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-<!DOCTYPE html><html><head><title>Dimensionality Reduction With PredictionIO</title><meta charset="utf-8"/><meta content="IE=edge,chrome=1" http-equiv="X-UA-Compatible"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><meta class="swiftype" name="title" data-type="string" content="Dimensionality Reduction With PredictionIO"/><link rel="canonical" href="https://predictionio.apache.org/machinelearning/dimensionalityreduction/"/><link href="/images/favicon/normal-b330020a.png" rel="shortcut icon"/><link href="/images/favicon/apple-c0febcf2.png" rel="apple-touch-icon"/><link href="//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,600italic,700italic,800italic,400,300,600,700,800" rel="stylesheet"/><link href="//maxcdn.bootstrapcdn.com/font-awesome/4.2.0/css/font-awesome.min.css" rel="stylesheet"/><link href="/stylesheets/application-eccfc6cb.css" rel="stylesheet" type="text/css"/><script src="//cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.2/html5shiv
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 div class="row"><div class="col-md-9 col-sm-11 col-xs-11"><div class="hidden-md hidden-lg" id="mobile-page-heading-wrapper"><p>PredictionIO Docs</p><h4>Dimensionality Reduction With PredictionIO</h4></div><h4 class="hidden-sm hidden-xs">PredictionIO Docs</h4></div><div class="col-md-3 col-sm-1 col-xs-1 hidden-md hidden-lg"><img id="left-menu-indicator" src="/images/icons/down-arrow-dfe9f7fe.png"/></div><div class="col-md-3 col-sm-12 col-xs-12 swiftype-wrapper"><div class="swiftype"><form class="search-form"><img class="search-box-toggler hidden-xs hidden-sm" src="/images/icons/search-glass-704bd4ff.png"/><div class="search-box"><img src="/images/icons/search-glass-704bd4ff.png"/><input type="text" id="st-search-input" class="st-search-input" placeholder="Search Doc..."/></div><img class="swiftype-row-hider hidden-md hidden-lg" src="/images/icons/drawer-toggle-active-fcbef12a.png"/></form></div></div><div class="mobile-left-menu-toggler hidden-md hidden-lg"></div></div></div></div><d
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 le</a> </li> <li> <a href="#principal-component-analysis">Principal Component Analysis</a> </li> <li> <a href="#modifying-the-engine-template">Modifying the Engine Template</a> </li> <li> <a href="#testing-the-engine">Testing the Engine</a> </li> </ul> </aside><hr/><a id="edit-page-link" href="https://github.com/apache/incubator-predictionio/tree/livedoc/docs/manual/source/machinelearning/dimensionalityreduction.html.md"><img src="/images/icons/edit-pencil-d6c1bb3d.png"/>Edit this page</a></div><div class="content-header hidden-sm hidden-xs"><div id="page-title"><h1>Dimensionality Reduction With PredictionIO</h1></div></div><div class="content"> <p>The purpose of this guide is to teach developers how to incorporate &quot;dimensionality reduction&quot; into a PredictionIO engine <a href="https://en.wikipedia.org/wiki/Principal_component_analysis">Principal Component Analysis</a> (PCA) on the <a href="https://www.kaggle.com/c/digit-recognizer">MNIST digit recognition dataset</a>. To d
 o this, you will be modifying the PredictionIO <a href="/gallery/template-gallery/#classification">classification engine template</a>. This guide will demonstrate how to import the specific data set in batch, and also how to change the engine components in order to incorporate the new sample data and implement PCA.</p><p>In machine learning, specifically in <a href="http://en.wikipedia.org/wiki/Supervised_learning">supervised learning</a>, the general problem at hand is to predict a numeric outcome \(y\) from a numeric vector \(\bf{x}\). The different components of \(\bf{x}\) are called <strong>features</strong>, and usually represent observed values such as a hospital patient&#39;s age, weight, height, sex, etc. There are subtle issues that begin to arise as the number of features contained in each feature vector increases. We briefly list some of the issues that arise as the number of features grows in size:</p> <ul> <li><p><strong>Computation:</strong> The time complexity of mach
