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<section id="polynomialfeatures">
<h1>PolynomialFeatures<a class="headerlink" href="#polynomialfeatures" title="Link to this heading">#</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="sklearn.preprocessing.PolynomialFeatures">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">sklearn.preprocessing.</span></span><span class="sig-name descname"><span class="pre">PolynomialFeatures</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">degree</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">interaction_only</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">include_bias</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">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'C'</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/4ee3afa55/sklearn/preprocessing/_polynomial.py#L103"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures" title="Link to this definition">#</a></dt>
<dd><p>Generate polynomial and interaction features.</p>
<p>Generate a new feature matrix consisting of all polynomial combinations
of the features with degree less than or equal to the specified degree.
For example, if an input sample is two dimensional and of the form
[a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2].</p>
<p>Read more in the <a class="reference internal" href="../preprocessing.html#polynomial-features"><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>
<dt><strong>degree</strong><span class="classifier">int or tuple (min_degree, max_degree), default=2</span></dt><dd><p>If a single int is given, it specifies the maximal degree of the
polynomial features. If a tuple <code class="docutils literal notranslate"><span class="pre">(min_degree,</span> <span class="pre">max_degree)</span></code> is passed,
then <code class="docutils literal notranslate"><span class="pre">min_degree</span></code> is the minimum and <code class="docutils literal notranslate"><span class="pre">max_degree</span></code> is the maximum
polynomial degree of the generated features. Note that <code class="docutils literal notranslate"><span class="pre">min_degree=0</span></code>
and <code class="docutils literal notranslate"><span class="pre">min_degree=1</span></code> are equivalent as outputting the degree zero term is
determined by <code class="docutils literal notranslate"><span class="pre">include_bias</span></code>.</p>
</dd>
<dt><strong>interaction_only</strong><span class="classifier">bool, default=False</span></dt><dd><p>If <code class="docutils literal notranslate"><span class="pre">True</span></code>, only interaction features are produced: features that are
products of at most <code class="docutils literal notranslate"><span class="pre">degree</span></code> <em>distinct</em> input features, i.e. terms with
power of 2 or higher of the same input feature are excluded:</p>
<ul class="simple">
<li><p>included: <code class="docutils literal notranslate"><span class="pre">x[0]</span></code>, <code class="docutils literal notranslate"><span class="pre">x[1]</span></code>, <code class="docutils literal notranslate"><span class="pre">x[0]</span> <span class="pre">*</span> <span class="pre">x[1]</span></code>, etc.</p></li>
<li><p>excluded: <code class="docutils literal notranslate"><span class="pre">x[0]</span> <span class="pre">**</span> <span class="pre">2</span></code>, <code class="docutils literal notranslate"><span class="pre">x[0]</span> <span class="pre">**</span> <span class="pre">2</span> <span class="pre">*</span> <span class="pre">x[1]</span></code>, etc.</p></li>
</ul>
</dd>
<dt><strong>include_bias</strong><span class="classifier">bool, default=True</span></dt><dd><p>If <code class="docutils literal notranslate"><span class="pre">True</span></code> (default), then include a bias column, the feature in which
all polynomial powers are zero (i.e. a column of ones - acts as an
intercept term in a linear model).</p>
</dd>
<dt><strong>order</strong><span class="classifier">{‘C’, ‘F’}, default=’C’</span></dt><dd><p>Order of output array in the dense case. <code class="docutils literal notranslate"><span class="pre">'F'</span></code> order is faster to
compute, but may slow down subsequent estimators.</p>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 0.21.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes<span class="colon">:</span></dt>
<dd class="field-even"><dl>
<dt><a class="reference internal" href="#sklearn.preprocessing.PolynomialFeatures.powers_" title="sklearn.preprocessing.PolynomialFeatures.powers_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">powers_</span></code></a><span class="classifier">ndarray of shape (<code class="docutils literal notranslate"><span class="pre">n_output_features_</span></code>, <code class="docutils literal notranslate"><span class="pre">n_features_in_</span></code>)</span></dt><dd><p>Exponent for each of the inputs in the output.</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">Added 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">Added in version 1.0.</span></p>
