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<ul>
<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.covariance</span></code>.MinCovDet</a><ul>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet"><code class="docutils literal notranslate"><span class="pre">MinCovDet</span></code></a><ul>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.correct_covariance"><code class="docutils literal notranslate"><span class="pre">MinCovDet.correct_covariance</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.error_norm"><code class="docutils literal notranslate"><span class="pre">MinCovDet.error_norm</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.fit"><code class="docutils literal notranslate"><span class="pre">MinCovDet.fit</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_metadata_routing"><code class="docutils literal notranslate"><span class="pre">MinCovDet.get_metadata_routing</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_params"><code class="docutils literal notranslate"><span class="pre">MinCovDet.get_params</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_precision"><code class="docutils literal notranslate"><span class="pre">MinCovDet.get_precision</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.mahalanobis"><code class="docutils literal notranslate"><span class="pre">MinCovDet.mahalanobis</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.reweight_covariance"><code class="docutils literal notranslate"><span class="pre">MinCovDet.reweight_covariance</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.score"><code class="docutils literal notranslate"><span class="pre">MinCovDet.score</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.set_params"><code class="docutils literal notranslate"><span class="pre">MinCovDet.set_params</span></code></a></li>
<li><a class="reference internal" href="#sklearn.covariance.MinCovDet.set_score_request"><code class="docutils literal notranslate"><span class="pre">MinCovDet.set_score_request</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#examples-using-sklearn-covariance-mincovdet">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.covariance.MinCovDet</span></code></a></li>
</ul>
</li>
</ul>
</div>
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<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 notranslate"><span class="pre">sklearn.covariance</span></code></a>.MinCovDet<a class="headerlink" href="#sklearn-covariance-mincovdet" title="Permalink to this heading">¶</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">sklearn.covariance.</span></span><span class="sig-name descname"><span class="pre">MinCovDet</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">store_precision</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">assume_centered</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">support_fraction</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">random_state</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_robust_covariance.py#L579"><span class="viewcode-link"><span class="pre">[source]</span></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 class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>store_precision</strong><span class="classifier">bool, default=True</span></dt><dd><p>Specify if the estimated precision is stored.</p>
</dd>
<dt><strong>assume_centered</strong><span class="classifier">bool, default=False</span></dt><dd><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>
</dd>
<dt><strong>support_fraction</strong><span class="classifier">float, default=None</span></dt><dd><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:
<code class="docutils literal notranslate"><span class="pre">(n_sample</span> <span class="pre">+</span> <span class="pre">n_features</span> <span class="pre">+</span> <span class="pre">1)</span> <span class="pre">/</span> <span class="pre">2</span></code>. The parameter must be in the range
(0, 1].</p>
</dd>
<dt><strong>random_state</strong><span class="classifier">int, RandomState instance or None, default=None</span></dt><dd><p>Determines the pseudo random number generator for shuffling the data.
Pass an int for reproducible results across multiple function calls.
See <a class="reference internal" href="../../glossary.html#term-random_state"><span class="xref std std-term">Glossary</span></a>.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><strong>raw_location_</strong><span class="classifier">ndarray of shape (n_features,)</span></dt><dd><p>The raw robust estimated location before correction and re-weighting.</p>
</dd>
<dt><strong>raw_covariance_</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>The raw robust estimated covariance before correction and re-weighting.</p>
</dd>
<dt><strong>raw_support_</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><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>
</dd>
<dt><strong>location_</strong><span class="classifier">ndarray of shape (n_features,)</span></dt><dd><p>Estimated robust location.</p>
</dd>
<dt><strong>covariance_</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Estimated robust covariance matrix.</p>
</dd>
<dt><strong>precision_</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Estimated pseudo inverse matrix.
