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<li><a class="reference internal" href="#">Using PowerTransformer to apply the Box-Cox transformation</a></li>
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<div class="sphx-glr-example-title section" id="using-powertransformer-to-apply-the-box-cox-transformation">
<span id="sphx-glr-auto-examples-preprocessing-plot-power-transformer-py"></span><h1>Using PowerTransformer to apply the Box-Cox transformation<a class="headerlink" href="#using-powertransformer-to-apply-the-box-cox-transformation" title="Permalink to this headline">¶</a></h1>
<p>This example demonstrates the use of the Box-Cox transform through
<code class="xref py py-class docutils literal"><span class="pre">preprocessing.PowerTransformer</span></code> to map data from various distributions
to a normal distribution.</p>
<p>Box-Cox is useful as a transformation in modeling problems where
homoscedasticity and normality are desired. Below are examples of Box-Cox
applied to six different probability distributions: Lognormal, Chi-squared,
Weibull, Gaussian, Uniform, and Bimodal.</p>
<p>Note that the transformation successfully maps the data to a normal
distribution when applied to certain datasets, but is ineffective with others.
This highlights the importance of visualizing the data before and after
transformation. Also note that while the standardize option is set to False for
the plot examples, by default, <code class="xref py py-class docutils literal"><span class="pre">preprocessing.PowerTransformer</span></code> also
applies zero-mean, unit-variance standardization to the transformed outputs.</p>
<img alt="../../_images/sphx_glr_plot_power_transformer_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_power_transformer_001.png" />
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="c1"># Author: Eric Chang <[email protected]></span>
<span class="c1"># License: BSD 3 clause</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">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.PowerTransformer.html#sklearn.preprocessing.PowerTransformer" title="View documentation for sklearn.preprocessing.PowerTransformer"><span class="n">PowerTransformer</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.preprocessing.minmax_scale.html#sklearn.preprocessing.minmax_scale" title="View documentation for sklearn.preprocessing.minmax_scale"><span class="n">minmax_scale</span></a>
<span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="n">N_SAMPLES</span> <span class="o">=</span> <span class="mi">3000</span>
<span class="n">FONT_SIZE</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">BINS</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">pt</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.PowerTransformer.html#sklearn.preprocessing.PowerTransformer" title="View documentation for sklearn.preprocessing.PowerTransformer"><span class="n">PowerTransformer</span></a><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s1">'box-cox'</span><span class="p">,</span> <span class="n">standardize</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="n">rng</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.RandomState.html#numpy.random.RandomState" title="View documentation for numpy.random.RandomState"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">304</span><span class="p">)</span>
<span class="n">size</span> <span class="o">=</span> <span class="p">(</span><span class="n">N_SAMPLES</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="c1"># lognormal distribution</span>
<span class="n">X_lognormal</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">lognormal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</span>
<span class="c1"># chi-squared distribution</span>
<span class="n">df</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">X_chisq</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">chisquare</span><span class="p">(</span><span class="n">df</span><span class="o">=</span><span class="n">df</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</span>
<span class="c1"># weibull distribution</span>
<span class="n">a</span> <span class="o">=</span> <span class="mi">50</span>
<span class="n">X_weibull</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">weibull</span><span class="p">(</span><span class="n">a</span><span class="o">=</span><span class="n">a</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</span>
<span class="c1"># gaussian distribution</span>
<span class="n">loc</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">X_gaussian</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="n">loc</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</span>
<span class="c1"># uniform distribution</span>
<span class="n">X_uniform</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</span>
<span class="c1"># bimodal distribution</span>
<span class="n">loc_a</span><span class="p">,</span> <span class="n">loc_b</span> <span class="o">=</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">105</span>
<span class="n">X_a</span><span class="p">,</span> <span class="n">X_b</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="n">loc_a</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">),</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="n">loc_b</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</span>
<span class="n">X_bimodal</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.html#numpy.concatenate" title="View documentation for numpy.concatenate"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span></a><span class="p">([</span><span class="n">X_a</span><span class="p">,</span> <span class="n">X_b</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="c1"># create plots</span>