</div>
</dd>
<dt><strong>n_output_features_</strong><span class="classifier">int</span></dt><dd><p>The total number of polynomial output features. The number of output
features is computed by iterating over all suitably sized combinations
of input features.</p>
</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.preprocessing.SplineTransformer.html#sklearn.preprocessing.SplineTransformer" title="sklearn.preprocessing.SplineTransformer"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SplineTransformer</span></code></a></dt><dd><p>Transformer that generates univariate B-spline bases for features.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>Be aware that the number of features in the output array scales
polynomially in the number of features of the input array, and
exponentially in the degree. High degrees can cause overfitting.</p>
<p>See <a class="reference internal" href="../../auto_examples/linear_model/plot_polynomial_interpolation.html#sphx-glr-auto-examples-linear-model-plot-polynomial-interpolation-py"><span class="std std-ref">examples/linear_model/plot_polynomial_interpolation.py</span></a></p>
<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.preprocessing</span> <span class="kn">import</span> <span class="n">PolynomialFeatures</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">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">X</span>
<span class="go">array([[0, 1],</span>
<span class="go"> [2, 3],</span>
<span class="go"> [4, 5]])</span>
<span class="gp">>>> </span><span class="n">poly</span> <span class="o">=</span> <span class="n">PolynomialFeatures</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">poly</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[ 1., 0., 1., 0., 0., 1.],</span>
<span class="go"> [ 1., 2., 3., 4., 6., 9.],</span>
<span class="go"> [ 1., 4., 5., 16., 20., 25.]])</span>
<span class="gp">>>> </span><span class="n">poly</span> <span class="o">=</span> <span class="n">PolynomialFeatures</span><span class="p">(</span><span class="n">interaction_only</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">poly</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="go">array([[ 1., 0., 1., 0.],</span>
<span class="go"> [ 1., 2., 3., 6.],</span>
<span class="go"> [ 1., 4., 5., 20.]])</span>
</pre></div>
</div>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.preprocessing.PolynomialFeatures.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/4ee3afa55/sklearn/preprocessing/_polynomial.py#L309"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.fit" title="Link to this definition">#</a></dt>
<dd><p>Compute number of output features.</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, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>The data.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd><p>Not used, present here 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>Fitted transformer.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.preprocessing.PolynomialFeatures.fit_transform">
<span class="sig-name descname"><span class="pre">fit_transform</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>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">fit_params</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/4ee3afa55/sklearn/base.py#L766"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.fit_transform" title="Link to this definition">#</a></dt>
<dd><p>Fit to data, then transform it.</p>
<p>Fits transformer to <code class="docutils literal notranslate"><span class="pre">X</span></code> and <code class="docutils literal notranslate"><span class="pre">y</span></code> with optional parameters <code class="docutils literal notranslate"><span class="pre">fit_params</span></code>
and returns a transformed version of <code class="docutils literal notranslate"><span class="pre">X</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</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Input samples.</p>
</dd>
<dt><strong>y</strong><span class="classifier">array-like of shape (n_samples,) or (n_samples, n_outputs), default=None</span></dt><dd><p>Target values (None for unsupervised transformations).</p>
</dd>
<dt><strong>**fit_params</strong><span class="classifier">dict</span></dt><dd><p>Additional fit parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X_new</strong><span class="classifier">ndarray array of shape (n_samples, n_features_new)</span></dt><dd><p>Transformed array.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.preprocessing.PolynomialFeatures.get_feature_names_out">
<span class="sig-name descname"><span class="pre">get_feature_names_out</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">input_features</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/4ee3afa55/sklearn/preprocessing/_polynomial.py#L270"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.get_feature_names_out" title="Link to this definition">#</a></dt>
