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<li><a class="reference internal" href="#">2.7. Novelty and Outlier Detection</a><ul>
<li><a class="reference internal" href="#overview-of-outlier-detection-methods">2.7.1. Overview of outlier detection methods</a></li>
<li><a class="reference internal" href="#novelty-detection">2.7.2. Novelty Detection</a><ul>
<li><a class="reference internal" href="#scaling-up-the-one-class-svm">2.7.2.1. Scaling up the One-Class SVM</a></li>
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<li><a class="reference internal" href="#id1">2.7.3. Outlier Detection</a><ul>
<li><a class="reference internal" href="#fitting-an-elliptic-envelope">2.7.3.1. Fitting an elliptic envelope</a></li>
<li><a class="reference internal" href="#isolation-forest">2.7.3.2. Isolation Forest</a></li>
<li><a class="reference internal" href="#local-outlier-factor">2.7.3.3. Local Outlier Factor</a></li>
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<li><a class="reference internal" href="#novelty-detection-with-local-outlier-factor">2.7.4. Novelty detection with Local Outlier Factor</a></li>
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<section id="novelty-and-outlier-detection">
<span id="outlier-detection"></span><h1><span class="section-number">2.7. </span>Novelty and Outlier Detection<a class="headerlink" href="#novelty-and-outlier-detection" title="Link to this heading">¶</a></h1>
<p>Many applications require being able to decide whether a new observation
belongs to the same distribution as existing observations (it is an
<em>inlier</em>), or should be considered as different (it is an <em>outlier</em>).
Often, this ability is used to clean real data sets. Two important
distinctions must be made:</p>
<dl class="field-list simple">
<dt class="field-odd">outlier detection<span class="colon">:</span></dt>
<dd class="field-odd"><p>The training data contains outliers which are defined as observations that
are far from the others. Outlier detection estimators thus try to fit the
regions where the training data is the most concentrated, ignoring the
deviant observations.</p>
</dd>
<dt class="field-even">novelty detection<span class="colon">:</span></dt>
<dd class="field-even"><p>The training data is not polluted by outliers and we are interested in
detecting whether a <strong>new</strong> observation is an outlier. In this context an
outlier is also called a novelty.</p>
</dd>
</dl>
<p>Outlier detection and novelty detection are both used for anomaly
detection, where one is interested in detecting abnormal or unusual
observations. Outlier detection is then also known as unsupervised anomaly
detection and novelty detection as semi-supervised anomaly detection. In the
context of outlier detection, the outliers/anomalies cannot form a
dense cluster as available estimators assume that the outliers/anomalies are
located in low density regions. On the contrary, in the context of novelty
detection, novelties/anomalies can form a dense cluster as long as they are in
a low density region of the training data, considered as normal in this
context.</p>
<p>The scikit-learn project provides a set of machine learning tools that
can be used both for novelty or outlier detection. This strategy is
implemented with objects learning in an unsupervised way from the data:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">estimator</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
</pre></div>
</div>
<p>new observations can then be sorted as inliers or outliers with a
<code class="docutils literal notranslate"><span class="pre">predict</span></code> method:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">estimator</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
</pre></div>
</div>
<p>Inliers are labeled 1, while outliers are labeled -1. The predict method
makes use of a threshold on the raw scoring function computed by the
estimator. This scoring function is accessible through the <code class="docutils literal notranslate"><span class="pre">score_samples</span></code>
method, while the threshold can be controlled by the <code class="docutils literal notranslate"><span class="pre">contamination</span></code>
parameter.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">decision_function</span></code> method is also defined from the scoring function,
in such a way that negative values are outliers and non-negative ones are
inliers:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">estimator</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a> does not support
<code class="docutils literal notranslate"><span class="pre">predict</span></code>, <code class="docutils literal notranslate"><span class="pre">decision_function</span></code> and <code class="docutils literal notranslate"><span class="pre">score_samples</span></code> methods by default
