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<div class="section" id="manifold-learning-on-handwritten-digits-locally-linear-embedding-isomap">
<span id="example-manifold-plot-lle-digits-py"></span><h1>Manifold learning on handwritten digits: Locally Linear Embedding, Isomap...<a class="headerlink" href="#manifold-learning-on-handwritten-digits-locally-linear-embedding-isomap" title="Permalink to this headline">¶</a></h1>
<p>An illustration of various embeddings on the digits dataset.</p>
<p>The RandomTreesEmbedding, from the <a class="reference internal" href="../../modules/classes.html#module-sklearn.ensemble" title="sklearn.ensemble"><code class="xref py py-mod docutils literal"><span class="pre">sklearn.ensemble</span></code></a> module, is not
technically a manifold embedding method, as it learn a high-dimensional
representation on which we apply a dimensionality reduction method.
However, it is often useful to cast a dataset into a representation in
which the classes are linearly-separable.</p>
<p>t-SNE will be initialized with the embedding that is generated by PCA in
this example, which is not the default setting. It ensures global stability
of the embedding, i.e., the embedding does not depend on random
initialization.</p>
<ul class="horizontal">
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_001.png"><img alt="../../_images/plot_lle_digits_001.png" src="../../_images/plot_lle_digits_001.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_002.png"><img alt="../../_images/plot_lle_digits_002.png" src="../../_images/plot_lle_digits_002.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_003.png"><img alt="../../_images/plot_lle_digits_003.png" src="../../_images/plot_lle_digits_003.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_004.png"><img alt="../../_images/plot_lle_digits_004.png" src="../../_images/plot_lle_digits_004.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_005.png"><img alt="../../_images/plot_lle_digits_005.png" src="../../_images/plot_lle_digits_005.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_006.png"><img alt="../../_images/plot_lle_digits_006.png" src="../../_images/plot_lle_digits_006.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_007.png"><img alt="../../_images/plot_lle_digits_007.png" src="../../_images/plot_lle_digits_007.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_008.png"><img alt="../../_images/plot_lle_digits_008.png" src="../../_images/plot_lle_digits_008.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_009.png"><img alt="../../_images/plot_lle_digits_009.png" src="../../_images/plot_lle_digits_009.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_010.png"><img alt="../../_images/plot_lle_digits_010.png" src="../../_images/plot_lle_digits_010.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_011.png"><img alt="../../_images/plot_lle_digits_011.png" src="../../_images/plot_lle_digits_011.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_012.png"><img alt="../../_images/plot_lle_digits_012.png" src="../../_images/plot_lle_digits_012.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/plot_lle_digits_013.png"><img alt="../../_images/plot_lle_digits_013.png" src="../../_images/plot_lle_digits_013.png" style="width: 376.0px; height: 282.0px;" /></a>
</li>
</ul>
<p><strong>Script output</strong>:</p>
<div class="highlight-python"><div class="highlight"><pre>Computing random projection
Computing PCA projection
Computing Linear Discriminant Analysis projection
Computing Isomap embedding
Done.