 ine learning algorithms often times depends on the number of features used. That is, the more features one uses for prediction, the more time it takes to train a model.</p></li> <li><p><strong>Prediction Performance:</strong> Often times there will be features that, when used in training, will actually decrease the predictive performance of a particular algorithm. </p></li> <li><p><strong>Curse of Dimensionality:</strong> It is harder to make inference and predictions in high dimensional spaces simply due to the fact that we need to sample a lot more observations. Think about it in this way, suppose that we sample 100 points lying on a flat solid square, and 100 points in a solid cube. The 100 points from the square will likely take up a larger proportion of its area, in comparison to the proportion of the cube&#39;s volume that the points sampled from it occupy. Hence we would need to sample more points from the cube in order to get better estimates of the different properties of t
 he cube, such as height, length, and width. This is shown in the following figure:</p></li> </ul> <table><thead> <tr> <th>100 Points Sampled From Unit Square</th> <th>100 Points Sampled From Unit Cube</th> </tr> </thead><tbody> <tr> <td></td> <td></td> </tr> <tr> <td><img alt="Square Samples" src="/images/machinelearning/featureselection/square100-df83c1ae.png"/></td> <td><img alt="Cube Samples" src="/images/machinelearning/featureselection/cube100-a8fe5433.png"/></td> </tr> <tr> <td></td> <td></td> </tr> </tbody></table> <p>Dimensionality reduction is the process of applying a transformation to your feature vectors in order to produce a vector with the same or less number of features. Principal component Analysis (PCA) is a technique for dimensionality reduction. This can be treated as a data processing technique, and so with respect to the <a href="/customize/">DASE</a> framework, it will fall into the Data Preparator engine component.</p><p>This guide will also help to solidify t
 he concept of taking an engine template and customizing it for a particular use case: hand-written numeric digit recognition.</p><h2 id='data-example' class='header-anchors'>Data Example</h2><p>As a guiding example, a base data set, the <a href="https://www.kaggle.com/c/digit-recognizer/data">MNIST digit recognition dataset</a>, is used. This is a perfect data set for dimensionality reduction, for, in this data set, the features that will be used for learning are pixel entries in a \(28 \times 28\) pixel image. There is really no direct interpretation of any one feature, so that you do not lose anything in applying a transformation that will treat the features as <a href="https://en.wikipedia.org/wiki/Linear_combination">linear combinations</a> of some set &quot;convenient&quot; vectors.</p><p>Now, we first pull the <a href="/gallery/template-gallery/#classification">classification engine template</a> via the following bash line</p><div class="highlight shell"><table style="border-s
 pacing: 0"><tbody><tr><td class="gutter gl" style="text-align: right"><pre class="lineno">1</pre></td><td class="code"><pre>git clone https://github.com/apache/incubator-predictionio-template-attribute-based-classifier.git &lt;Your new engine directory&gt;
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 /li><li class="level-1"><a class="expandible" href="#"><span>Apache Software Foundation</span></a><ul><li class="level-2"><a class="final" href="https://www.apache.org/"><span>Apache Homepage</span></a></li><li class="level-2"><a class="final" href="https://www.apache.org/licenses/"><span>License</span></a></li><li class="level-2"><a class="final" href="https://www.apache.org/foundation/sponsorship.html"><span>Sponsorship</span></a></li><li class="level-2"><a class="final" href="https://www.apache.org/foundation/thanks.html"><span>Thanks</span></a></li><li class="level-2"><a class="final" href="https://www.apache.org/security/"><span>Security</span></a></li></ul></li></ul></nav></div><div class="col-md-9 col-sm-12"><div class="content-header hidden-md hidden-lg"><div id="page-title"><h1>Dimensionality Reduction With PredictionIO</h1></div></div><div id="table-of-content-wrapper"><h5>On this page</h5><aside id="table-of-contents"><ul> <li> <a href="#data-example">Data Example</a> </l
 i> <li> <a href="#principal-component-analysis">Principal Component Analysis</a> </li> <li> <a href="#modifying-the-engine-template">Modifying the Engine Template</a> </li> <li> <a href="#testing-the-engine">Testing the Engine</a> </li> </ul> </aside><hr/><a id="edit-page-link" href="https://github.com/apache/predictionio/tree/livedoc/docs/manual/source/machinelearning/dimensionalityreduction.html.md"><img src="/images/icons/edit-pencil-d6c1bb3d.png"/>Edit this page</a></div><div class="content-header hidden-sm hidden-xs"><div id="page-title"><h1>Dimensionality Reduction With PredictionIO</h1></div></div><div class="content"> <p>The purpose of this guide is to teach developers how to incorporate &quot;dimensionality reduction&quot; into a PredictionIO engine <a href="https://en.wikipedia.org/wiki/Principal_component_analysis">Principal Component Analysis</a> (PCA) on the <a href="https://www.kaggle.com/c/digit-recognizer">MNIST digit recognition dataset</a>. To do this, you will be 