but only a <code class="docutils literal notranslate"><span class="pre">fit_predict</span></code> method, as this estimator was originally meant to
be applied for outlier detection. The scores of abnormality of the training
samples are accessible through the <code class="docutils literal notranslate"><span class="pre">negative_outlier_factor_</span></code> attribute.</p>
<p>If you really want to use <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a> for novelty
detection, i.e. predict labels or compute the score of abnormality of new
unseen data, you can instantiate the estimator with the <code class="docutils literal notranslate"><span class="pre">novelty</span></code> parameter
set to <code class="docutils literal notranslate"><span class="pre">True</span></code> before fitting the estimator. In this case, <code class="docutils literal notranslate"><span class="pre">fit_predict</span></code> is
not available.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p><strong>Novelty detection with Local Outlier Factor</strong></p>
<p>When <code class="docutils literal notranslate"><span class="pre">novelty</span></code> is set to <code class="docutils literal notranslate"><span class="pre">True</span></code> be aware that you must only use
<code class="docutils literal notranslate"><span class="pre">predict</span></code>, <code class="docutils literal notranslate"><span class="pre">decision_function</span></code> and <code class="docutils literal notranslate"><span class="pre">score_samples</span></code> on new unseen data
and not on the training samples as this would lead to wrong results.
I.e., the result of <code class="docutils literal notranslate"><span class="pre">predict</span></code> will not be the same as <code class="docutils literal notranslate"><span class="pre">fit_predict</span></code>.
The scores of abnormality of the training samples are always accessible
through the <code class="docutils literal notranslate"><span class="pre">negative_outlier_factor_</span></code> attribute.</p>
</div>
<p>The behavior of <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a> is summarized in the
following table.</p>
<table class="docutils align-default">
<thead>
<tr class="row-odd"><th class="head"><p>Method</p></th>
<th class="head"><p>Outlier detection</p></th>
<th class="head"><p>Novelty detection</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">fit_predict</span></code></p></td>
<td><p>OK</p></td>
<td><p>Not available</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">predict</span></code></p></td>
<td><p>Not available</p></td>
<td><p>Use only on new data</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">decision_function</span></code></p></td>
<td><p>Not available</p></td>
<td><p>Use only on new data</p></td>
</tr>
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">score_samples</span></code></p></td>
<td><p>Use <code class="docutils literal notranslate"><span class="pre">negative_outlier_factor_</span></code></p></td>
<td><p>Use only on new data</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">negative_outlier_factor_</span></code></p></td>
<td><p>OK</p></td>
<td><p>OK</p></td>
</tr>
</tbody>
</table>
<section id="overview-of-outlier-detection-methods">
<h2><span class="section-number">2.7.1. </span>Overview of outlier detection methods<a class="headerlink" href="#overview-of-outlier-detection-methods" title="Link to this heading">¶</a></h2>
<p>A comparison of the outlier detection algorithms in scikit-learn. Local
Outlier Factor (LOF) does not show a decision boundary in black as it
has no predict method to be applied on new data when it is used for outlier
detection.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/miscellaneous/plot_anomaly_comparison.html"><img alt="../_images/sphx_glr_plot_anomaly_comparison_001.png" src="../_images/sphx_glr_plot_anomaly_comparison_001.png" style="width: 700.0px; height: 625.0px;" /></a>
</figure>
<p><a class="reference internal" href="generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">ensemble.IsolationForest</span></code></a> and <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a>
perform reasonably well on the data sets considered here.
The <a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a> is known to be sensitive to outliers and thus
does not perform very well for outlier detection. That being said, outlier
detection in high-dimension, or without any assumptions on the distribution
of the inlying data is very challenging. <a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a> may still
be used with outlier detection but requires fine-tuning of its hyperparameter
<code class="docutils literal notranslate"><span class="pre">nu</span></code> to handle outliers and prevent overfitting.