Computing LLE embedding
Done. Reconstruction error: 1.63544e-06
Computing modified LLE embedding
Done. Reconstruction error: 0.360686
Computing Hessian LLE embedding
Done. Reconstruction error: 0.212807
Computing LTSA embedding
Done. Reconstruction error: 0.212805
Computing MDS embedding
Done. Stress: 142099041.007367
Computing Totally Random Trees embedding
Computing Spectral embedding
Computing t-SNE embedding
</pre></div>
</div>
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_lle_digits.py"><code class="xref download docutils literal"><span class="pre">plot_lle_digits.py</span></code></a></p>
<div class="highlight-python"><div class="highlight"><pre>
<span class="c1"># Authors: Fabian Pedregosa <[email protected]></span>
<span class="c1"># Olivier Grisel <[email protected]></span>
<span class="c1"># Mathieu Blondel <[email protected]></span>
<span class="c1"># Gael Varoquaux</span>
<span class="c1"># License: BSD 3 clause (C) INRIA 2011</span>
<span class="k">print</span><span class="p">(</span><span class="n">__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">numpy</span> <span class="kn">as</span> <span class="nn">np</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">matplotlib</span> <span class="kn">import</span> <a href="http://matplotlib.org/api/offsetbox_api.html#matplotlib.offsetbox"><span class="n">offsetbox</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="p">(</span><span class="n">manifold</span><span class="p">,</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">decomposition</span><span class="p">,</span> <span class="n">ensemble</span><span class="p">,</span>
<span class="n">discriminant_analysis</span><span class="p">,</span> <span class="n">random_projection</span><span class="p">)</span>
<span class="n">digits</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_digits.html#sklearn.datasets.load_digits"><span class="n">datasets</span><span class="o">.</span><span class="n">load_digits</span></a><span class="p">(</span><span class="n">n_class</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">digits</span><span class="o">.</span><span class="n">data</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">digits</span><span class="o">.</span><span class="n">target</span>
<span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span>
<span class="n">n_neighbors</span> <span class="o">=</span> <span class="mi">30</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Scale and visualize the embedding vectors</span>
<span class="k">def</span> <span class="nf">plot_embedding</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</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">np</span><span class="o">.</span><span class="n">max</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="o">=</span> <span class="p">(</span><span class="n">X</span> <span class="o">-</span> <span class="n">x_min</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">x_max</span> <span class="o">-</span> <span class="n">x_min</span><span class="p">)</span>
<a href="http://matplotlib.org/api/figure_api.html#matplotlib.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
<a href="http://matplotlib.org/api/text_api.html#matplotlib.text"><span class="n">plt</span><span class="o">.</span><span class="n">text</span></a><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">i</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="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="nb">str</span><span class="p">(</span><span class="n">digits</span><span class="o">.</span><span class="n">target</span><span class="p">[</span><span class="n">i</span><span class="p">]),</span>
<span class="n">color</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">Set1</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">/</span> <span class="mf">10.</span><span class="p">),</span>
<span class="n">fontdict</span><span class="o">=</span><span class="p">{</span><span class="s1">'weight'</span><span class="p">:</span> <span class="s1">'bold'</span><span class="p">,</span> <span class="s1">'size'</span><span class="p">:</span> <span class="mi">9</span><span class="p">})</span>
<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><a href="http://matplotlib.org/api/offsetbox_api.html#matplotlib.offsetbox"><span class="n">offsetbox</span></a><span class="p">,</span> <span class="s1">'AnnotationBbox'</span><span class="p">):</span>
<span class="c1"># only print thumbnails with matplotlib > 1.0</span>
<span class="n">shown_images</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.array.html#numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">]])</span> <span class="c1"># just something big</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">digits</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
<span class="n">dist</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.sum.html#numpy.sum"><span class="n">np</span><span class="o">.</span><span class="n">sum</span></a><span class="p">((</span><span class="n">X</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">shown_images</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">dist</span><span class="p">)</span> <span class="o"><</span> <span class="mf">4e-3</span><span class="p">:</span>
<span class="c1"># don't show points that are too close</span>
<span class="k">continue</span>
<span class="n">shown_images</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.r_.html#numpy.r_"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="n">shown_images</span><span class="p">,</span> <span class="p">[</span><span class="n">X</span><span class="p">[</span><span class="n">i</span><span class="p">]]]</span>
<span class="n">imagebox</span> <span class="o">=</span> <a href="http://matplotlib.org/api/offsetbox_api.html#matplotlib.offsetbox.AnnotationBbox"><span class="n">offsetbox</span><span class="o">.</span><span class="n">AnnotationBbox</span></a><span class="p">(</span>
<a href="http://matplotlib.org/api/offsetbox_api.html#matplotlib.offsetbox.OffsetImage"><span class="n">offsetbox</span><span class="o">.</span><span class="n">OffsetImage</span></a><span class="p">(</span><span class="n">digits</span><span class="o">.</span><span class="n">images</span><span class="p">[</span><span class="n">i</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">gray_r</span><span class="p">),</span>
<span class="n">X</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">add_artist</span><span class="p">(</span><span class="n">imagebox</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.xticks"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">([]),</span> <a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.yticks"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">([])</span>
