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<div class="section" id="sklearn-covariance-mincovdet">
<h1><a class="reference internal" href="../classes.html#module-sklearn.covariance" title="sklearn.covariance"><code class="xref py py-mod docutils literal"><span class="pre">sklearn.covariance</span></code></a>.MinCovDet<a class="headerlink" href="#sklearn-covariance-mincovdet" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.covariance.MinCovDet">
<em class="property">class </em><code class="descclassname">sklearn.covariance.</code><code class="descname">MinCovDet</code><span class="sig-paren">(</span><em>store_precision=True</em>, <em>assume_centered=False</em>, <em>support_fraction=None</em>, <em>random_state=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/robust_covariance.py#L501"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet" title="Permalink to this definition">¶</a></dt>
<dd><p>Minimum Covariance Determinant (MCD): robust estimator of covariance.</p>
<p>The Minimum Covariance Determinant covariance estimator is to be applied
on Gaussian-distributed data, but could still be relevant on data
drawn from a unimodal, symmetric distribution. It is not meant to be used
with multi-modal data (the algorithm used to fit a MinCovDet object is
likely to fail in such a case).
One should consider projection pursuit methods to deal with multi-modal
datasets.</p>
<p>Read more in the <a class="reference internal" href="../covariance.html#robust-covariance"><span>User Guide</span></a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>store_precision</strong> : bool</p>
<blockquote>
<div><p>Specify if the estimated precision is stored.</p>
</div></blockquote>
<p><strong>assume_centered</strong> : Boolean</p>
<blockquote>
<div><p>If True, the support of the robust location and the covariance
estimates is computed, and a covariance estimate is recomputed from
it, without centering the data.
Useful to work with data whose mean is significantly equal to
zero but is not exactly zero.
If False, the robust location and covariance are directly computed
with the FastMCD algorithm without additional treatment.</p>
</div></blockquote>
<p><strong>support_fraction</strong> : float, 0 < support_fraction < 1</p>
<blockquote>
<div><p>The proportion of points to be included in the support of the raw
MCD estimate. Default is None, which implies that the minimum
value of support_fraction will be used within the algorithm:
[n_sample + n_features + 1] / 2</p>
</div></blockquote>
<p><strong>random_state</strong> : integer or numpy.RandomState, optional</p>
<blockquote>
<div><p>The random generator used. If an integer is given, it fixes the
seed. Defaults to the global numpy random number generator.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Attributes:</th><td class="field-body"><p class="first"><strong>raw_location_</strong> : array-like, shape (n_features,)</p>
<blockquote>
<div><p>The raw robust estimated location before correction and re-weighting.</p>
</div></blockquote>
<p><strong>raw_covariance_</strong> : array-like, shape (n_features, n_features)</p>
<blockquote>
<div><p>The raw robust estimated covariance before correction and re-weighting.</p>
</div></blockquote>
<p><strong>raw_support_</strong> : array-like, shape (n_samples,)</p>
<blockquote>
<div><p>A mask of the observations that have been used to compute
the raw robust estimates of location and shape, before correction
and re-weighting.</p>
</div></blockquote>
<p><strong>location_</strong> : array-like, shape (n_features,)</p>
<blockquote>
<div><p>Estimated robust location</p>
</div></blockquote>
<p><strong>covariance_</strong> : array-like, shape (n_features, n_features)</p>
<blockquote>
<div><p>Estimated robust covariance matrix</p>
</div></blockquote>
<p><strong>precision_</strong> : array-like, shape (n_features, n_features)</p>
<blockquote>
<div><p>Estimated pseudo inverse matrix.