<a class="reference internal" href="generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">linear_model.SGDOneClassSVM</span></code></a> provides an implementation of a
linear One-Class SVM with a linear complexity in the number of samples. This
implementation is here used with a kernel approximation technique to obtain
results similar to <a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a> which uses a Gaussian kernel
by default. Finally, <a class="reference internal" href="generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-class docutils literal notranslate"><span class="pre">covariance.EllipticEnvelope</span></code></a> assumes the data is
Gaussian and learns an ellipse. For more details on the different estimators
refer to the example
<a class="reference internal" href="../auto_examples/miscellaneous/plot_anomaly_comparison.html#sphx-glr-auto-examples-miscellaneous-plot-anomaly-comparison-py"><span class="std std-ref">Comparing anomaly detection algorithms for outlier detection on toy datasets</span></a> and the
sections hereunder.</p>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p>See <a class="reference internal" href="../auto_examples/miscellaneous/plot_anomaly_comparison.html#sphx-glr-auto-examples-miscellaneous-plot-anomaly-comparison-py"><span class="std std-ref">Comparing anomaly detection algorithms for outlier detection on toy datasets</span></a>
for a comparison of the <a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a>, the
<a class="reference internal" href="generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">ensemble.IsolationForest</span></code></a>, the
<a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a> and
<a class="reference internal" href="generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-class docutils literal notranslate"><span class="pre">covariance.EllipticEnvelope</span></code></a>.</p></li>
<li><p>See <a class="reference internal" href="../auto_examples/miscellaneous/plot_outlier_detection_bench.html#sphx-glr-auto-examples-miscellaneous-plot-outlier-detection-bench-py"><span class="std std-ref">Evaluation of outlier detection estimators</span></a>
for an example showing how to evaluate outlier detection estimators,
the <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a> and the
<a class="reference internal" href="generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">ensemble.IsolationForest</span></code></a>, using ROC curves from
<a class="reference internal" href="generated/sklearn.metrics.RocCurveDisplay.html#sklearn.metrics.RocCurveDisplay" title="sklearn.metrics.RocCurveDisplay"><code class="xref py py-class docutils literal notranslate"><span class="pre">metrics.RocCurveDisplay</span></code></a>.</p></li>
</ul>
</aside>
</section>
<section id="novelty-detection">
<h2><span class="section-number">2.7.2. </span>Novelty Detection<a class="headerlink" href="#novelty-detection" title="Link to this heading">¶</a></h2>
<p>Consider a data set of <span class="math notranslate nohighlight">\(n\)</span> observations from the same
distribution described by <span class="math notranslate nohighlight">\(p\)</span> features. Consider now that we
add one more observation to that data set. Is the new observation so
different from the others that we can doubt it is regular? (i.e. does
it come from the same distribution?) Or on the contrary, is it so
similar to the other that we cannot distinguish it from the original
observations? This is the question addressed by the novelty detection
tools and methods.</p>
<p>In general, it is about to learn a rough, close frontier delimiting
the contour of the initial observations distribution, plotted in
embedding <span class="math notranslate nohighlight">\(p\)</span>-dimensional space. Then, if further observations
lay within the frontier-delimited subspace, they are considered as
coming from the same population than the initial
observations. Otherwise, if they lay outside the frontier, we can say
that they are abnormal with a given confidence in our assessment.</p>
<p>The One-Class SVM has been introduced by Schölkopf et al. for that purpose
and implemented in the <a class="reference internal" href="svm.html#svm"><span class="std std-ref">Support Vector Machines</span></a> module in the
<a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a> object. It requires the choice of a
kernel and a scalar parameter to define a frontier. The RBF kernel is
usually chosen although there exists no exact formula or algorithm to
set its bandwidth parameter. This is the default in the scikit-learn