 modifying the PredictionIO <a href="/gallery/template-gallery/#classification">classification engine template</a>. This guide will demonstrate how to import the specific data set in batch, and also how to change the engine components in order to incorporate the new sample data and implement PCA.</p><p>In machine learning, specifically in <a href="http://en.wikipedia.org/wiki/Supervised_learning">supervised learning</a>, the general problem at hand is to predict a numeric outcome \(y\) from a numeric vector \(\bf{x}\). The different components of \(\bf{x}\) are called <strong>features</strong>, and usually represent observed values such as a hospital patient&#39;s age, weight, height, sex, etc. There are subtle issues that begin to arise as the number of features contained in each feature vector increases. We briefly list some of the issues that arise as the number of features grows in size:</p> <ul> <li><p><strong>Computation:</strong> The time complexity of machine learning algorit
 hms often times depends on the number of features used. That is, the more features one uses for prediction, the more time it takes to train a model.</p></li> <li><p><strong>Prediction Performance:</strong> Often times there will be features that, when used in training, will actually decrease the predictive performance of a particular algorithm. </p></li> <li><p><strong>Curse of Dimensionality:</strong> It is harder to make inference and predictions in high dimensional spaces simply due to the fact that we need to sample a lot more observations. Think about it in this way, suppose that we sample 100 points lying on a flat solid square, and 100 points in a solid cube. The 100 points from the square will likely take up a larger proportion of its area, in comparison to the proportion of the cube&#39;s volume that the points sampled from it occupy. Hence we would need to sample more points from the cube in order to get better estimates of the different properties of the cube, such as hei
 ght, length, and width. This is shown in the following figure:</p></li> </ul> <table><thead> <tr> <th>100 Points Sampled From Unit Square</th> <th>100 Points Sampled From Unit Cube</th> </tr> </thead><tbody> <tr> <td></td> <td></td> </tr> <tr> <td><img alt="Square Samples" src="/images/machinelearning/featureselection/square100-df83c1ae.png"/></td> <td><img alt="Cube Samples" src="/images/machinelearning/featureselection/cube100-a8fe5433.png"/></td> </tr> <tr> <td></td> <td></td> </tr> </tbody></table> <p>Dimensionality reduction is the process of applying a transformation to your feature vectors in order to produce a vector with the same or less number of features. Principal component Analysis (PCA) is a technique for dimensionality reduction. This can be treated as a data processing technique, and so with respect to the <a href="/customize/">DASE</a> framework, it will fall into the Data Preparator engine component.</p><p>This guide will also help to solidify the concept of taking
  an engine template and customizing it for a particular use case: hand-written numeric digit recognition.</p><h2 id='data-example' class='header-anchors'>Data Example</h2><p>As a guiding example, a base data set, the <a href="https://www.kaggle.com/c/digit-recognizer/data">MNIST digit recognition dataset</a>, is used. This is a perfect data set for dimensionality reduction, for, in this data set, the features that will be used for learning are pixel entries in a \(28 \times 28\) pixel image. There is really no direct interpretation of any one feature, so that you do not lose anything in applying a transformation that will treat the features as <a href="https://en.wikipedia.org/wiki/Linear_combination">linear combinations</a> of some set &quot;convenient&quot; vectors.</p><p>Now, we first pull the <a href="/gallery/template-gallery/#classification">classification engine template</a> via the following bash line</p><div class="highlight shell"><table style="border-spacing: 0"><tbody><t
 r><td class="gutter gl" style="text-align: right"><pre class="lineno">1</pre></td><td class="code"><pre>git clone https://github.com/apache/predictionio-template-attribute-based-classifier.git &lt;Your new engine directory&gt;
