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<p class="first admonition-title">Note</p>
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<div class="sphx-glr-example-title section" id="comparison-of-manifold-learning-methods">
<span id="sphx-glr-auto-examples-manifold-plot-compare-methods-py"></span><h1>Comparison of Manifold Learning methods<a class="headerlink" href="#comparison-of-manifold-learning-methods" title="Permalink to this headline">¶</a></h1>
<p>An illustration of dimensionality reduction on the S-curve dataset
with various manifold learning methods.</p>
<p>For a discussion and comparison of these algorithms, see the
<a class="reference internal" href="../../modules/manifold.html#manifold"><span class="std std-ref">manifold module page</span></a></p>
<p>For a similar example, where the methods are applied to a
sphere dataset, see <a class="reference internal" href="plot_manifold_sphere.html#sphx-glr-auto-examples-manifold-plot-manifold-sphere-py"><span class="std std-ref">Manifold Learning methods on a severed sphere</span></a></p>
<p>Note that the purpose of the MDS is to find a low-dimensional
representation of the data (here 2D) in which the distances respect well
the distances in the original high-dimensional space, unlike other
manifold-learning algorithms, it does not seeks an isotropic
representation of the data in the low-dimensional space.</p>
<img alt="../../_images/sphx_glr_plot_compare_methods_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_compare_methods_001.png" />
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none"><div class="highlight"><pre><span></span>standard: 0.095 sec
ltsa: 0.2 sec
hessian: 0.36 sec
modified: 0.2 sec
Isomap: 0.36 sec
MDS: 2 sec
SpectralEmbedding: 0.1 sec
t-SNE: 6 sec
</pre></div>
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<div class="line"><br /></div>
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<div class="highlight-python"><div class="highlight"><pre><span></span><span class="c1"># Author: Jake Vanderplas -- <[email protected]></span>
<span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">time</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
<span class="kn">from</span> <span class="nn">matplotlib.ticker</span> <span class="kn">import</span> <a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">manifold</span><span class="p">,</span> <span class="n">datasets</span>
<span class="c1"># Next line to silence pyflakes. This import is needed.</span>
<span class="n">Axes3D</span>
<span class="n">n_points</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="n">X</span><span class="p">,</span> <span class="n">color</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_s_curve.html#sklearn.datasets.make_s_curve" title="View documentation for sklearn.datasets.samples_generator.make_s_curve"><span class="n">datasets</span><span class="o">.</span><span class="n">samples_generator</span><span class="o">.</span><span class="n">make_s_curve</span></a><span class="p">(</span><span class="n">n_points</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="n">n_neighbors</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">n_components</span> <span class="o">=</span> <span class="mi">2</span>
<span class="n">fig</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="View documentation for matplotlib.pyplot.suptitle"><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span></a><span class="p">(</span><span class="s2">"Manifold Learning with </span><span class="si">%i</span><span class="s2"> points, </span><span class="si">%i</span><span class="s2"> neighbors"</span>
<span class="o">%</span> <span class="p">(</span><span class="mi">1000</span><span class="p">,</span> <span class="n">n_neighbors</span><span class="p">),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">14</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">251</span><span class="p">,</span> <span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Spectral</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="o">-</span><span class="mi">72</span><span class="p">)</span>
<span class="n">methods</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'standard'</span><span class="p">,</span> <span class="s1">'ltsa'</span><span class="p">,</span> <span class="s1">'hessian'</span><span class="p">,</span> <span class="s1">'modified'</span><span class="p">]</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'LLE'</span><span class="p">,</span> <span class="s1">'LTSA'</span><span class="p">,</span> <span class="s1">'Hessian LLE'</span><span class="p">,</span> <span class="s1">'Modified LLE'</span><span class="p">]</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">method</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">methods</span><span class="p">):</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">Y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.LocallyLinearEmbedding.html#sklearn.manifold.LocallyLinearEmbedding" title="View documentation for sklearn.manifold.LocallyLinearEmbedding"><span class="n">manifold</span><span class="o">.</span><span class="n">LocallyLinearEmbedding</span></a><span class="p">(</span><span class="n">n_neighbors</span><span class="p">,</span> <span class="n">n_components</span><span class="p">,</span>
<span class="n">eigen_solver</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">,</span>
<span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">)</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="n">t1</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"</span><span class="si">%s</span><span class="s2">: </span><span class="si">%.2g</span><span class="s2"> sec"</span> <span class="o">%</span> <span class="p">(</span><span class="n">methods</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">252</span> <span class="o">+</span> <span class="n">i</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">Y</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Y</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Spectral</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"</span><span class="si">%s</span><span class="s2"> (</span><span class="si">%.2g</span><span class="s2"> sec)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">labels</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">Y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.Isomap.html#sklearn.manifold.Isomap" title="View documentation for sklearn.manifold.Isomap"><span class="n">manifold</span><span class="o">.</span><span class="n">Isomap</span></a><span class="p">(</span><span class="n">n_neighbors</span><span class="p">,</span> <span class="n">n_components</span><span class="p">)</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="n">t1</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Isomap: </span><span class="si">%.2g</span><span class="s2"> sec"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">257</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">Y</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Y</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Spectral</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Isomap (</span><span class="si">%.2g</span><span class="s2"> sec)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">mds</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.MDS.html#sklearn.manifold.MDS" title="View documentation for sklearn.manifold.MDS"><span class="n">manifold</span><span class="o">.</span><span class="n">MDS</span></a><span class="p">(</span><span class="n">n_components</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">n_init</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">mds</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="n">t1</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"MDS: </span><span class="si">%.2g</span><span class="s2"> sec"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">258</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">Y</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Y</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Spectral</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"MDS (</span><span class="si">%.2g</span><span class="s2"> sec)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">se</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.SpectralEmbedding.html#sklearn.manifold.SpectralEmbedding" title="View documentation for sklearn.manifold.SpectralEmbedding"><span class="n">manifold</span><span class="o">.</span><span class="n">SpectralEmbedding</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span>
<span class="n">n_neighbors</span><span class="o">=</span><span class="n">n_neighbors</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">se</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="n">t1</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"SpectralEmbedding: </span><span class="si">%.2g</span><span class="s2"> sec"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">259</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">Y</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Y</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Spectral</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"SpectralEmbedding (</span><span class="si">%.2g</span><span class="s2"> sec)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">tsne</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.TSNE.html#sklearn.manifold.TSNE" title="View documentation for sklearn.manifold.TSNE"><span class="n">manifold</span><span class="o">.</span><span class="n">TSNE</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="n">n_components</span><span class="p">,</span> <span class="n">init</span><span class="o">=</span><span class="s1">'pca'</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="n">Y</span> <span class="o">=</span> <span class="n">tsne</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="n">t1</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"t-SNE: </span><span class="si">%.2g</span><span class="s2"> sec"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">Y</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Y</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Spectral</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"t-SNE (</span><span class="si">%.2g</span><span class="s2"> sec)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><a href="https://matplotlib.org/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="View documentation for matplotlib.ticker.NullFormatter"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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