest for anomaly detection.</p>
<p>The IsolationForest ‘isolates’ observations by randomly selecting a feature
and then randomly selecting a split value between the maximum and minimum
values of the selected feature.</p>
<p>Since recursive partitioning can be represented by a tree structure, the
number of splittings required to isolate a sample is equivalent to the path
length from the root node to the terminating node.</p>
<p>This path length, averaged over a forest of such random trees, is a measure
of normality and our decision function.</p>
<p>Random partitioning produces noticeable shorter paths for anomalies.
Hence, when a forest of random trees collectively produce shorter path lengths
for particular samples, they are highly likely to be anomalies.</p>
<table class="docutils footnote" frame="void" id="id1" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[1]</td><td>Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. “Isolation forest.”
Data Mining, 2008. ICDM‘08. Eighth IEEE International Conference on.</td></tr>
</tbody>
</table>
<img alt="../../_images/sphx_glr_plot_isolation_forest_001.png" class="align-center" src="../../_images/sphx_glr_plot_isolation_forest_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">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="View documentation for sklearn.ensemble.IsolationForest"><span class="n">IsolationForest</span></a>
<span class="n">rng</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.RandomState.wald.html#numpy.random.RandomState" title="View documentation for numpy.random.RandomState"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
<span class="c1"># Generate train data</span>
<span class="n">X</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">X_train</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.r_.html#numpy.r_" title="View documentation for numpy.r_"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="n">X</span> <span class="o">+</span> <span class="mi">2</span><span class="p">,</span> <span class="n">X</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span>
<span class="c1"># Generate some regular novel observations</span>
<span class="n">X</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">X_test</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.r_.html#numpy.r_" title="View documentation for numpy.r_"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="n">X</span> <span class="o">+</span> <span class="mi">2</span><span class="p">,</span> <span class="n">X</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span>
<span class="c1"># Generate some abnormal novel observations</span>
<span class="n">X_outliers</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">low</span><span class="o">=-</span><span class="mi">4</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="c1"># fit the model</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="View documentation for sklearn.ensemble.IsolationForest"><span class="n">IsolationForest</span></a><span class="p">(</span><span class="n">max_samples</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">y_pred_train</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">y_pred_test</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="n">y_pred_outliers</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_outliers</span><span class="p">)</span>
<span class="c1"># plot the line, the samples, and the nearest vectors to the plane</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="View documentation for numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">50</span><span class="p">),</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"IsolationForest"</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.contourf.html#matplotlib.pyplot.contourf" title="View documentation for matplotlib.pyplot.contourf"><span class="n">plt</span><span class="o">.</span><span class="n">contourf</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Blues_r</span><span class="p">)</span>
<span class="n">b1</span> <span class="o">=</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_train</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_train</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s1">'white'</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">b2</span> <span class="o">=</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_test</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_test</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s1">'green'</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</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_outliers</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_outliers</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s1">'red'</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
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