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<li><a class="reference internal" href="#">Manifold Learning methods on a severed sphere</a></li>
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<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-manifold-plot-manifold-sphere-py"><span class="std std-ref">here</span></a>
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<section class="sphx-glr-example-title" id="manifold-learning-methods-on-a-severed-sphere">
<span id="sphx-glr-auto-examples-manifold-plot-manifold-sphere-py"></span><h1>Manifold Learning methods on a severed sphere<a class="headerlink" href="#manifold-learning-methods-on-a-severed-sphere" title="Permalink to this heading">¶</a></h1>
<p>An application of the different <a class="reference internal" href="../../modules/manifold.html#manifold"><span class="std std-ref">Manifold learning</span></a> techniques
on a spherical data-set. Here one can see the use of
dimensionality reduction in order to gain some intuition
regarding the manifold learning methods. Regarding the dataset,
the poles are cut from the sphere, as well as a thin slice down its
side. This enables the manifold learning techniques to
‘spread it open’ whilst projecting it onto two dimensions.</p>
<p>For a similar example, where the methods are applied to the
S-curve dataset, see <a class="reference internal" href="plot_compare_methods.html#sphx-glr-auto-examples-manifold-plot-compare-methods-py"><span class="std std-ref">Comparison of Manifold Learning methods</span></a></p>
<p>Note that the purpose of the <a class="reference internal" href="../../modules/manifold.html#multidimensional-scaling"><span class="std std-ref">MDS</span></a> 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. Here the manifold problem matches fairly
that of representing a flat map of the Earth, as with
<a class="reference external" href="https://en.wikipedia.org/wiki/Map_projection">map projection</a></p>
<img src="../../_images/sphx_glr_plot_manifold_sphere_001.png" srcset="../../_images/sphx_glr_plot_manifold_sphere_001.png" alt="Manifold Learning with 1000 points, 10 neighbors, LLE (0.058 sec), LTSA (0.092 sec), Hessian LLE (0.15 sec), Modified LLE (0.11 sec), Isomap (0.2 sec), MDS (0.6 sec), Spectral Embedding (0.044 sec), t-SNE (3.8 sec)" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>standard: 0.058 sec
ltsa: 0.092 sec
hessian: 0.15 sec
modified: 0.11 sec
ISO: 0.2 sec
MDS: 0.6 sec
Spectral Embedding: 0.044 sec
t-SNE: 3.8 sec
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Jaques Grobler <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.ticker</span> <span class="kn">import</span> <a href="https://matplotlib.org/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.utils.check_random_state.html#sklearn.utils.check_random_state" title="sklearn.utils.check_random_state" class="sphx-glr-backref-module-sklearn-utils sphx-glr-backref-type-py-function"><span class="n">check_random_state</span></a>
<span class="c1"># Unused but required import for doing 3d projections with matplotlib < 3.2</span>
<span class="kn">import</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="c1"># noqa: F401</span>
<span class="c1"># Variables for manifold learning.</span>
<span class="n">n_neighbors</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="c1"># Create our sphere.</span>
<span class="n">random_state</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.utils.check_random_state.html#sklearn.utils.check_random_state" title="sklearn.utils.check_random_state" class="sphx-glr-backref-module-sklearn-utils sphx-glr-backref-type-py-function"><span class="n">check_random_state</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">random_state</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n_samples</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/constants.html#numpy.pi" title="numpy.pi" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a> <span class="o">-</span> <span class="mf">0.55</span><span class="p">)</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">random_state</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n_samples</span><span class="p">)</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/constants.html#numpy.pi" title="numpy.pi" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a>
<span class="c1"># Sever the poles from the sphere.</span>
<span class="n">indices</span> <span class="o">=</span> <span class="p">(</span><span class="n">t</span> <span class="o"><</span> <span class="p">(</span><a href="https://numpy.org/doc/stable/reference/constants.html#numpy.pi" title="numpy.pi" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a> <span class="o">-</span> <span class="p">(</span><a href="https://numpy.org/doc/stable/reference/constants.html#numpy.pi" title="numpy.pi" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a> <span class="o">/</span> <span class="mi">8</span><span class="p">)))</span> <span class="o">&</span> <span class="p">(</span><span class="n">t</span> <span class="o">></span> <span class="p">((</span><a href="https://numpy.org/doc/stable/reference/constants.html#numpy.pi" title="numpy.pi" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a> <span class="o">/</span> <span class="mi">8</span><span class="p">)))</span>
<span class="n">colors</span> <span class="o">=</span> <span class="n">p</span><span class="p">[</span><span class="n">indices</span><span class="p">]</span>
<span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.sin.html#numpy.sin" title="numpy.sin" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">indices</span><span class="p">])</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.cos.html#numpy.cos" title="numpy.cos" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">cos</span></a><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="n">indices</span><span class="p">]),</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.sin.html#numpy.sin" title="numpy.sin" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">indices</span><span class="p">])</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.sin.html#numpy.sin" title="numpy.sin" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sin</span></a><span class="p">(</span><span class="n">p</span><span class="p">[</span><span class="n">indices</span><span class="p">]),</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.cos.html#numpy.cos" title="numpy.cos" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">cos</span></a><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">indices</span><span class="p">]),</span>
<span class="p">)</span>
<span class="c1"># Plot our dataset.</span>
<span class="n">fig</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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/stable/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="matplotlib.pyplot.suptitle" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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="s2">"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="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="n">p</span><span class="p">[</span><span class="n">indices</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">rainbow</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">40</span><span class="p">,</span> <span class="o">-</span><span class="mi">10</span><span class="p">)</span>