implementation. The <code class="docutils literal notranslate"><span class="pre">nu</span></code> parameter, also known as the margin of
the One-Class SVM, corresponds to the probability of finding a new,
but regular, observation outside the frontier.</p>
<aside class="topic">
<p class="topic-title">References:</p>
<ul class="simple">
<li><p><a class="reference external" href="https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/tr-99-87.pdf">Estimating the support of a high-dimensional distribution</a>
Schölkopf, Bernhard, et al. Neural computation 13.7 (2001): 1443-1471.</p></li>
</ul>
</aside>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p>See <a class="reference internal" href="../auto_examples/svm/plot_oneclass.html#sphx-glr-auto-examples-svm-plot-oneclass-py"><span class="std std-ref">One-class SVM with non-linear kernel (RBF)</span></a> for visualizing the
frontier learned around some data by a
<a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a> object.</p></li>
<li><p><a class="reference internal" href="../auto_examples/applications/plot_species_distribution_modeling.html#sphx-glr-auto-examples-applications-plot-species-distribution-modeling-py"><span class="std std-ref">Species distribution modeling</span></a></p></li>
</ul>
</aside>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/svm/plot_oneclass.html"><img alt="../_images/sphx_glr_plot_oneclass_001.png" src="../_images/sphx_glr_plot_oneclass_001.png" style="width: 480.0px; height: 360.0px;" /></a>
</figure>
<section id="scaling-up-the-one-class-svm">
<h3><span class="section-number">2.7.2.1. </span>Scaling up the One-Class SVM<a class="headerlink" href="#scaling-up-the-one-class-svm" title="Link to this heading">¶</a></h3>
<p>An online linear version of the One-Class SVM is implemented in
<a class="reference internal" href="generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">linear_model.SGDOneClassSVM</span></code></a>. This implementation scales linearly with
the number of samples and can be used with a kernel approximation to
approximate the solution of a kernelized <a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a> whose
complexity is at best quadratic in the number of samples. See section
<a class="reference internal" href="sgd.html#sgd-online-one-class-svm"><span class="std std-ref">Online One-Class SVM</span></a> for more details.</p>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p>See <a class="reference internal" href="../auto_examples/linear_model/plot_sgdocsvm_vs_ocsvm.html#sphx-glr-auto-examples-linear-model-plot-sgdocsvm-vs-ocsvm-py"><span class="std std-ref">One-Class SVM versus One-Class SVM using Stochastic Gradient Descent</span></a>
for an illustration of the approximation of a kernelized One-Class SVM
with the <code class="docutils literal notranslate"><span class="pre">linear_model.SGDOneClassSVM</span></code> combined with kernel approximation.</p></li>
</ul>
</aside>
</section>
</section>
<section id="id1">
<h2><span class="section-number">2.7.3. </span>Outlier Detection<a class="headerlink" href="#id1" title="Link to this heading">¶</a></h2>
<p>Outlier detection is similar to novelty detection in the sense that
the goal is to separate a core of regular observations from some
polluting ones, called <em>outliers</em>. Yet, in the case of outlier
detection, we don’t have a clean data set representing the population
of regular observations that can be used to train any tool.</p>
<section id="fitting-an-elliptic-envelope">
<h3><span class="section-number">2.7.3.1. </span>Fitting an elliptic envelope<a class="headerlink" href="#fitting-an-elliptic-envelope" title="Link to this heading">¶</a></h3>
<p>One common way of performing outlier detection is to assume that the
regular data come from a known distribution (e.g. data are Gaussian
distributed). From this assumption, we generally try to define the
“shape” of the data, and can define outlying observations as
observations which stand far enough from the fit shape.</p>
<p>The scikit-learn provides an object
<a class="reference internal" href="generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-class docutils literal notranslate"><span class="pre">covariance.EllipticEnvelope</span></code></a> that fits a robust covariance
estimate to the data, and thus fits an ellipse to the central data
points, ignoring points outside the central mode.</p>
<p>For instance, assuming that the inlier data are Gaussian distributed, it
will estimate the inlier location and covariance in a robust way (i.e.
without being influenced by outliers). The Mahalanobis distances
obtained from this estimate is used to derive a measure of outlyingness.
