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<li><a class="reference internal" href="#">Importance of Feature Scaling</a></li>
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<div class="sphx-glr-download-link-note admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Click <a class="reference internal" href="#sphx-glr-download-auto-examples-preprocessing-plot-scaling-importance-py"><span class="std std-ref">here</span></a> to download the full example code</p>
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<div class="sphx-glr-example-title section" id="importance-of-feature-scaling">
<span id="sphx-glr-auto-examples-preprocessing-plot-scaling-importance-py"></span><h1>Importance of Feature Scaling<a class="headerlink" href="#importance-of-feature-scaling" title="Permalink to this headline">¶</a></h1>
<p>Feature scaling through standardization (or Z-score normalization)
can be an important preprocessing step for many machine learning
algorithms. Standardization involves rescaling the features such
that they have the properties of a standard normal distribution
with a mean of zero and a standard deviation of one.</p>
<p>While many algorithms (such as SVM, K-nearest neighbors, and logistic
regression) require features to be normalized, intuitively we can
think of Principle Component Analysis (PCA) as being a prime example
of when normalization is important. In PCA we are interested in the
components that maximize the variance. If one component (e.g. human
height) varies less than another (e.g. weight) because of their
respective scales (meters vs. kilos), PCA might determine that the
direction of maximal variance more closely corresponds with the
‘weight’ axis, if those features are not scaled. As a change in
height of one meter can be considered much more important than the
change in weight of one kilogram, this is clearly incorrect.</p>
<p>To illustrate this, PCA is performed comparing the use of data with
<a class="reference internal" href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="sklearn.preprocessing.StandardScaler"><code class="xref py py-class docutils literal"><span class="pre">StandardScaler</span></code></a> applied,
to unscaled data. The results are visualized and a clear difference noted.
The 1st principal component in the unscaled set can be seen. It can be seen
that feature #13 dominates the direction, being a whole two orders of
magnitude above the other features. This is contrasted when observing
the principal component for the scaled version of the data. In the scaled
version, the orders of magnitude are roughly the same across all the features.</p>
<p>The dataset used is the Wine Dataset available at UCI. This dataset
has continuous features that are heterogeneous in scale due to differing
properties that they measure (i.e alcohol content, and malic acid).</p>
<p>The transformed data is then used to train a naive Bayes classifier, and a
clear difference in prediction accuracies is observed wherein the dataset
which is scaled before PCA vastly outperforms the unscaled version.</p>
<img alt="../../_images/sphx_glr_plot_scaling_importance_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_scaling_importance_001.png" />
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none"><div class="highlight"><pre><span></span>Prediction accuracy for the normal test dataset with PCA
81.48%
Prediction accuracy for the standardized test dataset with PCA
98.15%
PC 1 without scaling:
[ 1.76e-03 -8.36e-04 1.55e-04 -5.31e-03 2.02e-02 1.02e-03 1.53e-03
-1.12e-04 6.31e-04 2.33e-03 1.54e-04 7.43e-04 1.00e+00]
PC 1 with scaling:
[ 0.13 -0.26 -0.01 -0.23 0.16 0.39 0.42 -0.28 0.33 -0.11 0.3 0.38
0.28]
</pre></div>
</div>
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<div class="line"><br /></div>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="View documentation for sklearn.preprocessing.StandardScaler"><span class="n">StandardScaler</span></a>
<span class="kn">from</span> <span class="nn">sklearn.decomposition</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="View documentation for sklearn.decomposition.PCA"><span class="n">PCA</span></a>
<span class="kn">from</span> <span class="nn">sklearn.naive_bayes</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.naive_bayes.GaussianNB.html#sklearn.naive_bayes.GaussianNB" title="View documentation for sklearn.naive_bayes.GaussianNB"><span class="n">GaussianNB</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="k">import</span> <span class="n">metrics</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.datasets.load_wine.html#sklearn.datasets.load_wine" title="View documentation for sklearn.datasets.load_wine"><span class="n">load_wine</span></a>
<span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="k">import</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="View documentation for sklearn.pipeline.make_pipeline"><span class="n">make_pipeline</span></a>
<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="c1"># Code source: Tyler Lanigan <[email protected]></span>
<span class="c1"># Sebastian Raschka <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<span class="n">RANDOM_STATE</span> <span class="o">=</span> <span class="mi">42</span>
<span class="n">FIG_SIZE</span> <span class="o">=</span> <span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
<span class="n">features</span><span class="p">,</span> <span class="n">target</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.load_wine.html#sklearn.datasets.load_wine" title="View documentation for sklearn.datasets.load_wine"><span class="n">load_wine</span></a><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Make a train/test split using 30% test size</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.model_selection.train_test_split.html#sklearn.model_selection.train_test_split" title="View documentation for sklearn.model_selection.train_test_split"><span class="n">train_test_split</span></a><span class="p">(</span><span class="n">features</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span>
<span class="n">test_size</span><span class="o">=</span><span class="mf">0.30</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">RANDOM_STATE</span><span class="p">)</span>
<span class="c1"># Fit to data and predict using pipelined GNB and PCA.</span>
<span class="n">unscaled_clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="View documentation for sklearn.pipeline.make_pipeline"><span class="n">make_pipeline</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="View documentation for sklearn.decomposition.PCA"><span class="n">PCA</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> <a href="../../modules/generated/sklearn.naive_bayes.GaussianNB.html#sklearn.naive_bayes.GaussianNB" title="View documentation for sklearn.naive_bayes.GaussianNB"><span class="n">GaussianNB</span></a><span class="p">())</span>
<span class="n">unscaled_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">pred_test</span> <span class="o">=</span> <span class="n">unscaled_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="c1"># Fit to data and predict using pipelined scaling, GNB and PCA.</span>
