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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
Examp
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 "dimensionality reduction"
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'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'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 "convenient" 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
<Your new engine directory>
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class="level-2"><a class="final"
href="/datacollection/batchimport/"><span>Importing Data in
Batch</span></a></li><li class="level-2"><a class="final"
href="/datacollection/analytics/"><span>Using Analytics
Tools</span></a></li><li class="level-2"><a class="final"
href="/datacollection/plugin/"><span>Event Server Plugin</span></a></li><
/ul></li><li class="level-1"><a class="expandible" href="#"><span>Choosing an
Algorithm(s)</span></a><ul><li class="level-2"><a class="final"
href="/algorithm/"><span>Built-in Algorithm Libraries</span></a></li><li
class="level-2"><a class="final" href="/algorithm/switch/"><span>Switching to
Another Algorithm</span></a></li><li class="level-2"><a class="final"
href="/algorithm/multiple/"><span>Combining Multiple
Algorithms</span></a></li><li class="level-2"><a class="final"
href="/algorithm/custom/"><span>Adding Your Own
Algorithms</span></a></li></ul></li><li class="level-1"><a class="expandible"
href="#"><span>ML Tuning and Evaluation</span></a><ul><li class="level-2"><a
class="final" href="/evaluation/"><span>Overview</span></a></li><li
class="level-2"><a class="final"
href="/evaluation/paramtuning/"><span>Hyperparameter Tuning</span></a></li><li
class="level-2"><a class="final"
href="/evaluation/evaluationdashboard/"><span>Evaluation
Dashboard</span></a></li><li class="level-2">
<a class="final" href="/evaluation/metricchoose/"><span>Choosing Evaluation
Metrics</span></a></li><li class="level-2"><a class="final"
href="/evaluation/metricbuild/"><span>Building Evaluation
Metrics</span></a></li></ul></li><li class="level-1"><a class="expandible"
href="#"><span>System Architecture</span></a><ul><li class="level-2"><a
class="final" href="/system/"><span>Architecture Overview</span></a></li><li
class="level-2"><a class="final" href="/system/anotherdatastore/"><span>Using
Another Data Store</span></a></li></ul></li><li class="level-1"><a
class="expandible" href="#"><span>PredictionIO® Official
Templates</span></a><ul><li class="level-2"><a class="final"
href="/templates/"><span>Intro</span></a></li><li class="level-2"><a
class="expandible" href="#"><span>Recommendation</span></a><ul><li
class="level-3"><a class="final"
href="/templates/recommendation/quickstart/"><span>Quick
Start</span></a></li><li class="level-3"><a class="final"
href="/templates/recommendation
/dase/"><span>DASE</span></a></li><li class="level-3"><a class="final"
href="/templates/recommendation/evaluation/"><span>Evaluation
Explained</span></a></li><li class="level-3"><a class="final"
href="/templates/recommendation/how-to/"><span>How-To</span></a></li><li
class="level-3"><a class="final"
href="/templates/recommendation/reading-custom-events/"><span>Read Custom
Events</span></a></li><li class="level-3"><a class="final"
href="/templates/recommendation/customize-data-prep/"><span>Customize Data
Preparator</span></a></li><li class="level-3"><a class="final"
href="/templates/recommendation/customize-serving/"><span>Customize
Serving</span></a></li><li class="level-3"><a class="final"
href="/templates/recommendation/training-with-implicit-preference/"><span>Train
with Implicit Preference</span></a></li><li class="level-3"><a class="final"
href="/templates/recommendation/blacklist-items/"><span>Filter Recommended
Items by Blacklist in Query</span></a></li><li class="level-3"><a
class="final" href="/templates/recommendation/batch-evaluator/"><span>Batch
Persistable Evaluator</span></a></li></ul></li><li class="level-2"><a
class="expandible" href="#"><span>E-Commerce Recommendation</span></a><ul><li
class="level-3"><a class="final"
href="/templates/ecommercerecommendation/quickstart/"><span>Quick
Start</span></a></li><li class="level-3"><a class="final"
href="/templates/ecommercerecommendation/dase/"><span>DASE</span></a></li><li
class="level-3"><a class="final"
href="/templates/ecommercerecommendation/how-to/"><span>How-To</span></a></li><li
class="level-3"><a class="final"
href="/templates/ecommercerecommendation/train-with-rate-event/"><span>Train
with Rate Event</span></a></li><li class="level-3"><a class="final"
href="/templates/ecommercerecommendation/adjust-score/"><span>Adjust
Score</span></a></li></ul></li><li class="level-2"><a class="expandible"
href="#"><span>Similar Product</span></a><ul><li class="level-3"><a
class="final" href="/templates/sim
ilarproduct/quickstart/"><span>Quick Start</span></a></li><li
class="level-3"><a class="final"
href="/templates/similarproduct/dase/"><span>DASE</span></a></li><li
class="level-3"><a class="final"
href="/templates/similarproduct/how-to/"><span>How-To</span></a></li><li
class="level-3"><a class="final"
href="/templates/similarproduct/multi-events-multi-algos/"><span>Multiple
Events and Multiple Algorithms</span></a></li><li class="level-3"><a
class="final"
href="/templates/similarproduct/return-item-properties/"><span>Returns Item
Properties</span></a></li><li class="level-3"><a class="final"
href="/templates/similarproduct/train-with-rate-event/"><span>Train with Rate
Event</span></a></li><li class="level-3"><a class="final"
href="/templates/similarproduct/rid-user-set-event/"><span>Get Rid of Events
for Users</span></a></li><li class="level-3"><a class="final"
href="/templates/similarproduct/recommended-user/"><span>Recommend
Users</span></a></li></ul></li><li class="level-2"><a cl
ass="expandible" href="#"><span>Classification</span></a><ul><li
class="level-3"><a class="final"
href="/templates/classification/quickstart/"><span>Quick
Start</span></a></li><li class="level-3"><a class="final"
href="/templates/classification/dase/"><span>DASE</span></a></li><li
class="level-3"><a class="final"
href="/templates/classification/how-to/"><span>How-To</span></a></li><li
class="level-3"><a class="final"
href="/templates/classification/add-algorithm/"><span>Use Alternative
Algorithm</span></a></li><li class="level-3"><a class="final"
href="/templates/classification/reading-custom-properties/"><span>Read Custom
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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 "dimensionality reduction"
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'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'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 "convenient" 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
<Your new engine directory>
</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
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