(stored only if store_precision is True)</p>
</div></blockquote>
<p><strong>support_</strong> : array-like, shape (n_samples,)</p>
<blockquote>
<div><p>A mask of the observations that have been used to compute
the robust estimates of location and shape.</p>
</div></blockquote>
<p><strong>dist_</strong> : array-like, shape (n_samples,)</p>
<blockquote class="last">
<div><p>Mahalanobis distances of the training set (on which <cite>fit</cite> is called)
observations.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">References</p>
<table class="docutils citation" frame="void" id="rouseeuw1984" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label">[Rouseeuw1984]</td><td><em>(<a class="fn-backref" href="#id1">1</a>, <a class="fn-backref" href="#id4">2</a>, <a class="fn-backref" href="#id5">3</a>)</em> <cite>P. J. Rousseeuw. Least median of squares regression.
J. Am Stat Ass, 79:871, 1984.</cite></td></tr>
</tbody>
</table>
<table class="docutils citation" frame="void" id="rouseeuw1999" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[Rouseeuw1999]</a></td><td><cite>A Fast Algorithm for the Minimum Covariance Determinant
Estimator, 1999, American Statistical Association and the American
Society for Quality, TECHNOMETRICS</cite></td></tr>
</tbody>
</table>
<table class="docutils citation" frame="void" id="butler1993" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id3">[Butler1993]</a></td><td><cite>R. W. Butler, P. L. Davies and M. Jhun,
Asymptotics For The Minimum Covariance Determinant Estimator,
The Annals of Statistics, 1993, Vol. 21, No. 3, 1385-1400</cite></td></tr>
</tbody>
</table>
<p class="rubric">Methods</p>
<table border="1" class="longtable docutils">
<colgroup>
<col width="10%" />
<col width="90%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.correct_covariance" title="sklearn.covariance.MinCovDet.correct_covariance"><code class="xref py py-obj docutils literal"><span class="pre">correct_covariance</span></code></a>(data)</td>
<td>Apply a correction to raw Minimum Covariance Determinant estimates.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.error_norm" title="sklearn.covariance.MinCovDet.error_norm"><code class="xref py py-obj docutils literal"><span class="pre">error_norm</span></code></a>(comp_cov[, norm, scaling, squared])</td>
<td>Computes the Mean Squared Error between two covariance estimators.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.fit" title="sklearn.covariance.MinCovDet.fit"><code class="xref py py-obj docutils literal"><span class="pre">fit</span></code></a>(X[, y])</td>
<td>Fits a Minimum Covariance Determinant with the FastMCD algorithm.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_params" title="sklearn.covariance.MinCovDet.get_params"><code class="xref py py-obj docutils literal"><span class="pre">get_params</span></code></a>([deep])</td>
<td>Get parameters for this estimator.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_precision" title="sklearn.covariance.MinCovDet.get_precision"><code class="xref py py-obj docutils literal"><span class="pre">get_precision</span></code></a>()</td>
<td>Getter for the precision matrix.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.mahalanobis" title="sklearn.covariance.MinCovDet.mahalanobis"><code class="xref py py-obj docutils literal"><span class="pre">mahalanobis</span></code></a>(observations)</td>
<td>Computes the squared Mahalanobis distances of given observations.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.reweight_covariance" title="sklearn.covariance.MinCovDet.reweight_covariance"><code class="xref py py-obj docutils literal"><span class="pre">reweight_covariance</span></code></a>(data)</td>
<td>Re-weight raw Minimum Covariance Determinant estimates.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.score" title="sklearn.covariance.MinCovDet.score"><code class="xref py py-obj docutils literal"><span class="pre">score</span></code></a>(X_test[, y])</td>
<td>Computes the log-likelihood of a Gaussian data set with <cite>self.covariance_</cite> as an estimator of its covariance matrix.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.covariance.MinCovDet.set_params" title="sklearn.covariance.MinCovDet.set_params"><code class="xref py py-obj docutils literal"><span class="pre">set_params</span></code></a>(**params)</td>
<td>Set the parameters of this estimator.</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><em>store_precision=True</em>, <em>assume_centered=False</em>, <em>support_fraction=None</em>, <em>random_state=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/robust_covariance.py#L584"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.__init__" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.correct_covariance">
<code class="descname">correct_covariance</code><span class="sig-paren">(</span><em>data</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/robust_covariance.py#L640"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.correct_covariance" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply a correction to raw Minimum Covariance Determinant estimates.</p>
<p>Correction using the empirical correction factor suggested
by Rousseeuw and Van Driessen in <a class="reference internal" href="#rouseeuw1984" id="id4">[Rouseeuw1984]</a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>data</strong> : array-like, shape (n_samples, n_features)</p>
<blockquote>
<div><p>The data matrix, with p features and n samples.