<dd><p>Get output feature names for transformation.</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>input_features</strong><span class="classifier">array-like of str or None, default=None</span></dt><dd><p>Input features.</p>
<ul class="simple">
<li><p>If <code class="docutils literal notranslate"><span class="pre">input_features</span> <span class="pre">is</span> <span class="pre">None</span></code>, then <code class="docutils literal notranslate"><span class="pre">feature_names_in_</span></code> is
used as feature names in. If <code class="docutils literal notranslate"><span class="pre">feature_names_in_</span></code> is not defined,
then the following input feature names are generated:
<code class="docutils literal notranslate"><span class="pre">["x0",</span> <span class="pre">"x1",</span> <span class="pre">...,</span> <span class="pre">"x(n_features_in_</span> <span class="pre">-</span> <span class="pre">1)"]</span></code>.</p></li>
<li><p>If <code class="docutils literal notranslate"><span class="pre">input_features</span></code> is an array-like, then <code class="docutils literal notranslate"><span class="pre">input_features</span></code> must
match <code class="docutils literal notranslate"><span class="pre">feature_names_in_</span></code> if <code class="docutils literal notranslate"><span class="pre">feature_names_in_</span></code> is defined.</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>feature_names_out</strong><span class="classifier">ndarray of str objects</span></dt><dd><p>Transformed feature names.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.preprocessing.PolynomialFeatures.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/4ee3afa55/sklearn/utils/_metadata_requests.py#L1497"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.get_metadata_routing" title="Link 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.preprocessing.PolynomialFeatures.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/4ee3afa55/sklearn/base.py#L221"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.get_params" title="Link 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 property">
<dt class="sig sig-object py" id="sklearn.preprocessing.PolynomialFeatures.powers_">
<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">powers_</span></span><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.powers_" title="Link to this definition">#</a></dt>
<dd><p>Exponent for each of the inputs in the output.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="sklearn.preprocessing.PolynomialFeatures.set_output">
<span class="sig-name descname"><span class="pre">set_output</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">transform</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/4ee3afa55/sklearn/utils/_set_output.py#L392"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.set_output" title="Link to this definition">#</a></dt>
<dd><p>Set output container.</p>
<p>See <a class="reference internal" href="../../auto_examples/miscellaneous/plot_set_output.html#sphx-glr-auto-examples-miscellaneous-plot-set-output-py"><span class="std std-ref">Introducing the set_output API</span></a>
for an example on how to use the API.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl>
<dt><strong>transform</strong><span class="classifier">{“default”, “pandas”, “polars”}, default=None</span></dt><dd><p>Configure output of <code class="docutils literal notranslate"><span class="pre">transform</span></code> and <code class="docutils literal notranslate"><span class="pre">fit_transform</span></code>.</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">"default"</span></code>: Default output format of a transformer</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"pandas"</span></code>: DataFrame output</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">"polars"</span></code>: Polars output</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">None</span></code>: Transform configuration is unchanged</p></li>
</ul>
<div class="versionadded">
<p><span class="versionmodified added">Added in version 1.4: </span><code class="docutils literal notranslate"><span class="pre">"polars"</span></code> option was added.</p>
</div>
</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.preprocessing.PolynomialFeatures.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/4ee3afa55/sklearn/base.py#L245"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.set_params" title="Link 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.preprocessing.PolynomialFeatures.transform">
<span class="sig-name descname"><span class="pre">transform</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/4ee3afa55/sklearn/preprocessing/_polynomial.py#L406"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sklearn.preprocessing.PolynomialFeatures.transform" title="Link to this definition">#</a></dt>
