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<li><a class="reference internal" href="#">Various Agglomerative Clustering on a 2D embedding of digits</a></li>
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<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-cluster-plot-digits-linkage-py"><span class="std std-ref">Go to the end</span></a>
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<section class="sphx-glr-example-title" id="various-agglomerative-clustering-on-a-2d-embedding-of-digits">
<span id="sphx-glr-auto-examples-cluster-plot-digits-linkage-py"></span><h1>Various Agglomerative Clustering on a 2D embedding of digits<a class="headerlink" href="#various-agglomerative-clustering-on-a-2d-embedding-of-digits" title="Link to this heading">¶</a></h1>
<p>An illustration of various linkage option for agglomerative clustering on
a 2D embedding of the digits dataset.</p>
<p>The goal of this example is to show intuitively how the metrics behave, and
not to find good clusters for the digits. This is why the example works on a
2D embedding.</p>
<p>What this example shows us is the behavior “rich getting richer” of
agglomerative clustering that tends to create uneven cluster sizes.</p>
<p>This behavior is pronounced for the average linkage strategy,
that ends up with a couple of clusters with few datapoints.</p>
<p>The case of single linkage is even more pathologic with a very
large cluster covering most digits, an intermediate size (clean)
cluster with most zero digits and all other clusters being drawn
from noise points around the fringes.</p>
<p>The other linkage strategies lead to more evenly distributed
clusters that are therefore likely to be less sensible to a
random resampling of the dataset.</p>
<ul class="sphx-glr-horizontal">
<li><img src="../../_images/sphx_glr_plot_digits_linkage_001.png" srcset="../../_images/sphx_glr_plot_digits_linkage_001.png" alt="ward linkage" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_digits_linkage_002.png" srcset="../../_images/sphx_glr_plot_digits_linkage_002.png" alt="average linkage" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_digits_linkage_003.png" srcset="../../_images/sphx_glr_plot_digits_linkage_003.png" alt="complete linkage" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_digits_linkage_004.png" srcset="../../_images/sphx_glr_plot_digits_linkage_004.png" alt="single linkage" class = "sphx-glr-multi-img"/></li>
</ul>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Computing embedding
Done.
ward : 0.06s
average : 0.06s
complete : 0.05s
single : 0.02s
</pre></div>
</div>
<div class="line-block">
<div class="line"><br /></div>
</div>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Authors: Gael Varoquaux</span>
<span class="c1"># License: BSD 3 clause (C) INRIA 2014</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">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">manifold</span>
<span class="n">digits</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_digits.html#sklearn.datasets.load_digits" title="sklearn.datasets.load_digits" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">datasets</span><span class="o">.</span><span class="n">load_digits</span></a><span class="p">()</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">digits</span><span class="o">.</span><span class="n">data</span><span class="p">,</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>
<a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html#numpy.random.seed" title="numpy.random.seed" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># ----------------------------------------------------------------------</span>
<span class="c1"># Visualize the clustering</span>
<span class="k">def</span> <span class="nf">plot_clustering</span><span class="p">(</span><span class="n">X_red</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="kc">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> <a href="https://numpy.org/doc/stable/reference/generated/numpy.min.html#numpy.min" title="numpy.min" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">min</span></a><span class="p">(</span><span class="n">X_red</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.max.html#numpy.max" title="numpy.max" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">max</span></a><span class="p">(</span><span class="n">X_red</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">X_red</span> <span class="o">=</span> <span class="p">(</span><span class="n">X_red</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="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">6</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="k">for</span> <span class="n">digit</span> <span class="ow">in</span> <span class="n">digits</span><span class="o">.</span><span class="n">target_names</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="o">*</span><span class="n">X_red</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="n">digit</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
<span class="n">marker</span><span class="o">=</span><span class="sa">f</span><span class="s2">"$</span><span class="si">{</span><span class="n">digit</span><span class="si">}</span><span class="s2">$"</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">c</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">nipy_spectral</span><span class="p">(</span><span class="n">labels</span><span class="p">[</span><span class="n">y</span> <span class="o">==</span> <span class="n">digit</span><span class="p">]</span> <span class="o">/</span> <span class="mi">10</span><span class="p">),</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" 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">xticks</span></a><span class="p">([])</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" 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">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="kc">None</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="n">title</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">17</span><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">"off"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" 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">tight_layout</span></a><span class="p">(</span><span class="n">rect</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.03</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.95</span><span class="p">])</span>