This strategy is illustrated below.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/covariance/plot_mahalanobis_distances.html"><img alt="../_images/sphx_glr_plot_mahalanobis_distances_001.png" src="../_images/sphx_glr_plot_mahalanobis_distances_001.png" style="width: 750.0px; height: 375.0px;" /></a>
</figure>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p>See <a class="reference internal" href="../auto_examples/covariance/plot_mahalanobis_distances.html#sphx-glr-auto-examples-covariance-plot-mahalanobis-distances-py"><span class="std std-ref">Robust covariance estimation and Mahalanobis distances relevance</span></a> for
an illustration of the difference between using a standard
(<a class="reference internal" href="generated/sklearn.covariance.EmpiricalCovariance.html#sklearn.covariance.EmpiricalCovariance" title="sklearn.covariance.EmpiricalCovariance"><code class="xref py py-class docutils literal notranslate"><span class="pre">covariance.EmpiricalCovariance</span></code></a>) or a robust estimate
(<a class="reference internal" href="generated/sklearn.covariance.MinCovDet.html#sklearn.covariance.MinCovDet" title="sklearn.covariance.MinCovDet"><code class="xref py py-class docutils literal notranslate"><span class="pre">covariance.MinCovDet</span></code></a>) of location and covariance to
assess the degree of outlyingness of an observation.</p></li>
</ul>
</aside>
<aside class="topic">
<p class="topic-title">References:</p>
<ul class="simple">
<li><p>Rousseeuw, P.J., Van Driessen, K. “A fast algorithm for the minimum
covariance determinant estimator” Technometrics 41(3), 212 (1999)</p></li>
</ul>
</aside>
</section>
<section id="isolation-forest">
<span id="id2"></span><h3><span class="section-number">2.7.3.2. </span>Isolation Forest<a class="headerlink" href="#isolation-forest" title="Link to this heading">¶</a></h3>
<p>One efficient way of performing outlier detection in high-dimensional datasets
is to use random forests.
The <a class="reference internal" href="generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">ensemble.IsolationForest</span></code></a> ‘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 noticeably 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>
<p>The implementation of <a class="reference internal" href="generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">ensemble.IsolationForest</span></code></a> is based on an ensemble
of <a class="reference internal" href="generated/sklearn.tree.ExtraTreeRegressor.html#sklearn.tree.ExtraTreeRegressor" title="sklearn.tree.ExtraTreeRegressor"><code class="xref py py-class docutils literal notranslate"><span class="pre">tree.ExtraTreeRegressor</span></code></a>. Following Isolation Forest original paper,
the maximum depth of each tree is set to <span class="math notranslate nohighlight">\(\lceil \log_2(n) \rceil\)</span> where
<span class="math notranslate nohighlight">\(n\)</span> is the number of samples used to build the tree (see (Liu et al.,
2008) for more details).</p>
<p>This algorithm is illustrated below.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/ensemble/plot_isolation_forest.html"><img alt="../_images/sphx_glr_plot_isolation_forest_003.png" src="../_images/sphx_glr_plot_isolation_forest_003.png" style="width: 480.0px; height: 360.0px;" /></a>
</figure>
<p id="iforest-warm-start">The <a class="reference internal" href="generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">ensemble.IsolationForest</span></code></a> supports <code class="docutils literal notranslate"><span class="pre">warm_start=True</span></code> which
allows you to add more trees to an already fitted model:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">IsolationForest</span>
<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span> <span class="mi">50</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">clf</span> <span class="o">=</span> <span class="n">IsolationForest</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">warm_start</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="c1"># fit 10 trees </span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span> <span class="c1"># add 10 more trees </span>
<span class="gp">>>> </span><span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="c1"># fit the added trees </span>
</pre></div>
</div>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p>See <a class="reference internal" href="../auto_examples/ensemble/plot_isolation_forest.html#sphx-glr-auto-examples-ensemble-plot-isolation-forest-py"><span class="std std-ref">IsolationForest example</span></a> for
an illustration of the use of IsolationForest.</p></li>
<li><p>See <a class="reference internal" href="../auto_examples/miscellaneous/plot_anomaly_comparison.html#sphx-glr-auto-examples-miscellaneous-plot-anomaly-comparison-py"><span class="std std-ref">Comparing anomaly detection algorithms for outlier detection on toy datasets</span></a>
for a comparison of <a class="reference internal" href="generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">ensemble.IsolationForest</span></code></a> with
<a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a>,
<a class="reference internal" href="generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">svm.OneClassSVM</span></code></a> (tuned to perform like an outlier detection
method), <a class="reference internal" href="generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">linear_model.SGDOneClassSVM</span></code></a>, and a covariance-based
outlier detection with <a class="reference internal" href="generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-class docutils literal notranslate"><span class="pre">covariance.EllipticEnvelope</span></code></a>.</p></li>
</ul>
</aside>
<aside class="topic">
<p class="topic-title">References:</p>
<ul class="simple">
<li><p>Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. “Isolation forest.”
