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<li><a class="reference internal" href="#">Kernel Density Estimate of Species Distributions</a><ul>
<li><a class="reference internal" href="#references">References</a></li>
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<p><a class="reference internal" href="#sphx-glr-download-auto-examples-neighbors-plot-species-kde-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
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<section class="sphx-glr-example-title" id="kernel-density-estimate-of-species-distributions">
<span id="sphx-glr-auto-examples-neighbors-plot-species-kde-py"></span><h1>Kernel Density Estimate of Species Distributions<a class="headerlink" href="#kernel-density-estimate-of-species-distributions" title="Link to this heading">¶</a></h1>
<p>This shows an example of a neighbors-based query (in particular a kernel
density estimate) on geospatial data, using a Ball Tree built upon the
Haversine distance metric – i.e. distances over points in latitude/longitude.
The dataset is provided by Phillips et. al. (2006).
If available, the example uses
<a class="reference external" href="https://matplotlib.org/basemap/">basemap</a>
to plot the coast lines and national boundaries of South America.</p>
<p>This example does not perform any learning over the data
(see <a class="reference internal" href="../applications/plot_species_distribution_modeling.html#sphx-glr-auto-examples-applications-plot-species-distribution-modeling-py"><span class="std std-ref">Species distribution modeling</span></a> for
an example of classification based on the attributes in this dataset). It
simply shows the kernel density estimate of observed data points in
geospatial coordinates.</p>
<p>The two species are:</p>
<blockquote>
<div><ul class="simple">
<li><p><a class="reference external" href="https://www.iucnredlist.org/species/3038/47437046">“Bradypus variegatus”</a> ,
the Brown-throated Sloth.</p></li>
<li><p><a class="reference external" href="http://www.iucnredlist.org/details/13408/0">“Microryzomys minutus”</a> ,
also known as the Forest Small Rice Rat, a rodent that lives in Peru,
Colombia, Ecuador, Peru, and Venezuela.</p></li>
</ul>
</div></blockquote>
<section id="references">
<h2>References<a class="headerlink" href="#references" title="Link to this heading">¶</a></h2>
<blockquote>
<div><ul class="simple">
<li><p><a class="reference external" href="http://rob.schapire.net/papers/ecolmod.pdf">“Maximum entropy modeling of species geographic distributions”</a>
S. J. Phillips, R. P. Anderson, R. E. Schapire - Ecological Modelling,
190:231-259, 2006.</p></li>
</ul>
</div></blockquote>
<img src="../../_images/sphx_glr_plot_species_kde_001.png" srcset="../../_images/sphx_glr_plot_species_kde_001.png" alt="Bradypus Variegatus, Microryzomys Minutus" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>- computing KDE in spherical coordinates
- plot coastlines from coverage
- computing KDE in spherical coordinates
- plot coastlines from coverage
</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"># Author: Jake Vanderplas <[email protected]></span>
<span class="c1">#</span>
<span class="c1"># License: BSD 3 clause</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">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">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_species_distributions.html#sklearn.datasets.fetch_species_distributions" title="sklearn.datasets.fetch_species_distributions" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_species_distributions</span></a>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.neighbors.KernelDensity.html#sklearn.neighbors.KernelDensity" title="sklearn.neighbors.KernelDensity" class="sphx-glr-backref-module-sklearn-neighbors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KernelDensity</span></a>
<span class="c1"># if basemap is available, we'll use it.</span>
<span class="c1"># otherwise, we'll improvise later...</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">mpl_toolkits.basemap</span> <span class="kn">import</span> <span class="n">Basemap</span>
<span class="n">basemap</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
<span class="n">basemap</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">def</span> <span class="nf">construct_grids</span><span class="p">(</span><span class="n">batch</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Construct the map grid from the batch object</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> batch : Batch object</span>
<span class="sd"> The object returned by :func:`fetch_species_distributions`</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> (xgrid, ygrid) : 1-D arrays</span>
<span class="sd"> The grid corresponding to the values in batch.coverages</span>
<span class="sd"> """</span>
<span class="c1"># x,y coordinates for corner cells</span>
<span class="n">xmin</span> <span class="o">=</span> <span class="n">batch</span><span class="o">.</span><span class="n">x_left_lower_corner</span> <span class="o">+</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span>
<span class="n">xmax</span> <span class="o">=</span> <span class="n">xmin</span> <span class="o">+</span> <span class="p">(</span><span class="n">batch</span><span class="o">.</span><span class="n">Nx</span> <span class="o">*</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>
<span class="n">ymin</span> <span class="o">=</span> <span class="n">batch</span><span class="o">.</span><span class="n">y_left_lower_corner</span> <span class="o">+</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span>
