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     <h1><a href="../ml">FlinkML</a> - Distance Metrics</h1>


 <ul id="markdown-toc">
   <li><a href="#description" id="markdown-toc-description">Description</a></li>
   <li><a href="#built-in-implementations" id="markdown-toc-built-in-implementations">Built-in Implementations</a></li>
   <li><a href="#custom-implementation" id="markdown-toc-custom-implementation">Custom Implementation</a></li>
 </ul>

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

 <p>Different metrics of distance are convenient for different types of analysis. Flink ML provides
 built-in implementations for many standard distance metrics. You can create custom
 distance metrics by implementing the <code>DistanceMetric</code> trait.</p>

 <h2 id="built-in-implementations">Built-in Implementations</h2>

 <p>Currently, FlinkML supports the following metrics:</p>

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

     <tbody>
       <tr>
         <td><strong>Euclidean Distance</strong></td>
         <td>
           $$d(\x, \y) = \sqrt{\sum_{i=1}^n \left(x_i - y_i \right)^2}$$
         </td>
       </tr>
       <tr>
         <td><strong>Squared Euclidean Distance</strong></td>
         <td>
           $$d(\x, \y) = \sum_{i=1}^n \left(x_i - y_i \right)^2$$
         </td>
       </tr>
       <tr>
         <td><strong>Cosine Similarity</strong></td>
         <td>
           $$d(\x, \y) = 1 - \frac{\x^T \y}{\Vert \x \Vert \Vert \y \Vert}$$
         </td>
       </tr>
       <tr>
         <td><strong>Chebyshev Distance</strong></td>
         <td>
           $$d(\x, \y) = \max_{i}\left(\left \vert x_i - y_i \right\vert \right)$$
         </td>
       </tr>
       <tr>
         <td><strong>Manhattan Distance</strong></td>
         <td>
           $$d(\x, \y) = \sum_{i=1}^n \left\vert x_i - y_i \right\vert$$
         </td>
       </tr>
       <tr>
         <td><strong>Minkowski Distance</strong></td>
         <td>
           $$d(\x, \y) = \left( \sum_{i=1}^{n} \left( x_i - y_i \right)^p \right)^{\rfrac{1}{p}}$$
         </td>
       </tr>
       <tr>
         <td><strong>Tanimoto Distance</strong></td>
         <td>
           $$d(\x, \y) = 1 - \frac{\x^T\y}{\Vert \x \Vert^2 + \Vert \y \Vert^2 - \x^T\y}$$
           with $\x$ and $\y$ being bit-vectors
         </td>
       </tr>
     </tbody>
   </table>

 <h2 id="custom-implementation">Custom Implementation</h2>

 <p>You can create your own distance metric by implementing the <code>DistanceMetric</code> trait.</p>

 <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">class</span> <span class="nc">MyDistance</span> <span class="k">extends</span> <span class="nc">DistanceMetric</span> <span class="o">{</span>
   <span class="k">override</span> <span class="k">def</span> <span class="n">distance</span><span class="o">(</span><span class="n">a</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">,</span> <span class="n">b</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">)</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// your implementation for distance metric</span>
 <span class="o">}</span>

 <span class="k">object</span> <span class="nc">MyDistance</span> <span class="o">{</span>
   <span class="k">def</span> <span class="n">apply</span><span class="o">()</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MyDistance</span><span class="o">()</span>
 <span class="o">}</span>

 <span class="k">val</span> <span class="n">myMetric</span> <span class="k">=</span> <span class="nc">MyDistance</span><span class="o">()</span></code></pre></div>


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	<h1><a href="../ml">FlinkML</a> - Distance Metrics</h1>



	<ul id="markdown-toc">
	<li><a href="#description" id="markdown-toc-description">Description</a></li>
	<li><a href="#built-in-implementations" id="markdown-toc-built-in-implementations">Built-in Implementations</a></li>
	<li><a href="#custom-implementation" id="markdown-toc-custom-implementation">Custom Implementation</a></li>
	</ul>

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

	<p>Different metrics of distance are convenient for different types of analysis. Flink ML provides
	built-in implementations for many standard distance metrics. You can create custom
	distance metrics by implementing the <code>DistanceMetric</code> trait.</p>

	<h2 id="built-in-implementations">Built-in Implementations</h2>

	<p>Currently, FlinkML supports the following metrics:</p>

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

	<tbody>
	<tr>
	<td><strong>Euclidean Distance</strong></td>
	<td>
	$$d(\x, \y) = \sqrt{\sum_{i=1}^n \left(x_i - y_i \right)^2}$$
	</td>
	</tr>
	<tr>
	<td><strong>Squared Euclidean Distance</strong></td>
	<td>
	$$d(\x, \y) = \sum_{i=1}^n \left(x_i - y_i \right)^2$$
	</td>
	</tr>
	<tr>
	<td><strong>Cosine Similarity</strong></td>
	<td>
	$$d(\x, \y) = 1 - \frac{\x^T \y}{\Vert \x \Vert \Vert \y \Vert}$$
	</td>
	</tr>
	<tr>
	<td><strong>Chebyshev Distance</strong></td>
	<td>
	$$d(\x, \y) = \max_{i}\left(\left \vert x_i - y_i \right\vert \right)$$
	</td>
	</tr>
	<tr>
	<td><strong>Manhattan Distance</strong></td>
	<td>
	$$d(\x, \y) = \sum_{i=1}^n \left\vert x_i - y_i \right\vert$$
	</td>
	</tr>
	<tr>
	<td><strong>Minkowski Distance</strong></td>
	<td>
	$$d(\x, \y) = \left( \sum_{i=1}^{n} \left( x_i - y_i \right)^p \right)^{\rfrac{1}{p}}$$
	</td>
	</tr>
	<tr>
	<td><strong>Tanimoto Distance</strong></td>
	<td>
	$$d(\x, \y) = 1 - \frac{\x^T\y}{\Vert \x \Vert^2 + \Vert \y \Vert^2 - \x^T\y}$$
	with $\x$ and $\y$ being bit-vectors
	</td>
	</tr>
	</tbody>
	</table>

	<h2 id="custom-implementation">Custom Implementation</h2>

	<p>You can create your own distance metric by implementing the <code>DistanceMetric</code> trait.</p>

	<div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">class</span> <span class="nc">MyDistance</span> <span class="k">extends</span> <span class="nc">DistanceMetric</span> <span class="o">{</span>
	<span class="k">override</span> <span class="k">def</span> <span class="n">distance</span><span class="o">(</span><span class="n">a</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">,</span> <span class="n">b</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">)</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// your implementation for distance metric</span>
	<span class="o">}</span>

	<span class="k">object</span> <span class="nc">MyDistance</span> <span class="o">{</span>
	<span class="k">def</span> <span class="n">apply</span><span class="o">()</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MyDistance</span><span class="o">()</span>
	<span class="o">}</span>

	<span class="k">val</span> <span class="n">myMetric</span> <span class="k">=</span> <span class="nc">MyDistance</span><span class="o">()</span></code></pre></div>


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