(stored only if store_precision is True)</p>
</dd>
<dt><strong>support_</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>A mask of the observations that have been used to compute
the robust estimates of location and shape.</p>
</dd>
<dt><strong>dist_</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Mahalanobis distances of the training set (on which <a class="reference internal" href="#sklearn.covariance.MinCovDet.fit" title="sklearn.covariance.MinCovDet.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit</span></code></a> is
called) observations.</p>
</dd>
<dt><strong>n_features_in_</strong><span class="classifier">int</span></dt><dd><p>Number of features seen during <a class="reference internal" href="../../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 0.24.</span></p>
</div>
</dd>
<dt><strong>feature_names_in_</strong><span class="classifier">ndarray of shape (<code class="docutils literal notranslate"><span class="pre">n_features_in_</span></code>,)</span></dt><dd><p>Names of features seen during <a class="reference internal" href="../../glossary.html#term-fit"><span class="xref std std-term">fit</span></a>. Defined only when <code class="docutils literal notranslate"><span class="pre">X</span></code>
has feature names that are all strings.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.0.</span></p>
</div>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-obj docutils literal notranslate"><span class="pre">EllipticEnvelope</span></code></a></dt><dd><p>An object for detecting outliers in a Gaussian distributed dataset.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.EmpiricalCovariance.html#sklearn.covariance.EmpiricalCovariance" title="sklearn.covariance.EmpiricalCovariance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">EmpiricalCovariance</span></code></a></dt><dd><p>Maximum likelihood covariance estimator.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.GraphicalLasso.html#sklearn.covariance.GraphicalLasso" title="sklearn.covariance.GraphicalLasso"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GraphicalLasso</span></code></a></dt><dd><p>Sparse inverse covariance estimation with an l1-penalized estimator.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.GraphicalLassoCV.html#sklearn.covariance.GraphicalLassoCV" title="sklearn.covariance.GraphicalLassoCV"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GraphicalLassoCV</span></code></a></dt><dd><p>Sparse inverse covariance with cross-validated choice of the l1 penalty.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.LedoitWolf.html#sklearn.covariance.LedoitWolf" title="sklearn.covariance.LedoitWolf"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LedoitWolf</span></code></a></dt><dd><p>LedoitWolf Estimator.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.OAS.html#sklearn.covariance.OAS" title="sklearn.covariance.OAS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OAS</span></code></a></dt><dd><p>Oracle Approximating Shrinkage Estimator.</p>
</dd>
<dt><a class="reference internal" href="sklearn.covariance.ShrunkCovariance.html#sklearn.covariance.ShrunkCovariance" title="sklearn.covariance.ShrunkCovariance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ShrunkCovariance</span></code></a></dt><dd><p>Covariance estimator with shrinkage.</p>
</dd>
</dl>
</div>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r9f63e655f7bd-rouseeuw1984" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>Rouseeuw1984<span class="fn-bracket">]</span></span>
<p>P. J. Rousseeuw. Least median of squares regression.
J. Am Stat Ass, 79:871, 1984.</p>
</div>
<div class="citation" id="r9f63e655f7bd-rousseeuw" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>Rousseeuw<span class="fn-bracket">]</span></span>
<p>A Fast Algorithm for the Minimum Covariance Determinant
Estimator, 1999, American Statistical Association and the American
Society for Quality, TECHNOMETRICS</p>
</div>
<div class="citation" id="r9f63e655f7bd-butlerdavies" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>ButlerDavies<span class="fn-bracket">]</span></span>
<p>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</p>
</div>
</div>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></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="kn">from</span> <span class="nn">sklearn.covariance</span> <span class="kn">import</span> <span class="n">MinCovDet</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_gaussian_quantiles</span>
<span class="gp">>>> </span><span class="n">real_cov</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="mf">.8</span><span class="p">,</span> <span class="mf">.3</span><span class="p">],</span>
<span class="gp">... </span> <span class="p">[</span><span class="mf">.3</span><span class="p">,</span> <span class="mf">.4</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">multivariate_normal</span><span class="p">(</span><span class="n">mean</span><span class="o">=</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="gp">... </span> <span class="n">cov</span><span class="o">=</span><span class="n">real_cov</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">size</span><span class="o">=</span><span class="mi">500</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">cov</span> <span class="o">=</span> <span class="n">MinCovDet</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</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="gp">>>> </span><span class="n">cov</span><span class="o">.</span><span class="n">covariance_</span>
<span class="go">array([[0.7411..., 0.2535...],</span>
<span class="go"> [0.2535..., 0.3053...]])</span>