<span class="n">ymax</span> <span class="o">=</span> <span class="n">ymin</span> <span class="o">+</span> <span class="p">(</span><span class="n">batch</span><span class="o">.</span><span class="n">Ny</span> <span class="o">*</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>
<span class="c1"># x coordinates of the grid cells</span>
<span class="n">xgrid</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">,</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>
<span class="c1"># y coordinates of the grid cells</span>
<span class="n">ygrid</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span><span class="p">,</span> <span class="n">batch</span><span class="o">.</span><span class="n">grid_size</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span><span class="p">)</span>
<span class="c1"># Get matrices/arrays of species IDs and locations</span>
<span class="n">data</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_species_distributions.html#sklearn.datasets.fetch_species_distributions" title="sklearn.datasets.fetch_species_distributions" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_species_distributions</span></a><span class="p">()</span>
<span class="n">species_names</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"Bradypus Variegatus"</span><span class="p">,</span> <span class="s2">"Microryzomys Minutus"</span><span class="p">]</span>
<span class="n">Xtrain</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.vstack.html#numpy.vstack" title="numpy.vstack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">vstack</span></a><span class="p">([</span><span class="n">data</span><span class="p">[</span><span class="s2">"train"</span><span class="p">][</span><span class="s2">"dd lat"</span><span class="p">],</span> <span class="n">data</span><span class="p">[</span><span class="s2">"train"</span><span class="p">][</span><span class="s2">"dd long"</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span>
<span class="n">ytrain</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="p">[</span><span class="n">d</span><span class="o">.</span><span class="n">decode</span><span class="p">(</span><span class="s2">"ascii"</span><span class="p">)</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s2">"micro"</span><span class="p">)</span> <span class="k">for</span> <span class="n">d</span> <span class="ow">in</span> <span class="n">data</span><span class="p">[</span><span class="s2">"train"</span><span class="p">][</span><span class="s2">"species"</span><span class="p">]],</span>
<span class="n">dtype</span><span class="o">=</span><span class="s2">"int"</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">Xtrain</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">180.0</span> <span class="c1"># Convert lat/long to radians</span>
<span class="c1"># Set up the data grid for the contour plot</span>
<span class="n">xgrid</span><span class="p">,</span> <span class="n">ygrid</span> <span class="o">=</span> <span class="n">construct_grids</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">xgrid</span><span class="p">[::</span><span class="mi">5</span><span class="p">],</span> <span class="n">ygrid</span><span class="p">[::</span><span class="mi">5</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">land_reference</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">coverages</span><span class="p">[</span><span class="mi">6</span><span class="p">][::</span><span class="mi">5</span><span class="p">,</span> <span class="p">::</span><span class="mi">5</span><span class="p">]</span>
<span class="n">land_mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">land_reference</span> <span class="o">></span> <span class="o">-</span><span class="mi">9999</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="n">xy</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.vstack.html#numpy.vstack" title="numpy.vstack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">vstack</span></a><span class="p">([</span><span class="n">Y</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">X</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span><span class="o">.</span><span class="n">T</span>
<span class="n">xy</span> <span class="o">=</span> <span class="n">xy</span><span class="p">[</span><span class="n">land_mask</span><span class="p">]</span>
<span class="n">xy</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">180.0</span>
<span class="c1"># Plot map of South America with distributions of each species</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">fig</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">left</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">wspace</span><span class="o">=</span><span class="mf">0.05</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="mi">2</span><span class="p">):</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" 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">subplot</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># construct a kernel density estimate of the distribution</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">" - computing KDE in spherical coordinates"</span><span class="p">)</span>
<span class="n">kde</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.neighbors.KernelDensity.html#sklearn.neighbors.KernelDensity" title="sklearn.neighbors.KernelDensity" class="sphx-glr-backref-module-sklearn-neighbors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KernelDensity</span></a><span class="p">(</span>