<dd><p>Transform data to polynomial features.</p>
<dl class="field-list">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl>
<dt><strong>X</strong><span class="classifier">{array-like, sparse matrix} of shape (n_samples, n_features)</span></dt><dd><p>The data to transform, row by row.</p>
<p>Prefer CSR over CSC for sparse input (for speed), but CSC is
required if the degree is 4 or higher. If the degree is less than
4 and the input format is CSC, it will be converted to CSR, have
its polynomial features generated, then converted back to CSC.</p>
<p>If the degree is 2 or 3, the method described in “Leveraging
Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices
Using K-Simplex Numbers” by Andrew Nystrom and John Hughes is
used, which is much faster than the method used on CSC input. For
this reason, a CSC input will be converted to CSR, and the output
will be converted back to CSC prior to being returned, hence the
preference of CSR.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>XP</strong><span class="classifier">{ndarray, sparse matrix} of shape (n_samples, NP)</span></dt><dd><p>The matrix of features, where <code class="docutils literal notranslate"><span class="pre">NP</span></code> is the number of polynomial
features generated from the combination of inputs. If a sparse
matrix is provided, it will be converted into a sparse
<code class="docutils literal notranslate"><span class="pre">csr_matrix</span></code>.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
</dd></dl>
<section id="gallery-examples">
<h2>Gallery examples<a class="headerlink" href="#gallery-examples" title="Link to this heading">#</a></h2>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="We are pleased to announce the release of scikit-learn 0.24! Many bug fixes and improvements were added, as well as some new key features. We detail below a few of the major features of this release. For an exhaustive list of all the changes, please refer to the release notes <release_notes_0_24>."><img alt="" src="../../_images/sphx_glr_plot_release_highlights_0_24_0_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/release_highlights/plot_release_highlights_0_24_0.html#sphx-glr-auto-examples-release-highlights-plot-release-highlights-0-24-0-py"><span class="std std-ref">Release Highlights for scikit-learn 0.24</span></a></p>
<div class="sphx-glr-thumbnail-title">Release Highlights for scikit-learn 0.24</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This notebook introduces different strategies to leverage time-related features for a bike sharing demand regression task that is highly dependent on business cycles (days, weeks, months) and yearly season cycles."><img alt="" src="../../_images/sphx_glr_plot_cyclical_feature_engineering_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/applications/plot_cyclical_feature_engineering.html#sphx-glr-auto-examples-applications-plot-cyclical-feature-engineering-py"><span class="std std-ref">Time-related feature engineering</span></a></p>
<div class="sphx-glr-thumbnail-title">Time-related feature engineering</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example compares two different bayesian regressors:"><img alt="" src="../../_images/sphx_glr_plot_ard_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/linear_model/plot_ard.html#sphx-glr-auto-examples-linear-model-plot-ard-py"><span class="std std-ref">Comparing Linear Bayesian Regressors</span></a></p>
<div class="sphx-glr-thumbnail-title">Comparing Linear Bayesian Regressors</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the use of log-linear Poisson regression on the French Motor Third-Party Liability Claims dataset from [1]_ and compares it with a linear model fitted with the usual least squared error and a non-linear GBRT model fitted with the Poisson loss (and a log-link)."><img alt="" src="../../_images/sphx_glr_plot_poisson_regression_non_normal_loss_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/linear_model/plot_poisson_regression_non_normal_loss.html#sphx-glr-auto-examples-linear-model-plot-poisson-regression-non-normal-loss-py"><span class="std std-ref">Poisson regression and non-normal loss</span></a></p>
<div class="sphx-glr-thumbnail-title">Poisson regression and non-normal loss</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to approximate a function with polynomials up to degree degree by using ridge regression. We show two different ways given n_samples of 1d points x_i:"><img alt="" src="../../_images/sphx_glr_plot_polynomial_interpolation_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/linear_model/plot_polynomial_interpolation.html#sphx-glr-auto-examples-linear-model-plot-polynomial-interpolation-py"><span class="std std-ref">Polynomial and Spline interpolation</span></a></p>