Data Mining, 2008. ICDM’08. Eighth IEEE International Conference on.</p></li>
</ul>
</aside>
</section>
<section id="local-outlier-factor">
<span id="id3"></span><h3><span class="section-number">2.7.3.3. </span>Local Outlier Factor<a class="headerlink" href="#local-outlier-factor" title="Link to this heading">¶</a></h3>
<p>Another efficient way to perform outlier detection on moderately high dimensional
datasets is to use the Local Outlier Factor (LOF) algorithm.</p>
<p>The <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a> (LOF) algorithm computes a score
(called local outlier factor) reflecting the degree of abnormality of the
observations.
It measures the local density deviation of a given data point with respect to
its neighbors. The idea is to detect the samples that have a substantially
lower density than their neighbors.</p>
<p>In practice the local density is obtained from the k-nearest neighbors.
The LOF score of an observation is equal to the ratio of the
average local density of its k-nearest neighbors, and its own local density:
a normal instance is expected to have a local density similar to that of its
neighbors, while abnormal data are expected to have much smaller local density.</p>
<p>The number k of neighbors considered, (alias parameter n_neighbors) is typically
chosen 1) greater than the minimum number of objects a cluster has to contain,
so that other objects can be local outliers relative to this cluster, and 2)
smaller than the maximum number of close by objects that can potentially be
local outliers.
In practice, such information is generally not available, and taking
n_neighbors=20 appears to work well in general.
When the proportion of outliers is high (i.e. greater than 10 %, as in the
example below), n_neighbors should be greater (n_neighbors=35 in the example
below).</p>
<p>The strength of the LOF algorithm is that it takes both local and global
properties of datasets into consideration: it can perform well even in datasets
where abnormal samples have different underlying densities.
The question is not, how isolated the sample is, but how isolated it is
with respect to the surrounding neighborhood.</p>
<p>When applying LOF for outlier detection, there are no <code class="docutils literal notranslate"><span class="pre">predict</span></code>,
<code class="docutils literal notranslate"><span class="pre">decision_function</span></code> and <code class="docutils literal notranslate"><span class="pre">score_samples</span></code> methods but only a <code class="docutils literal notranslate"><span class="pre">fit_predict</span></code>
method. The scores of abnormality of the training samples are accessible
through the <code class="docutils literal notranslate"><span class="pre">negative_outlier_factor_</span></code> attribute.