<span class="n">bandwidth</span><span class="o">=</span><span class="mf">0.04</span><span class="p">,</span> <span class="n">metric</span><span class="o">=</span><span class="s2">"haversine"</span><span class="p">,</span> <span class="n">kernel</span><span class="o">=</span><span class="s2">"gaussian"</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s2">"ball_tree"</span>
<span class="p">)</span>
<span class="n">kde</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">Xtrain</span><span class="p">[</span><span class="n">ytrain</span> <span class="o">==</span> <span class="n">i</span><span class="p">])</span>
<span class="c1"># evaluate only on the land: -9999 indicates ocean</span>
<span class="n">Z</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.full.html#numpy.full" title="numpy.full" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">full</span></a><span class="p">(</span><span class="n">land_mask</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="o">-</span><span class="mi">9999</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="s2">"int"</span><span class="p">)</span>
<span class="n">Z</span><span class="p">[</span><span class="n">land_mask</span><span class="p">]</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.exp.html#numpy.exp" title="numpy.exp" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">exp</span></a><span class="p">(</span><span class="n">kde</span><span class="o">.</span><span class="n">score_samples</span><span class="p">(</span><span class="n">xy</span><span class="p">))</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">reshape</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="c1"># plot contours of the density</span>
<span class="n">levels</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">Z</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="mi">25</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contourf.html#matplotlib.pyplot.contourf" title="matplotlib.pyplot.contourf" 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">contourf</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="n">levels</span><span class="o">=</span><span class="n">levels</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">Reds</span><span class="p">)</span>
<span class="k">if</span> <span class="n">basemap</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">" - plot coastlines using basemap"</span><span class="p">)</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">Basemap</span><span class="p">(</span>
<span class="n">projection</span><span class="o">=</span><span class="s2">"cyl"</span><span class="p">,</span>
<span class="n">llcrnrlat</span><span class="o">=</span><span class="n">Y</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
<span class="n">urcrnrlat</span><span class="o">=</span><span class="n">Y</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span>
<span class="n">llcrnrlon</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
<span class="n">urcrnrlon</span><span class="o">=</span><span class="n">X</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span>
<span class="n">resolution</span><span class="o">=</span><span class="s2">"c"</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">m</span><span class="o">.</span><span class="n">drawcoastlines</span><span class="p">()</span>
<span class="n">m</span><span class="o">.</span><span class="n">drawcountries</span><span class="p">()</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">" - plot coastlines from coverage"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contour.html#matplotlib.pyplot.contour" title="matplotlib.pyplot.contour" 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">contour</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">land_reference</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">9998</span><span class="p">],</span> <span class="n">colors</span><span class="o">=</span><span class="s2">"k"</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="s2">"solid"</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>
<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">species_names</span><span class="p">[</span><span class="n">i</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><a class="reference download internal" download="" href="../../_downloads/02a1306a494b46cc56c930ceec6e8c4a/plot_species_kde.py"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">plot_species_kde.py</span></code></a></p>
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<p class="rubric">Related examples</p>
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<p><a class="reference internal" href="../applications/plot_species_distribution_modeling.html#sphx-glr-auto-examples-applications-plot-species-distribution-modeling-py"><span class="std std-ref">Species distribution modeling</span></a></p>
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<p><a class="reference internal" href="plot_kde_1d.html#sphx-glr-auto-examples-neighbors-plot-kde-1d-py"><span class="std std-ref">Simple 1D Kernel Density Estimation</span></a></p>
<div class="sphx-glr-thumbnail-title">Simple 1D Kernel Density Estimation</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Plot the density estimation of a mixture of two Gaussians. Data is generated from two Gaussians..."><img alt="" src="../../_images/sphx_glr_plot_gmm_pdf_thumb.png" />
<p><a class="reference internal" href="../mixture/plot_gmm_pdf.html#sphx-glr-auto-examples-mixture-plot-gmm-pdf-py"><span class="std std-ref">Density Estimation for a Gaussian mixture</span></a></p>
<div class="sphx-glr-thumbnail-title">Density Estimation for a Gaussian mixture</div>
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