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<a class="navbar-brand" href="week43-bs.html">Week 43: Deep Learning: Recurrent Neural Networks and other Deep Learning Methods. Principal Component analysis</a>
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<!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Reading Recommendations</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Summary on Deep Learning Methods</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>Recurrent neural networks: Overarching view</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>Formatting the Data</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>Predicting New Points With A Trained Recurrent Neural Network</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Other Things to Try</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Other Types of Recurrent Neural Networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Writing Our First Generative Adversarial Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Training Step</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>Exploring the Latent Space</b></a></li>
<!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;"><b>Getting Results</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Interpolating Between MNIST Digits</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>More on the covariance</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Reminding ourselves about Linear Regression</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>Simple Example</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Correlation Matrix again</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Implementing it</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>First Step</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>Exploring</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>Diagonalize the sample covariance matrix to obtain the principal components</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec55" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Randomized PCA</a></li>
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<h2 id="___sec24" class="anchor">Getting Results </h2>
We see that the generator generates images that look like MNIST
numbers: \( 1, 4, 7, 9 \). Let's try to tweak it a bit more to see if we are able
to generate a similar plot where we generate every MNIST number. Let us now try
to 'move' a bit around in the latent space. <b>Note</b>: decrease the plot number if
these following cells take too long to run on your computer.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>plot_number <span style="color: #666666">=</span> <span style="color: #666666">225</span>
generated_images <span style="color: #666666">=</span> generate_images(generate_latent_points(number<span style="color: #666666">=</span>plot_number,
scale_means<span style="color: #666666">=5</span>,
scale_stds<span style="color: #666666">=1</span>))
plot_result(generated_images, number<span style="color: #666666">=</span>plot_number)
generated_images <span style="color: #666666">=</span> generate_images(generate_latent_points(number<span style="color: #666666">=</span>plot_number,
scale_means<span style="color: #666666">=-5</span>,
scale_stds<span style="color: #666666">=1</span>))
plot_result(generated_images, number<span style="color: #666666">=</span>plot_number)
generated_images <span style="color: #666666">=</span> generate_images(generate_latent_points(number<span style="color: #666666">=</span>plot_number,
scale_means<span style="color: #666666">=1</span>,
scale_stds<span style="color: #666666">=5</span>))
plot_result(generated_images, number<span style="color: #666666">=</span>plot_number)
</pre></div>
<p>
Again, we have found something interesting. <em>Moving</em> around using our means
takes us from digit to digit, while <em>moving</em> around using our standard
deviations seem to increase the number of different digits! In the last image
above, we can barely make out every MNIST digit. Let us make on last plot using
this information by upping the standard deviation of our Gaussian noises.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>plot_number <span style="color: #666666">=</span> <span style="color: #666666">400</span>
generated_images <span style="color: #666666">=</span> generate_images(generate_latent_points(number<span style="color: #666666">=</span>plot_number,
scale_means<span style="color: #666666">=1</span>,
scale_stds<span style="color: #666666">=10</span>))
plot_result(generated_images, number<span style="color: #666666">=</span>plot_number)
</pre></div>
<p>
A pretty cool result! We see that our generator indeed has learned a
distribution which qualitatively looks a whole lot like the MNIST dataset.
<p>
<p>
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