<span class="k">if</span> <span class="n">title</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Plot images of the digits</span>
<span class="n">n_img_per_row</span> <span class="o">=</span> <span class="mi">20</span>
<span class="n">img</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.6.0/reference/generated/numpy.zeros.html#numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">((</span><span class="mi">10</span> <span class="o">*</span> <span class="n">n_img_per_row</span><span class="p">,</span> <span class="mi">10</span> <span class="o">*</span> <span class="n">n_img_per_row</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_img_per_row</span><span class="p">):</span>
<span class="n">ix</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_img_per_row</span><span class="p">):</span>
<span class="n">iy</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">*</span> <span class="n">j</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">img</span><span class="p">[</span><span class="n">ix</span><span class="p">:</span><span class="n">ix</span> <span class="o">+</span> <span class="mi">8</span><span class="p">,</span> <span class="n">iy</span><span class="p">:</span><span class="n">iy</span> <span class="o">+</span> <span class="mi">8</span><span class="p">]</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">i</span> <span class="o">*</span> <span class="n">n_img_per_row</span> <span class="o">+</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">img</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">binary</span><span class="p">)</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.xticks"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">([])</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.yticks"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">([])</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'A selection from the 64-dimensional digits dataset'</span><span class="p">)</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Random 2D projection using a random unitary matrix</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing random projection"</span><span class="p">)</span>
<span class="n">rp</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.random_projection.SparseRandomProjection.html#sklearn.random_projection.SparseRandomProjection"><span class="n">random_projection</span><span class="o">.</span><span class="n">SparseRandomProjection</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">42</span><span class="p">)</span>
<span class="n">X_projected</span> <span class="o">=</span> <span class="n">rp</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">plot_embedding</span><span class="p">(</span><span class="n">X_projected</span><span class="p">,</span> <span class="s2">"Random Projection of the digits"</span><span class="p">)</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Projection on to the first 2 principal components</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing PCA projection"</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">X_pca</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD"><span class="n">decomposition</span><span class="o">.</span><span class="n">TruncatedSVD</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="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_pca</span><span class="p">,</span>
<span class="s2">"Principal Components projection of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Projection on to the first 2 linear discriminant components</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing Linear Discriminant Analysis projection"</span><span class="p">)</span>
<span class="n">X2</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="n">X2</span><span class="o">.</span><span class="n">flat</span><span class="p">[::</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mf">0.01</span> <span class="c1"># Make X invertible</span>
<span class="n">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">X_lda</span> <span class="o">=</span> <span class="n">discriminant_analysis</span><span class="o">.</span><span class="n">LinearDiscriminantAnalysis</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">X2</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_lda</span><span class="p">,</span>
<span class="s2">"Linear Discriminant projection of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Isomap projection of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing Isomap embedding"</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">X_iso</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.Isomap.html#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="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">X</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Done."</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_iso</span><span class="p">,</span>
<span class="s2">"Isomap projection of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Locally linear embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing LLE embedding"</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.LocallyLinearEmbedding.html#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="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">method</span><span class="o">=</span><span class="s1">'standard'</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">X_lle</span> <span class="o">=</span> <span class="n">clf</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="k">print</span><span class="p">(</span><span class="s2">"Done. Reconstruction error: </span><span class="si">%g</span><span class="s2">"</span> <span class="o">%</span> <span class="n">clf</span><span class="o">.</span><span class="n">reconstruction_error_</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_lle</span><span class="p">,</span>
<span class="s2">"Locally Linear Embedding of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Modified Locally linear embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing modified LLE embedding"</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.LocallyLinearEmbedding.html#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="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">method</span><span class="o">=</span><span class="s1">'modified'</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">X_mlle</span> <span class="o">=</span> <span class="n">clf</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="k">print</span><span class="p">(</span><span class="s2">"Done. Reconstruction error: </span><span class="si">%g</span><span class="s2">"</span> <span class="o">%</span> <span class="n">clf</span><span class="o">.</span><span class="n">reconstruction_error_</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_mlle</span><span class="p">,</span>