<span class="gp">>>> </span><span class="n">cov</span><span class="o">.</span><span class="n">location_</span>
<span class="go">array([0.0813... , 0.0427...])</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="autosummary longtable docutils align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.correct_covariance" title="sklearn.covariance.MinCovDet.correct_covariance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">correct_covariance</span></code></a>(data)</p></td>
<td><p>Apply a correction to raw Minimum Covariance Determinant estimates.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.error_norm" title="sklearn.covariance.MinCovDet.error_norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">error_norm</span></code></a>(comp_cov[, norm, scaling, squared])</p></td>
<td><p>Compute the Mean Squared Error between two covariance estimators.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.fit" title="sklearn.covariance.MinCovDet.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(X[, y])</p></td>
<td><p>Fit a Minimum Covariance Determinant with the FastMCD algorithm.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_metadata_routing" title="sklearn.covariance.MinCovDet.get_metadata_routing"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_metadata_routing</span></code></a>()</p></td>
<td><p>Get metadata routing of this object.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_params" title="sklearn.covariance.MinCovDet.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>([deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.get_precision" title="sklearn.covariance.MinCovDet.get_precision"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_precision</span></code></a>()</p></td>
<td><p>Getter for the precision matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.mahalanobis" title="sklearn.covariance.MinCovDet.mahalanobis"><code class="xref py py-obj docutils literal notranslate"><span class="pre">mahalanobis</span></code></a>(X)</p></td>
<td><p>Compute the squared Mahalanobis distances of given observations.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.reweight_covariance" title="sklearn.covariance.MinCovDet.reweight_covariance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">reweight_covariance</span></code></a>(data)</p></td>
<td><p>Re-weight raw Minimum Covariance Determinant estimates.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.score" title="sklearn.covariance.MinCovDet.score"><code class="xref py py-obj docutils literal notranslate"><span class="pre">score</span></code></a>(X_test[, y])</p></td>
<td><p>Compute the log-likelihood of <code class="docutils literal notranslate"><span class="pre">X_test</span></code> under the estimated Gaussian model.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.set_params" title="sklearn.covariance.MinCovDet.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(**params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.MinCovDet.set_score_request" title="sklearn.covariance.MinCovDet.set_score_request"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_score_request</span></code></a>(*[, X_test])</p></td>
<td><p>Request metadata passed to the <code class="docutils literal notranslate"><span class="pre">score</span></code> method.</p></td>
</tr>
</tbody>
</table>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.correct_covariance">
<span class="sig-name descname"><span class="pre">correct_covariance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_robust_covariance.py#L778"><span class="viewcode-link"><span class="pre">[source]</span></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="#r491365aeaa84-rvd" id="id4">[RVD]</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>data</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><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>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>covariance_corrected</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Corrected robust covariance estimate.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r491365aeaa84-rvd" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id4">RVD</a><span class="fn-bracket">]</span></span>
<p>A Fast Algorithm for the Minimum Covariance
Determinant Estimator, 1999, American Statistical Association
and the American Society for Quality, TECHNOMETRICS</p>
</div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.error_norm">
<span class="sig-name descname"><span class="pre">error_norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">comp_cov</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'frobenius'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scaling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">squared</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_empirical_covariance.py#L282"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.error_norm" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the Mean Squared Error between two covariance estimators.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>comp_cov</strong><span class="classifier">array-like of shape (n_features, n_features)</span></dt><dd><p>The covariance to compare with.</p>
</dd>
<dt><strong>norm</strong><span class="classifier">{“frobenius”, “spectral”}, default=”frobenius”</span></dt><dd><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 notranslate"><span class="pre">(comp_cov</span> <span class="pre">-</span> <span class="pre">self.covariance_)</span></code>.</p>
</dd>
<dt><strong>scaling</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True (default), the squared error norm is divided by n_features.
