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     <h1><a href="../ml">FlinkML</a> - Standard Scaler</h1>


 <ul id="markdown-toc">
   <li><a href="#description" id="markdown-toc-description">Description</a></li>
   <li><a href="#operations" id="markdown-toc-operations">Operations</a>    <ul>
       <li><a href="#fit" id="markdown-toc-fit">Fit</a></li>
       <li><a href="#transform" id="markdown-toc-transform">Transform</a></li>
     </ul>
   </li>
   <li><a href="#parameters" id="markdown-toc-parameters">Parameters</a></li>
   <li><a href="#examples" id="markdown-toc-examples">Examples</a></li>
 </ul>

 <h2 id="description">Description</h2>

 <p>The standard scaler scales the given data set, so that all features will have a user specified mean and variance.
  In case the user does not provide a specific mean and standard deviation, the standard scaler transforms the features of the input data set to have mean equal to 0 and standard deviation equal to 1.
  Given a set of input data $x_1, x_2,… x_n$, with mean:</p>

 <script type="math/tex; mode=display">\bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_{i}</script>

 <p>and standard deviation:</p>

 <script type="math/tex; mode=display">\sigma_{x}=\sqrt{ \frac{1}{n} \sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}</script>

 <p>The scaled data set $z_1, z_2,…,z_n$ will be:</p>

 <script type="math/tex; mode=display">z_{i}= std \left (\frac{x_{i} - \bar{x}  }{\sigma_{x}}\right ) + mean</script>

 <p>where $\textit{std}$ and $\textit{mean}$ are the user specified values for the standard deviation and mean.</p>

 <h2 id="operations">Operations</h2>

 <p><code>StandardScaler</code> is a <code>Transformer</code>.
 As such, it supports the <code>fit</code> and <code>transform</code> operation.</p>

 <h3 id="fit">Fit</h3>

 <p>StandardScaler is trained on all subtypes of <code>Vector</code> or <code>LabeledVector</code>:</p>

 <ul>
   <li><code>fit[T &lt;: Vector]: DataSet[T] =&gt; Unit</code></li>
   <li><code>fit: DataSet[LabeledVector] =&gt; Unit</code></li>
 </ul>

 <h3 id="transform">Transform</h3>

 <p>StandardScaler transforms all subtypes of <code>Vector</code> or <code>LabeledVector</code> into the respective type:</p>

 <ul>
   <li><code>transform[T &lt;: Vector]: DataSet[T] =&gt; DataSet[T]</code></li>
   <li><code>transform: DataSet[LabeledVector] =&gt; DataSet[LabeledVector]</code></li>
 </ul>

 <h2 id="parameters">Parameters</h2>

 <p>The standard scaler implementation can be controlled by the following two parameters:</p>

 <table class="table table-bordered">
   <thead>
     <tr>
       <th class="text-left" style="width: 20%">Parameters</th>
       <th class="text-center">Description</th>
     </tr>
   </thead>

   <tbody>
     <tr>
       <td><strong>Mean</strong></td>
       <td>
         <p>
           The mean of the scaled data set. (Default value: <strong>0.0</strong>)
         </p>
       </td>
     </tr>
     <tr>
       <td><strong>Std</strong></td>
       <td>
         <p>
           The standard deviation of the scaled data set. (Default value: <strong>1.0</strong>)
         </p>
       </td>
     </tr>
   </tbody>
 </table>

 <h2 id="examples">Examples</h2>

 <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="c1">// Create standard scaler transformer</span>
 <span class="k">val</span> <span class="n">scaler</span> <span class="k">=</span> <span class="nc">StandardScaler</span><span class="o">()</span>
 <span class="o">.</span><span class="n">setMean</span><span class="o">(</span><span class="mf">10.0</span><span class="o">)</span>
 <span class="o">.</span><span class="n">setStd</span><span class="o">(</span><span class="mf">2.0</span><span class="o">)</span>

 <span class="c1">// Obtain data set to be scaled</span>
 <span class="k">val</span> <span class="n">dataSet</span><span class="k">:</span> <span class="kt">DataSet</span><span class="o">[</span><span class="kt">Vector</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span>

 <span class="c1">// Learn the mean and standard deviation of the training data</span>
 <span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">dataSet</span><span class="o">)</span>

 <span class="c1">// Scale the provided data set to have mean=10.0 and std=2.0</span>
 <span class="k">val</span> <span class="n">scaledDS</span> <span class="k">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">dataSet</span><span class="o">)</span></code></pre></div>