The data set must be the one which was used to compute
the raw estimates.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>covariance_corrected</strong> : array-like, shape (n_features, n_features)</p>
<blockquote class="last">
<div><p>Corrected robust covariance estimate.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.error_norm">
<code class="descname">error_norm</code><span class="sig-paren">(</span><em>comp_cov</em>, <em>norm='frobenius'</em>, <em>scaling=True</em>, <em>squared=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L213"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.error_norm" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the Mean Squared Error between two covariance estimators.
(In the sense of the Frobenius norm).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>comp_cov</strong> : array-like, shape = [n_features, n_features]</p>
<blockquote>
<div><p>The covariance to compare with.</p>
</div></blockquote>
<p><strong>norm</strong> : str</p>
<blockquote>
<div><p>The type of norm used to compute the error. Available error types:
- ‘frobenius’ (default): sqrt(tr(A^t.A))
- ‘spectral’: sqrt(max(eigenvalues(A^t.A))
where A is the error <code class="docutils literal"><span class="pre">(comp_cov</span> <span class="pre">-</span> <span class="pre">self.covariance_)</span></code>.</p>
</div></blockquote>
<p><strong>scaling</strong> : bool</p>
<blockquote>
<div><p>If True (default), the squared error norm is divided by n_features.
If False, the squared error norm is not rescaled.</p>
</div></blockquote>
<p><strong>squared</strong> : bool</p>
<blockquote>
<div><p>Whether to compute the squared error norm or the error norm.
If True (default), the squared error norm is returned.
If False, the error norm is returned.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>The Mean Squared Error (in the sense of the Frobenius norm) between</strong> :</p>
<p class="last"><strong>`self` and `comp_cov` covariance estimators.</strong> :</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/robust_covariance.py#L591"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fits a Minimum Covariance Determinant with the FastMCD algorithm.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array-like, shape = [n_samples, n_features]</p>
<blockquote>
<div><p>Training data, where n_samples is the number of samples
and n_features is the number of features.</p>
</div></blockquote>
<p><strong>y</strong> : not used, present for API consistence purpose.</p>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>self</strong> : object</p>
<blockquote class="last">
<div><p>Returns self.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.get_params">
<code class="descname">get_params</code><span class="sig-paren">(</span><em>deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/base.py#L199"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>deep: boolean, optional</strong> :</p>
<blockquote>
<div><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>params</strong> : mapping of string to any</p>
<blockquote class="last">
<div><p>Parameter names mapped to their values.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.get_precision">
<code class="descname">get_precision</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L140"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.get_precision" title="Permalink to this definition">¶</a></dt>
<dd><p>Getter for the precision matrix.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>precision_</strong> : array-like,</p>
<blockquote class="last">
<div><p>The precision matrix associated to the current covariance object.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.mahalanobis">
<code class="descname">mahalanobis</code><span class="sig-paren">(</span><em>observations</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L265"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.mahalanobis" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the squared Mahalanobis distances of given observations.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>observations</strong> : array-like, shape = [n_observations, n_features]</p>
<blockquote>
<div><p>The observations, the Mahalanobis distances of the which we
compute. Observations are assumed to be drawn from the same
distribution than the data used in fit.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>mahalanobis_distance</strong> : array, shape = [n_observations,]</p>
<blockquote class="last">
<div><p>Squared Mahalanobis distances of the observations.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.reweight_covariance">
<code class="descname">reweight_covariance</code><span class="sig-paren">(</span><em>data</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/robust_covariance.py#L664"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.reweight_covariance" title="Permalink to this definition">¶</a></dt>
<dd><p>Re-weight raw Minimum Covariance Determinant estimates.</p>
<p>Re-weight observations using Rousseeuw’s method (equivalent to
deleting outlying observations from the data set before
computing location and covariance estimates). <a class="reference internal" href="#rouseeuw1984" id="id5">[Rouseeuw1984]</a></p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>data</strong> : array-like, shape (n_samples, n_features)</p>
<blockquote>
<div><p>The data matrix, with p features and n samples.