<span class="n">sphere_data</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
<span class="c1"># Perform Locally Linear Embedding Manifold learning</span>
<span class="n">methods</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"standard"</span><span class="p">,</span> <span class="s2">"ltsa"</span><span class="p">,</span> <span class="s2">"hessian"</span><span class="p">,</span> <span class="s2">"modified"</span><span class="p">]</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"LLE"</span><span class="p">,</span> <span class="s2">"LTSA"</span><span class="p">,</span> <span class="s2">"Hessian LLE"</span><span class="p">,</span> <span class="s2">"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> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">trans_data</span> <span class="o">=</span> <span class="p">(</span>
<a href="../../modules/generated/sklearn.manifold.LocallyLinearEmbedding.html#sklearn.manifold.LocallyLinearEmbedding" title="sklearn.manifold.LocallyLinearEmbedding" class="sphx-glr-backref-module-sklearn-manifold sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="o">=</span><span class="n">n_neighbors</span><span class="p">,</span> <span class="n">n_components</span><span class="o">=</span><span class="mi">2</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">sphere_data</span><span class="p">)</span>
<span class="o">.</span><span class="n">T</span>
<span class="p">)</span>
<span class="n">t1</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="nb">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/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">trans_data</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">trans_data</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">colors</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">rainbow</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<span class="c1"># Perform Isomap Manifold learning.</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">trans_data</span> <span class="o">=</span> <span class="p">(</span>
<a href="../../modules/generated/sklearn.manifold.Isomap.html#sklearn.manifold.Isomap" title="sklearn.manifold.Isomap" class="sphx-glr-backref-module-sklearn-manifold sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="o">=</span><span class="n">n_neighbors</span><span class="p">,</span> <span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">sphere_data</span><span class="p">)</span>
<span class="o">.</span><span class="n">T</span>
<span class="p">)</span>
<span class="n">t1</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="nb">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="s2">"ISO"</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/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">trans_data</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">trans_data</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">colors</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">rainbow</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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="s2">"Isomap"</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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<span class="c1"># Perform Multi-dimensional scaling.</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><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="sklearn.manifold.MDS" class="sphx-glr-backref-module-sklearn-manifold sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">manifold</span><span class="o">.</span><span class="n">MDS</span></a><span class="p">(</span><span class="mi">2</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">normalized_stress</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">)</span>
<span class="n">trans_data</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">sphere_data</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="n">t1</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="nb">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/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">trans_data</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">trans_data</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">colors</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">rainbow</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<span class="c1"># Perform Spectral Embedding.</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><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="sklearn.manifold.SpectralEmbedding" class="sphx-glr-backref-module-sklearn-manifold sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="mi">2</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">trans_data</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">sphere_data</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="n">t1</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Spectral Embedding: </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/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">trans_data</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">trans_data</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">colors</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">rainbow</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Spectral Embedding (</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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<span class="c1"># Perform t-distributed stochastic neighbor embedding.</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><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="sklearn.manifold.TSNE" class="sphx-glr-backref-module-sklearn-manifold sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="mi">2</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">trans_data</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">sphere_data</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="n">t1</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="nb">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/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">trans_data</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">trans_data</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">colors</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">rainbow</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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/stable/api/ticker_api.html#matplotlib.ticker.NullFormatter" title="matplotlib.ticker.NullFormatter" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">NullFormatter</span></a><span class="p">())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"tight"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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