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	<h1><a href="../ml">FlinkML</a> - Standard Scaler</h1>



	<ul id="markdown-toc">
	<li><a href="#description" id="markdown-toc-description">Description</a></li>
	<li><a href="#operations" id="markdown-toc-operations">Operations</a> <ul>
	<li><a href="#fit" id="markdown-toc-fit">Fit</a></li>
	<li><a href="#transform" id="markdown-toc-transform">Transform</a></li>
	</ul>
	</li>
	<li><a href="#parameters" id="markdown-toc-parameters">Parameters</a></li>
	<li><a href="#examples" id="markdown-toc-examples">Examples</a></li>
	</ul>

	<h2 id="description">Description</h2>

	<p>The standard scaler scales the given data set, so that all features will have a user specified mean and variance.
	In case the user does not provide a specific mean and standard deviation, the standard scaler transforms the features of the input data set to have mean equal to 0 and standard deviation equal to 1.
	Given a set of input data $x_1, x_2,… x_n$, with mean:</p>

	<script type="math/tex; mode=display">\bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_{i}</script>

	<p>and standard deviation:</p>

	<script type="math/tex; mode=display">\sigma_{x}=\sqrt{ \frac{1}{n} \sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}</script>

	<p>The scaled data set $z_1, z_2,…,z_n$ will be:</p>

	<script type="math/tex; mode=display">z_{i}= std \left (\frac{x_{i} - \bar{x} }{\sigma_{x}}\right ) + mean</script>

	<p>where $\textit{std}$ and $\textit{mean}$ are the user specified values for the standard deviation and mean.</p>

	<h2 id="operations">Operations</h2>

	<p><code>StandardScaler</code> is a <code>Transformer</code>.
	As such, it supports the <code>fit</code> and <code>transform</code> operation.</p>

	<h3 id="fit">Fit</h3>

	<p>StandardScaler is trained on all subtypes of <code>Vector</code> or <code>LabeledVector</code>:</p>

	<ul>
	<li><code>fit[T <: Vector]: DataSet[T] => Unit</code></li>
	<li><code>fit: DataSet[LabeledVector] => Unit</code></li>
	</ul>

	<h3 id="transform">Transform</h3>

	<p>StandardScaler transforms all subtypes of <code>Vector</code> or <code>LabeledVector</code> into the respective type:</p>

	<ul>
	<li><code>transform[T <: Vector]: DataSet[T] => DataSet[T]</code></li>
	<li><code>transform: DataSet[LabeledVector] => DataSet[LabeledVector]</code></li>
	</ul>

	<h2 id="parameters">Parameters</h2>

	<p>The standard scaler implementation can be controlled by the following two parameters:</p>

	<table class="table table-bordered">
	<thead>
	<tr>
	<th class="text-left" style="width: 20%">Parameters</th>
	<th class="text-center">Description</th>
	</tr>
	</thead>

	<tbody>
	<tr>
	<td><strong>Mean</strong></td>
	<td>
	<p>
	The mean of the scaled data set. (Default value: <strong>0.0</strong>)
	</p>
	</td>
	</tr>
	<tr>
	<td><strong>Std</strong></td>
	<td>
	<p>
	The standard deviation of the scaled data set. (Default value: <strong>1.0</strong>)
	</p>
	</td>
	</tr>
	</tbody>
	</table>

	<h2 id="examples">Examples</h2>

	<div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="c1">// Create standard scaler transformer</span>
	<span class="k">val</span> <span class="n">scaler</span> <span class="k">=</span> <span class="nc">StandardScaler</span><span class="o">()</span>
	<span class="o">.</span><span class="n">setMean</span><span class="o">(</span><span class="mf">10.0</span><span class="o">)</span>
	<span class="o">.</span><span class="n">setStd</span><span class="o">(</span><span class="mf">2.0</span><span class="o">)</span>

	<span class="c1">// Obtain data set to be scaled</span>
	<span class="k">val</span> <span class="n">dataSet</span><span class="k">:</span> <span class="kt">DataSet</span><span class="o">[</span><span class="kt">Vector</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span>

	<span class="c1">// Learn the mean and standard deviation of the training data</span>
	<span class="n">scaler</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">dataSet</span><span class="o">)</span>

	<span class="c1">// Scale the provided data set to have mean=10.0 and std=2.0</span>
	<span class="k">val</span> <span class="n">scaledDS</span> <span class="k">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">transform</span><span class="o">(</span><span class="n">dataSet</span><span class="o">)</span></code></pre></div>


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