<span class="n">distributions</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">(</span><span class="s1">'Lognormal'</span><span class="p">,</span> <span class="n">X_lognormal</span><span class="p">),</span>
<span class="p">(</span><span class="s1">'Chi-squared'</span><span class="p">,</span> <span class="n">X_chisq</span><span class="p">),</span>
<span class="p">(</span><span class="s1">'Weibull'</span><span class="p">,</span> <span class="n">X_weibull</span><span class="p">),</span>
<span class="p">(</span><span class="s1">'Gaussian'</span><span class="p">,</span> <span class="n">X_gaussian</span><span class="p">),</span>
<span class="p">(</span><span class="s1">'Uniform'</span><span class="p">,</span> <span class="n">X_uniform</span><span class="p">),</span>
<span class="p">(</span><span class="s1">'Bimodal'</span><span class="p">,</span> <span class="n">X_bimodal</span><span class="p">)</span>
<span class="p">]</span>
<span class="n">colors</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'firebrick'</span><span class="p">,</span> <span class="s1">'darkorange'</span><span class="p">,</span> <span class="s1">'goldenrod'</span><span class="p">,</span>
<span class="s1">'seagreen'</span><span class="p">,</span> <span class="s1">'royalblue'</span><span class="p">,</span> <span class="s1">'darkorchid'</span><span class="p">]</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="View documentation for matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">ncols</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">axes</span> <span class="o">=</span> <span class="n">axes</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
<span class="n">axes_idxs</span> <span class="o">=</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</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="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">9</span><span class="p">),</span> <span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="mi">10</span><span class="p">),</span> <span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">11</span><span class="p">)]</span>
<span class="n">axes_list</span> <span class="o">=</span> <span class="p">[(</span><span class="n">axes</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">axes</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="n">axes_idxs</span><span class="p">]</span>
<span class="k">for</span> <span class="n">distribution</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="n">axes</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">distributions</span><span class="p">,</span> <span class="n">colors</span><span class="p">,</span> <span class="n">axes_list</span><span class="p">):</span>
<span class="n">name</span><span class="p">,</span> <span class="n">X</span> <span class="o">=</span> <span class="n">distribution</span>
<span class="c1"># scale all distributions to the range [0, 10]</span>
<span class="n">X</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.preprocessing.minmax_scale.html#sklearn.preprocessing.minmax_scale" title="View documentation for sklearn.preprocessing.minmax_scale"><span class="n">minmax_scale</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">feature_range</span><span class="o">=</span><span class="p">(</span><span class="mf">1e-10</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="c1"># perform power transform</span>
<span class="n">X_trans</span> <span class="o">=</span> <span class="n">pt</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">lmbda</span> <span class="o">=</span> <span class="nb">round</span><span class="p">(</span><span class="n">pt</span><span class="o">.</span><span class="n">lambdas_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">ax_original</span><span class="p">,</span> <span class="n">ax_trans</span> <span class="o">=</span> <span class="n">axes</span>
<span class="n">ax_original</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">BINS</span><span class="p">)</span>
<span class="n">ax_original</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="n">FONT_SIZE</span><span class="p">)</span>
<span class="n">ax_original</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="s1">'both'</span><span class="p">,</span> <span class="n">which</span><span class="o">=</span><span class="s1">'major'</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="n">FONT_SIZE</span><span class="p">)</span>
<span class="n">ax_trans</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">X_trans</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">BINS</span><span class="p">)</span>
<span class="n">ax_trans</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'{} after Box-Cox, $\lambda$ = {}'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">lmbda</span><span class="p">),</span>
<span class="n">fontsize</span><span class="o">=</span><span class="n">FONT_SIZE</span><span class="p">)</span>
<span class="n">ax_trans</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="s1">'both'</span><span class="p">,</span> <span class="n">which</span><span class="o">=</span><span class="s1">'major'</span><span class="p">,</span> <span class="n">labelsize</span><span class="o">=</span><span class="n">FONT_SIZE</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="View documentation for matplotlib.pyplot.tight_layout"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
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