If False, the squared error norm is not rescaled.</p>
</dd>
<dt><strong>squared</strong><span class="classifier">bool, default=True</span></dt><dd><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>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>result</strong><span class="classifier">float</span></dt><dd><p>The Mean Squared Error (in the sense of the Frobenius norm) between
<code class="docutils literal notranslate"><span class="pre">self</span></code> and <code class="docutils literal notranslate"><span class="pre">comp_cov</span></code> covariance estimators.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.fit">
<span class="sig-name descname"><span class="pre">fit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_robust_covariance.py#L724"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit a Minimum Covariance Determinant with the FastMCD algorithm.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Training data, where <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> is the number of samples
and <code class="docutils literal notranslate"><span class="pre">n_features</span></code> is the number of features.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present for API consistency by convention.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Returns the instance itself.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.get_metadata_routing">
<span class="sig-name descname"><span class="pre">get_metadata_routing</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/utils/_metadata_requests.py#L1243"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.get_metadata_routing" title="Permalink to this definition">¶</a></dt>
<dd><p>Get metadata routing of this object.</p>
<p>Please check <a class="reference internal" href="../../metadata_routing.html#metadata-routing"><span class="std std-ref">User Guide</span></a> on how the routing
mechanism works.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>routing</strong><span class="classifier">MetadataRequest</span></dt><dd><p>A <a class="reference internal" href="sklearn.utils.metadata_routing.MetadataRequest.html#sklearn.utils.metadata_routing.MetadataRequest" title="sklearn.utils.metadata_routing.MetadataRequest"><code class="xref py py-class docutils literal notranslate"><span class="pre">MetadataRequest</span></code></a> encapsulating
routing information.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.get_params">
<span class="sig-name descname"><span class="pre">get_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">deep</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/base.py#L178"><span class="viewcode-link"><span class="pre">[source]</span></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>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">dict</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.get_precision">
<span class="sig-name descname"><span class="pre">get_precision</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_empirical_covariance.py#L209"><span class="viewcode-link"><span class="pre">[source]</span></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>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>precision_</strong><span class="classifier">array-like of shape (n_features, n_features)</span></dt><dd><p>The precision matrix associated to the current covariance object.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.mahalanobis">
<span class="sig-name descname"><span class="pre">mahalanobis</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_empirical_covariance.py#L333"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.mahalanobis" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the squared Mahalanobis distances of given observations.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><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>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>dist</strong><span class="classifier">ndarray of shape (n_samples,)</span></dt><dd><p>Squared Mahalanobis distances of the observations.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.reweight_covariance">
<span class="sig-name descname"><span class="pre">reweight_covariance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_robust_covariance.py#L818"><span class="viewcode-link"><span class="pre">[source]</span></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) described
in <a class="reference internal" href="#r9465bad4668c-rvdriessen" id="id6">[RVDriessen]</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>data</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><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>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>location_reweighted</strong><span class="classifier">ndarray of shape (n_features,)</span></dt><dd><p>Re-weighted robust location estimate.</p>
</dd>
<dt><strong>covariance_reweighted</strong><span class="classifier">ndarray of shape (n_features, n_features)</span></dt><dd><p>Re-weighted robust covariance estimate.</p>
</dd>
<dt><strong>support_reweighted</strong><span class="classifier">ndarray of shape (n_samples,), dtype=bool</span></dt><dd><p>A mask of the observations that have been used to compute
the re-weighted robust location and covariance estimates.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r9465bad4668c-rvdriessen" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id6">RVDriessen</a><span class="fn-bracket">]</span></span>
<p>A Fast Algorithm for the Minimum Covariance
Determinant Estimator, 1999, American Statistical Association
and the American Society for Quality, TECHNOMETRICS</p>
</div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.score">
<span class="sig-name descname"><span class="pre">score</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X_test</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/covariance/_empirical_covariance.py#L251"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the log-likelihood of <code class="docutils literal notranslate"><span class="pre">X_test</span></code> under the estimated Gaussian model.</p>
<p>The Gaussian model is defined by its mean and covariance matrix which are
represented respectively by <code class="docutils literal notranslate"><span class="pre">self.location_</span></code> and <code class="docutils literal notranslate"><span class="pre">self.covariance_</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X_test</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Test data of which we compute the likelihood, where <code class="docutils literal notranslate"><span class="pre">n_samples</span></code> is
the number of samples and <code class="docutils literal notranslate"><span class="pre">n_features</span></code> is the number of features.
