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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.datasets</span></code>.make_low_rank_matrix</a></li>
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<div class="section" id="sklearn-datasets-make-low-rank-matrix">
<h1><a class="reference internal" href="../classes.html#module-sklearn.datasets" title="sklearn.datasets"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.datasets</span></code></a>.make_low_rank_matrix<a class="headerlink" href="#sklearn-datasets-make-low-rank-matrix" title="Permalink to this headline">¶</a></h1>
<dl class="py function">
<dt id="sklearn.datasets.make_low_rank_matrix">
<code class="sig-prename descclassname">sklearn.datasets.</code><code class="sig-name descname">make_low_rank_matrix</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">n_samples</span><span class="o">=</span><span class="default_value">100</span></em>, <em class="sig-param"><span class="n">n_features</span><span class="o">=</span><span class="default_value">100</span></em>, <em class="sig-param"><span class="o">*</span></em>, <em class="sig-param"><span class="n">effective_rank</span><span class="o">=</span><span class="default_value">10</span></em>, <em class="sig-param"><span class="n">tail_strength</span><span class="o">=</span><span class="default_value">0.5</span></em>, <em class="sig-param"><span class="n">random_state</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/23d876161/sklearn/datasets/_samples_generator.py#L1104"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.datasets.make_low_rank_matrix" title="Permalink to this definition">¶</a></dt>
<dd><p>Generate a mostly low rank matrix with bell-shaped singular values.</p>
<p>Most of the variance can be explained by a bell-shaped curve of width
effective_rank: the low rank part of the singular values profile is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tail_strength</span><span class="p">)</span> <span class="o">*</span> <span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span> <span class="o">*</span> <span class="p">(</span><span class="n">i</span> <span class="o">/</span> <span class="n">effective_rank</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
<p>The remaining singular values’ tail is fat, decreasing as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">tail_strength</span> <span class="o">*</span> <span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">0.1</span> <span class="o">*</span> <span class="n">i</span> <span class="o">/</span> <span class="n">effective_rank</span><span class="p">)</span><span class="o">.</span>
</pre></div>
</div>
<p>The low rank part of the profile can be considered the structured
signal part of the data while the tail can be considered the noisy
part of the data that cannot be summarized by a low number of linear
components (singular vectors).</p>
<dl class="simple">
<dt>This kind of singular profiles is often seen in practice, for instance:</dt><dd><ul class="simple">
<li><p>gray level pictures of faces</p></li>
<li><p>TF-IDF vectors of text documents crawled from the web</p></li>
</ul>
</dd>
</dl>
<p>Read more in the <a class="reference internal" href="../../datasets/sample_generators.html#sample-generators"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>n_samples</strong><span class="classifier">int, default=100</span></dt><dd><p>The number of samples.</p>
</dd>
<dt><strong>n_features</strong><span class="classifier">int, default=100</span></dt><dd><p>The number of features.</p>
</dd>
<dt><strong>effective_rank</strong><span class="classifier">int, default=10</span></dt><dd><p>The approximate number of singular vectors required to explain most of
the data by linear combinations.</p>
</dd>
<dt><strong>tail_strength</strong><span class="classifier">float, default=0.5</span></dt><dd><p>The relative importance of the fat noisy tail of the singular values
profile. The value should be between 0 and 1.</p>
</dd>
<dt><strong>random_state</strong><span class="classifier">int, RandomState instance or None, default=None</span></dt><dd><p>Determines random number generation for dataset creation. Pass an int
for reproducible output 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">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X</strong><span class="classifier">ndarray of shape (n_samples, n_features)</span></dt><dd><p>The matrix.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
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