<div class="sphx-glr-thumbnail-title">Polynomial and Spline interpolation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Here a sine function is fit with a polynomial of order 3, for values close to zero."><img alt="" src="../../_images/sphx_glr_plot_robust_fit_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/linear_model/plot_robust_fit.html#sphx-glr-auto-examples-linear-model-plot-robust-fit-py"><span class="std std-ref">Robust linear estimator fitting</span></a></p>
<div class="sphx-glr-thumbnail-title">Robust linear estimator fitting</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="The default configuration for displaying a pipeline in a Jupyter Notebook is 'diagram' where set_config(display='diagram'). To deactivate HTML representation, use set_config(display='text')."><img alt="" src="../../_images/sphx_glr_plot_pipeline_display_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/miscellaneous/plot_pipeline_display.html#sphx-glr-auto-examples-miscellaneous-plot-pipeline-display-py"><span class="std std-ref">Displaying Pipelines</span></a></p>
<div class="sphx-glr-thumbnail-title">Displaying Pipelines</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the problems of underfitting and overfitting and how we can use linear regression with polynomial features to approximate nonlinear functions. The plot shows the function that we want to approximate, which is a part of the cosine function. In addition, the samples from the real function and the approximations of different models are displayed. The models have polynomial features of different degrees. We can see that a linear function (polynomial with degree 1) is not sufficient to fit the training samples. This is called underfitting. A polynomial of degree 4 approximates the true function almost perfectly. However, for higher degrees the model will overfit the training data, i.e. it learns the noise of the training data. We evaluate quantitatively overfitting / underfitting by using cross-validation. We calculate the mean squared error (MSE) on the validation set, the higher, the less likely the model generalizes correctly from the training data."><img alt="" src="../../_images/sphx_glr_plot_underfitting_overfitting_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/model_selection/plot_underfitting_overfitting.html#sphx-glr-auto-examples-model-selection-plot-underfitting-overfitting-py"><span class="std std-ref">Underfitting vs. Overfitting</span></a></p>
<div class="sphx-glr-thumbnail-title">Underfitting vs. Overfitting</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="SVCs aim to find a hyperplane that effectively separates the classes in their training data by maximizing the margin between the outermost data points of each class. This is achieved by finding the best weight vector w that defines the decision boundary hyperplane and minimizes the sum of hinge losses for misclassified samples, as measured by the hinge_loss function. By default, regularization is applied with the parameter C=1, which allows for a certain degree of misclassification tolerance."><img alt="" src="../../_images/sphx_glr_plot_svm_kernels_thumb.png" />
<p><a class="reference internal" href="../../auto_examples/svm/plot_svm_kernels.html#sphx-glr-auto-examples-svm-plot-svm-kernels-py"><span class="std std-ref">Plot classification boundaries with different SVM Kernels</span></a></p>
<div class="sphx-glr-thumbnail-title">Plot classification boundaries with different SVM Kernels</div>
</div></div></section>
</section>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures"><code class="docutils literal notranslate"><span class="pre">PolynomialFeatures</span></code></a><ul class="nav section-nav flex-column visible">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.fit"><code class="docutils literal notranslate"><span class="pre">fit</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.fit_transform"><code class="docutils literal notranslate"><span class="pre">fit_transform</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.get_feature_names_out"><code class="docutils literal notranslate"><span class="pre">get_feature_names_out</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.get_metadata_routing"><code class="docutils literal notranslate"><span class="pre">get_metadata_routing</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.get_params"><code class="docutils literal notranslate"><span class="pre">get_params</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.powers_"><code class="docutils literal notranslate"><span class="pre">powers_</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.set_output"><code class="docutils literal notranslate"><span class="pre">set_output</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.set_params"><code class="docutils literal notranslate"><span class="pre">set_params</span></code></a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#sklearn.preprocessing.PolynomialFeatures.transform"><code class="docutils literal notranslate"><span class="pre">transform</span></code></a></li>
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