<span class="c1"># ----------------------------------------------------------------------</span>
<span class="c1"># 2D embedding of the digits dataset</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Computing embedding"</span><span class="p">)</span>
<span class="n">X_red</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="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Done."</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">sklearn.cluster</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.cluster.AgglomerativeClustering.html#sklearn.cluster.AgglomerativeClustering" title="sklearn.cluster.AgglomerativeClustering" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">AgglomerativeClustering</span></a>
<span class="k">for</span> <span class="n">linkage</span> <span class="ow">in</span> <span class="p">(</span><span class="s2">"ward"</span><span class="p">,</span> <span class="s2">"average"</span><span class="p">,</span> <span class="s2">"complete"</span><span class="p">,</span> <span class="s2">"single"</span><span class="p">):</span>
<span class="n">clustering</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.AgglomerativeClustering.html#sklearn.cluster.AgglomerativeClustering" title="sklearn.cluster.AgglomerativeClustering" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">AgglomerativeClustering</span></a><span class="p">(</span><span class="n">linkage</span><span class="o">=</span><span class="n">linkage</span><span class="p">,</span> <span class="n">n_clusters</span><span class="o">=</span><span class="mi">10</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">clustering</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_red</span><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="se">\t</span><span class="si">%.2f</span><span class="s2">s"</span> <span class="o">%</span> <span class="p">(</span><span class="n">linkage</span><span class="p">,</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="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">plot_clustering</span><span class="p">(</span><span class="n">X_red</span><span class="p">,</span> <span class="n">clustering</span><span class="o">.</span><span class="n">labels_</span><span class="p">,</span> <span class="s2">"</span><span class="si">%s</span><span class="s2"> linkage"</span> <span class="o">%</span> <span class="n">linkage</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>
</pre></div>
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<p class="rubric">Related examples</p>
<div class="sphx-glr-thumbnails"><div class="sphx-glr-thumbcontainer" tooltip="This example shows the effect of imposing a connectivity graph to capture local structure in th..."><img alt="" src="../../_images/sphx_glr_plot_agglomerative_clustering_thumb.png" />
<p><a class="reference internal" href="plot_agglomerative_clustering.html#sphx-glr-auto-examples-cluster-plot-agglomerative-clustering-py"><span class="std std-ref">Agglomerative clustering with and without structure</span></a></p>
<div class="sphx-glr-thumbnail-title">Agglomerative clustering with and without structure</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example shows characteristics of different linkage methods for hierarchical clustering on ..."><img alt="" src="../../_images/sphx_glr_plot_linkage_comparison_thumb.png" />
<p><a class="reference internal" href="plot_linkage_comparison.html#sphx-glr-auto-examples-cluster-plot-linkage-comparison-py"><span class="std std-ref">Comparing different hierarchical linkage methods on toy datasets</span></a></p>
<div class="sphx-glr-thumbnail-title">Comparing different hierarchical linkage methods on toy datasets</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="We illustrate various embedding techniques on the digits dataset."><img alt="" src="../../_images/sphx_glr_plot_lle_digits_thumb.png" />
<p><a class="reference internal" href="../manifold/plot_lle_digits.html#sphx-glr-auto-examples-manifold-plot-lle-digits-py"><span class="std std-ref">Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…</span></a></p>
<div class="sphx-glr-thumbnail-title">Manifold learning on handwritten digits: Locally Linear Embedding, Isomap...</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This dataset is made up of 1797 8x8 images. Each image, like the one shown below, is of a hand-..."><img alt="" src="../../_images/sphx_glr_plot_digits_last_image_thumb.png" />
<p><a class="reference internal" href="../datasets/plot_digits_last_image.html#sphx-glr-auto-examples-datasets-plot-digits-last-image-py"><span class="std std-ref">The Digit Dataset</span></a></p>
<div class="sphx-glr-thumbnail-title">The Digit Dataset</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="This example employs several unsupervised learning techniques to extract the stock market struc..."><img alt="" src="../../_images/sphx_glr_plot_stock_market_thumb.png" />
<p><a class="reference internal" href="../applications/plot_stock_market.html#sphx-glr-auto-examples-applications-plot-stock-market-py"><span class="std std-ref">Visualizing the stock market structure</span></a></p>
<div class="sphx-glr-thumbnail-title">Visualizing the stock market structure</div>
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