Note that <code class="docutils literal notranslate"><span class="pre">predict</span></code>, <code class="docutils literal notranslate"><span class="pre">decision_function</span></code> and <code class="docutils literal notranslate"><span class="pre">score_samples</span></code> can be used
on new unseen data when LOF is applied for novelty detection, i.e. when the
<code class="docutils literal notranslate"><span class="pre">novelty</span></code> parameter is set to <code class="docutils literal notranslate"><span class="pre">True</span></code>, but the result of <code class="docutils literal notranslate"><span class="pre">predict</span></code> may
differ from that of <code class="docutils literal notranslate"><span class="pre">fit_predict</span></code>. See <a class="reference internal" href="#novelty-with-lof"><span class="std std-ref">Novelty detection with Local Outlier Factor</span></a>.</p>
<p>This strategy is illustrated below.</p>
<figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/neighbors/plot_lof_outlier_detection.html"><img alt="../_images/sphx_glr_plot_lof_outlier_detection_001.png" src="../_images/sphx_glr_plot_lof_outlier_detection_001.png" style="width: 480.0px; height: 360.0px;" /></a>
</figure>
<aside class="topic">
<p class="topic-title">Examples:</p>
<ul class="simple">
<li><p>See <a class="reference internal" href="../auto_examples/neighbors/plot_lof_outlier_detection.html#sphx-glr-auto-examples-neighbors-plot-lof-outlier-detection-py"><span class="std std-ref">Outlier detection with Local Outlier Factor (LOF)</span></a>
for an illustration of the use of <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a>.</p></li>
<li><p>See <a class="reference internal" href="../auto_examples/miscellaneous/plot_anomaly_comparison.html#sphx-glr-auto-examples-miscellaneous-plot-anomaly-comparison-py"><span class="std std-ref">Comparing anomaly detection algorithms for outlier detection on toy datasets</span></a>
for a comparison with other anomaly detection methods.</p></li>
</ul>
</aside>
<aside class="topic">
<p class="topic-title">References:</p>
<ul class="simple">
<li><p>Breunig, Kriegel, Ng, and Sander (2000)
<a class="reference external" href="https://www.dbs.ifi.lmu.de/Publikationen/Papers/LOF.pdf">LOF: identifying density-based local outliers.</a>
Proc. ACM SIGMOD</p></li>
</ul>
</aside>
</section>
</section>
<section id="novelty-detection-with-local-outlier-factor">
<span id="novelty-with-lof"></span><h2><span class="section-number">2.7.4. </span>Novelty detection with Local Outlier Factor<a class="headerlink" href="#novelty-detection-with-local-outlier-factor" title="Link to this heading">¶</a></h2>
<p>To use <a class="reference internal" href="generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">neighbors.LocalOutlierFactor</span></code></a> for novelty detection, i.e.
predict labels or compute the score of abnormality of new unseen data, you
need to instantiate the estimator with the <code class="docutils literal notranslate"><span class="pre">novelty</span></code> parameter
set to <code class="docutils literal notranslate"><span class="pre">True</span></code> before fitting the estimator:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">lof</span> <span class="o">=</span> <span class="n">LocalOutlierFactor</span><span class="p">(</span><span class="n">novelty</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">lof</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that <code class="docutils literal notranslate"><span class="pre">fit_predict</span></code> is not available in this case to avoid inconsistencies.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p><strong>Novelty detection with Local Outlier Factor`</strong></p>
<p>When <code class="docutils literal notranslate"><span class="pre">novelty</span></code> is set to <code class="docutils literal notranslate"><span class="pre">True</span></code> be aware that you must only use
<code class="docutils literal notranslate"><span class="pre">predict</span></code>, <code class="docutils literal notranslate"><span class="pre">decision_function</span></code> and <code class="docutils literal notranslate"><span class="pre">score_samples</span></code> on new unseen data
and not on the training samples as this would lead to wrong results.
I.e., the result of <code class="docutils literal notranslate"><span class="pre">predict</span></code> will not be the same as <code class="docutils literal notranslate"><span class="pre">fit_predict</span></code>.
The scores of abnormality of the training samples are always accessible
through the <code class="docutils literal notranslate"><span class="pre">negative_outlier_factor_</span></code> attribute.</p>
</div>
<p>Novelty detection with Local Outlier Factor is illustrated below.</p>
<blockquote>
<div><figure class="align-center">
<a class="reference external image-reference" href="../auto_examples/neighbors/plot_lof_novelty_detection.html"><img alt="../_images/sphx_glr_plot_lof_novelty_detection_001.png" src="../_images/sphx_glr_plot_lof_novelty_detection_001.png" style="width: 480.0px; height: 360.0px;" /></a>
</figure>
</div></blockquote>
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