<code class="docutils literal notranslate"><span class="pre">X_test</span></code> is assumed to be drawn from the same distribution than
the data used in fit (including centering).</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present for API consistency by convention.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>res</strong><span class="classifier">float</span></dt><dd><p>The log-likelihood of <code class="docutils literal notranslate"><span class="pre">X_test</span></code> with <code class="docutils literal notranslate"><span class="pre">self.location_</span></code> and <code class="docutils literal notranslate"><span class="pre">self.covariance_</span></code>
as estimators of the Gaussian model mean and covariance matrix respectively.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.set_params">
<span class="sig-name descname"><span class="pre">set_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">params</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/base.py#L202"><span class="viewcode-link"><span class="pre">[source]</span></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 <a class="reference internal" href="sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline"><code class="xref py py-class docutils literal notranslate"><span class="pre">Pipeline</span></code></a>). The latter have
parameters of the form <code class="docutils literal notranslate"><span class="pre"><component>__<parameter></span></code> so that it’s
possible to update each component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">estimator instance</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.covariance.MinCovDet.set_score_request">
<span class="sig-name descname"><span class="pre">set_score_request</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">X_test</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.12)"><span class="pre">Union</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><span class="pre">bool</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.12)"><span class="pre">None</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.12)"><span class="pre">str</span></a><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">'$UNCHANGED$'</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference internal" href="#sklearn.covariance.MinCovDet" title="sklearn.covariance._robust_covariance.MinCovDet"><span class="pre">MinCovDet</span></a></span></span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/3f89022fa/sklearn/utils/_metadata_requests.py#L1033"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.covariance.MinCovDet.set_score_request" title="Permalink to this definition">¶</a></dt>
<dd><p>Request metadata passed to the <code class="docutils literal notranslate"><span class="pre">score</span></code> method.</p>
<p>Note that this method is only relevant if
<code class="docutils literal notranslate"><span class="pre">enable_metadata_routing=True</span></code> (see <a class="reference internal" href="sklearn.set_config.html#sklearn.set_config" title="sklearn.set_config"><code class="xref py py-func docutils literal notranslate"><span class="pre">sklearn.set_config</span></code></a>).
Please see <a class="reference internal" href="../../metadata_routing.html#metadata-routing"><span class="std std-ref">User Guide</span></a> on how the routing
mechanism works.</p>
<p>The options for each parameter are:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">True</span></code>: metadata is requested, and passed to <code class="docutils literal notranslate"><span class="pre">score</span></code> if provided. The request is ignored if metadata is not provided.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">False</span></code>: metadata is not requested and the meta-estimator will not pass it to <code class="docutils literal notranslate"><span class="pre">score</span></code>.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">None</span></code>: metadata is not requested, and the meta-estimator will raise an error if the user provides it.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">str</span></code>: metadata should be passed to the meta-estimator with this given alias instead of the original name.</p></li>
</ul>
<p>The default (<code class="docutils literal notranslate"><span class="pre">sklearn.utils.metadata_routing.UNCHANGED</span></code>) retains the
existing request. This allows you to change the request for some
parameters and not others.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.3.</span></p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>This method is only relevant if this estimator is used as a
sub-estimator of a meta-estimator, e.g. used inside a
<a class="reference internal" href="sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline" title="sklearn.pipeline.Pipeline"><code class="xref py py-class docutils literal notranslate"><span class="pre">Pipeline</span></code></a>. Otherwise it has no effect.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X_test</strong><span class="classifier">str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED</span></dt><dd><p>Metadata routing for <code class="docutils literal notranslate"><span class="pre">X_test</span></code> parameter in <code class="docutils literal notranslate"><span class="pre">score</span></code>.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>The updated object.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</dd></dl>
<section id="examples-using-sklearn-covariance-mincovdet">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.covariance.MinCovDet</span></code><a class="headerlink" href="#examples-using-sklearn-covariance-mincovdet" title="Permalink to this heading">¶</a></h2>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example shows covariance estimation with Mahalanobis distances on Gaussian distributed dat..."><img alt="" src="../../_images/sphx_glr_plot_mahalanobis_distances_thumb.png" />
<p><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></p>
<div class="sphx-glr-thumbnail-title">Robust covariance estimation and Mahalanobis distances relevance</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="The usual covariance maximum likelihood estimate is very sensitive to the presence of outliers ..."><img alt="" src="../../_images/sphx_glr_plot_robust_vs_empirical_covariance_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/covariance/plot_robust_vs_empirical_covariance.html#sphx-glr-auto-examples-covariance-plot-robust-vs-empirical-covariance-py"><span class="std std-ref">Robust vs Empirical covariance estimate</span></a></p>
<div class="sphx-glr-thumbnail-title">Robust vs Empirical covariance estimate</div>
</div></div><div class="clearer"></div></section>
</section>
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