<span class="n">std_clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="View documentation for sklearn.pipeline.make_pipeline"><span class="n">make_pipeline</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler" title="View documentation for sklearn.preprocessing.StandardScaler"><span class="n">StandardScaler</span></a><span class="p">(),</span> <a href="../../modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA" title="View documentation for sklearn.decomposition.PCA"><span class="n">PCA</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> <a href="../../modules/generated/sklearn.naive_bayes.GaussianNB.html#sklearn.naive_bayes.GaussianNB" title="View documentation for sklearn.naive_bayes.GaussianNB"><span class="n">GaussianNB</span></a><span class="p">())</span>
<span class="n">std_clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">pred_test_std</span> <span class="o">=</span> <span class="n">std_clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
<span class="c1"># Show prediction accuracies in scaled and unscaled data.</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\n</span><span class="s1">Prediction accuracy for the normal test dataset with PCA'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="si">{:.2%}</span><span class="se">\n</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><a href="../../modules/generated/sklearn.metrics.accuracy_score.html#sklearn.metrics.accuracy_score" title="View documentation for sklearn.metrics.accuracy_score"><span class="n">metrics</span><span class="o">.</span><span class="n">accuracy_score</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">pred_test</span><span class="p">)))</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\n</span><span class="s1">Prediction accuracy for the standardized test dataset with PCA'</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="si">{:.2%}</span><span class="se">\n</span><span class="s1">'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><a href="../../modules/generated/sklearn.metrics.accuracy_score.html#sklearn.metrics.accuracy_score" title="View documentation for sklearn.metrics.accuracy_score"><span class="n">metrics</span><span class="o">.</span><span class="n">accuracy_score</span></a><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">pred_test_std</span><span class="p">)))</span>
<span class="c1"># Extract PCA from pipeline</span>
<span class="n">pca</span> <span class="o">=</span> <span class="n">unscaled_clf</span><span class="o">.</span><span class="n">named_steps</span><span class="p">[</span><span class="s1">'pca'</span><span class="p">]</span>
<span class="n">pca_std</span> <span class="o">=</span> <span class="n">std_clf</span><span class="o">.</span><span class="n">named_steps</span><span class="p">[</span><span class="s1">'pca'</span><span class="p">]</span>
<span class="c1"># Show first principal components</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\n</span><span class="s1">PC 1 without scaling:</span><span class="se">\n</span><span class="s1">'</span><span class="p">,</span> <span class="n">pca</span><span class="o">.</span><span class="n">components_</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\n</span><span class="s1">PC 1 with scaling:</span><span class="se">\n</span><span class="s1">'</span><span class="p">,</span> <span class="n">pca_std</span><span class="o">.</span><span class="n">components_</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="c1"># Use PCA without and with scale on X_train data for visualization.</span>
<span class="n">X_train_transformed</span> <span class="o">=</span> <span class="n">pca</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">)</span>
<span class="n">scaler</span> <span class="o">=</span> <span class="n">std_clf</span><span class="o">.</span><span class="n">named_steps</span><span class="p">[</span><span class="s1">'standardscaler'</span><span class="p">]</span>
<span class="n">X_train_std_transformed</span> <span class="o">=</span> <span class="n">pca_std</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X_train</span><span class="p">))</span>
<span class="c1"># visualize standardized vs. untouched dataset with PCA performed</span>
<span class="n">fig</span><span class="p">,</span> <span class="p">(</span><span class="n">ax1</span><span class="p">,</span> <span class="n">ax2</span><span class="p">)</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">ncols</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="n">FIG_SIZE</span><span class="p">)</span>
<span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="nb">range</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="s1">'blue'</span><span class="p">,</span> <span class="s1">'red'</span><span class="p">,</span> <span class="s1">'green'</span><span class="p">),</span> <span class="p">(</span><span class="s1">'^'</span><span class="p">,</span> <span class="s1">'s'</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">)):</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_train_transformed</span><span class="p">[</span><span class="n">y_train</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">X_train_transformed</span><span class="p">[</span><span class="n">y_train</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="n">c</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'class </span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="n">l</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="n">marker</span><span class="o">=</span><span class="n">m</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">l</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="nb">range</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="s1">'blue'</span><span class="p">,</span> <span class="s1">'red'</span><span class="p">,</span> <span class="s1">'green'</span><span class="p">),</span> <span class="p">(</span><span class="s1">'^'</span><span class="p">,</span> <span class="s1">'s'</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">)):</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_train_std_transformed</span><span class="p">[</span><span class="n">y_train</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">X_train_std_transformed</span><span class="p">[</span><span class="n">y_train</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="n">c</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s1">'class </span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="n">l</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="n">marker</span><span class="o">=</span><span class="n">m</span>
<span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Training dataset after PCA'</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Standardized training dataset after PCA'</span><span class="p">)</span>
<span class="k">for</span> <span class="n">ax</span> <span class="ow">in</span> <span class="p">(</span><span class="n">ax1</span><span class="p">,</span> <span class="n">ax2</span><span class="p">):</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">'1st principal component'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'2nd principal component'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'upper right'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">grid</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>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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