The data set must be the one which was used to compute
the raw estimates.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>location_reweighted</strong> : array-like, shape (n_features, )</p>
<blockquote>
<div><p>Re-weighted robust location estimate.</p>
</div></blockquote>
<p><strong>covariance_reweighted</strong> : array-like, shape (n_features, n_features)</p>
<blockquote>
<div><p>Re-weighted robust covariance estimate.</p>
</div></blockquote>
<p><strong>support_reweighted</strong> : array-like, type boolean, shape (n_samples,)</p>
<blockquote class="last">
<div><p>A mask of the observations that have been used to compute
the re-weighted robust location and covariance estimates.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.score">
<code class="descname">score</code><span class="sig-paren">(</span><em>X_test</em>, <em>y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/covariance/empirical_covariance_.py#L184"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the log-likelihood of a Gaussian data set with
<cite>self.covariance_</cite> as an estimator of its covariance matrix.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X_test</strong> : array-like, shape = [n_samples, n_features]</p>
<blockquote>
<div><p>Test data of which we compute the likelihood, where n_samples is
the number of samples and n_features is the number of features.
X_test is assumed to be drawn from the same distribution than
the data used in fit (including centering).</p>
</div></blockquote>
<p><strong>y</strong> : not used, present for API consistence purpose.</p>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>res</strong> : float</p>
<blockquote class="last">
<div><p>The likelihood of the data set with <cite>self.covariance_</cite> as an
estimator of its covariance matrix.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.covariance.MinCovDet.set_params">
<code class="descname">set_params</code><span class="sig-paren">(</span><em>**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/base.py#L236"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The former have parameters of the form
<code class="docutils literal"><span class="pre"><component>__<parameter></span></code> so that it’s possible to update each
component of a nested object.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><strong>self</strong> :</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<div class="section" id="examples-using-sklearn-covariance-mincovdet">
<h2>Examples using <code class="docutils literal"><span class="pre">sklearn.covariance.MinCovDet</span></code><a class="headerlink" href="#examples-using-sklearn-covariance-mincovdet" title="Permalink to this headline">¶</a></h2>
<div class="thumbnailContainer" tooltip="An example to show covariance estimation with the Mahalanobis distances on Gaussian distributed..."><div class="figure" id="id6">
<a class="reference external image-reference" href="./../../auto_examples/covariance/plot_mahalanobis_distances.html"><img alt="../../_images/plot_mahalanobis_distances1.png" src="../../_images/plot_mahalanobis_distances1.png" /></a>
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/covariance/plot_mahalanobis_distances.html#example-covariance-plot-mahalanobis-distances-py"><span>Robust covariance estimation and Mahalanobis distances relevance</span></a></span></p>
</div>
</div><div class="thumbnailContainer" tooltip="The usual covariance maximum likelihood estimate is very sensitive to the presence of outliers ..."><div class="figure" id="id7">
<a class="reference external image-reference" href="./../../auto_examples/covariance/plot_robust_vs_empirical_covariance.html"><img alt="../../_images/plot_robust_vs_empirical_covariance1.png" src="../../_images/plot_robust_vs_empirical_covariance1.png" /></a>
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/covariance/plot_robust_vs_empirical_covariance.html#example-covariance-plot-robust-vs-empirical-covariance-py"><span>Robust vs Empirical covariance estimate</span></a></span></p>
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