<span class="s2">"Modified Locally Linear Embedding of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># HLLE embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing Hessian LLE embedding"</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.LocallyLinearEmbedding.html#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="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">method</span><span class="o">=</span><span class="s1">'hessian'</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">X_hlle</span> <span class="o">=</span> <span class="n">clf</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="k">print</span><span class="p">(</span><span class="s2">"Done. Reconstruction error: </span><span class="si">%g</span><span class="s2">"</span> <span class="o">%</span> <span class="n">clf</span><span class="o">.</span><span class="n">reconstruction_error_</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_hlle</span><span class="p">,</span>
<span class="s2">"Hessian Locally Linear Embedding of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># LTSA embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing LTSA embedding"</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.LocallyLinearEmbedding.html#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="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">method</span><span class="o">=</span><span class="s1">'ltsa'</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">X_ltsa</span> <span class="o">=</span> <span class="n">clf</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="k">print</span><span class="p">(</span><span class="s2">"Done. Reconstruction error: </span><span class="si">%g</span><span class="s2">"</span> <span class="o">%</span> <span class="n">clf</span><span class="o">.</span><span class="n">reconstruction_error_</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_ltsa</span><span class="p">,</span>
<span class="s2">"Local Tangent Space Alignment of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># MDS embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing MDS embedding"</span><span class="p">)</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.MDS.html#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="o">=</span><span class="mi">2</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">max_iter</span><span class="o">=</span><span class="mi">100</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">X_mds</span> <span class="o">=</span> <span class="n">clf</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="k">print</span><span class="p">(</span><span class="s2">"Done. Stress: </span><span class="si">%f</span><span class="s2">"</span> <span class="o">%</span> <span class="n">clf</span><span class="o">.</span><span class="n">stress_</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_mds</span><span class="p">,</span>
<span class="s2">"MDS embedding of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Random Trees embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing Totally Random Trees embedding"</span><span class="p">)</span>
<span class="n">hasher</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.RandomTreesEmbedding.html#sklearn.ensemble.RandomTreesEmbedding"><span class="n">ensemble</span><span class="o">.</span><span class="n">RandomTreesEmbedding</span></a><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">200</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">max_depth</span><span class="o">=</span><span class="mi">5</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">X_transformed</span> <span class="o">=</span> <span class="n">hasher</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">pca</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD"><span class="n">decomposition</span><span class="o">.</span><span class="n">TruncatedSVD</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">X_reduced</span> <span class="o">=</span> <span class="n">pca</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X_transformed</span><span class="p">)</span>
<span class="n">plot_embedding</span><span class="p">(</span><span class="n">X_reduced</span><span class="p">,</span>
<span class="s2">"Random forest embedding of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># Spectral embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing Spectral embedding"</span><span class="p">)</span>
<span class="n">embedder</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.manifold.SpectralEmbedding.html#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="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">eigen_solver</span><span class="o">=</span><span class="s2">"arpack"</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">X_se</span> <span class="o">=</span> <span class="n">embedder</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">plot_embedding</span><span class="p">(</span><span class="n">X_se</span><span class="p">,</span>
<span class="s2">"Spectral embedding of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="c1">#----------------------------------------------------------------------</span>
<span class="c1"># t-SNE embedding of the digits dataset</span>
<span class="k">print</span><span class="p">(</span><span class="s2">"Computing t-SNE embedding"</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"><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">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">t0</span> <span class="o">=</span> <span class="n">time</span><span class="p">()</span>
<span class="n">X_tsne</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">plot_embedding</span><span class="p">(</span><span class="n">X_tsne</span><span class="p">,</span>
<span class="s2">"t-SNE embedding of the digits (time </span><span class="si">%.2f</span><span class="s2">s)"</span> <span class="o">%</span>
<span class="p">(</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<a href="http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
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<p><strong>Total running time of the example:</strong> 36.53 seconds
( 0 minutes 36.53 seconds)</p>
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