 </pre></td></tr></tbody></table> </div> <p>You should immediately be prompted with the following message:</p><div class="highlight shell"><table style="border-spacing: 0"><tbody><tr><td class="gutter gl" style="text-align: right"><pre class="lineno">1</pre></td><td class="code"><pre>Please enter the template<span class="s1">'s Scala package name (e.g. com.mycompany):
 </span></pre></td></tr></tbody></table> </div> <p>Go ahead and input <code>FeatureReduction</code>, and feel free to just press enter for the remaining message prompts. For the remainder of this guide, you will be working in your new engine directory, so go ahead and <code>cd</code> into your new engine directory. At this point, go ahead and run the command</p><div class="highlight shell"><table style="border-spacing: 0"><tbody><tr><td class="gutter gl" style="text-align: right"><pre class="lineno">1</pre></td><td class="code"><pre>pio build
 </pre></td></tr></tbody></table> </div> <p>This will make sure that the PredictionIO dependency version for your project matches the version installed on your computer. Now, download the MNIST <code>train.csv</code> data set from the link above, and put this file in the <code>data</code> directory contained in the new engine directory.</p><h3 id='<strong>optional</strong>:-visualizing-observations' class='header-anchors' ><strong>Optional</strong>: Visualizing Observations</h3><p>If you want to actually convert the observation pixel data to an image go ahead and create a Python script called <code>picture_processing.py</code> into your data directory and copy and paste the following code into the script:</p><div class="highlight python"><table style="border-spacing: 0"><tbody><tr><td class="gutter gl" style="text-align: right"><pre class="lineno">1
@@ -734,7 +734,7 @@ pio deploy
 
 <span class="n">os</span><span class="o">.</span><span class="n">system</span><span class="p">(</span><span class="n">qry</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s">"..."</span><span class="p">,</span> <span class="nb">str</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">obs_num</span><span class="p">])[</span><span class="mi">1</span> <span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">]))</span>
 </pre></td></tr></tbody></table> </div> <p>In your engine directory file, you can now use the following line to query the engine with a test observation by using the command</p><div class="highlight shell"><table style="border-spacing: 0"><tbody><tr><td class="gutter gl" style="text-align: right"><pre class="lineno">1</pre></td><td class="code"><pre>python data/query.py k
-</pre></td></tr></tbody></table> </div> <p>where you replace <code>k</code> with a number between 0 and 27,999 (corresponds to test observations). This will generate the digit image first, and then immediately return the predicted digit for your reference.</p></div></div></div></div><footer><div class="container"><div class="seperator"></div><div class="row"><div class="col-md-6 footer-link-column"><div class="footer-link-column-row"><h4>Community</h4><ul><li><a href="//predictionio.apache.org/install/" target="blank">Download</a></li><li><a href="//predictionio.apache.org/" target="blank">Docs</a></li><li><a href="//github.com/apache/incubator-predictionio" target="blank">GitHub</a></li><li><a href="mailto:user-subscribe@predictionio.apache.org" target="blank">Subscribe to User Mailing List</a></li><li><a href="//stackoverflow.com/questions/tagged/predictionio" target="blank">Stackoverflow</a></li></ul></div></div><div class="col-md-6 footer-link-column"><div class="footer-link-col
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+</pre></td></tr></tbody></table> </div> <p>where you replace <code>k</code> with a number between 0 and 27,999 (corresponds to test observations). This will generate the digit image first, and then immediately return the predicted digit for your reference.</p></div></div></div></div><footer><div class="container"><div class="seperator"></div><div class="row"><div class="col-md-6 footer-link-column"><div class="footer-link-column-row"><h4>Community</h4><ul><li><a href="//predictionio.apache.org/install/" target="blank">Download</a></li><li><a href="//predictionio.apache.org/" target="blank">Docs</a></li><li><a href="//github.com/apache/predictionio" target="blank">GitHub</a></li><li><a href="mailto:user-subscribe@predictionio.apache.org" target="blank">Subscribe to User Mailing List</a></li><li><a href="//stackoverflow.com/questions/tagged/predictionio" target="blank">Stackoverflow</a></li></ul></div></div><div class="col-md-6 footer-link-column"><div class="footer-link-column-row"><
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