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<div class="section" id="stimuli-data-analysis">
<h1>Stimuli data analysis<a class="headerlink" href="#stimuli-data-analysis" title="Permalink to this headline">¶</a></h1>
<p>You can enable stimuli data reporting with the following section (the
name of the section must start with <code class="docutils literal notranslate"><span class="pre">env.StimuliData</span></code>):</p>
<div class="highlight-ini notranslate"><div class="highlight"><pre><span></span><span class="k">[env.StimuliData-raw]</span>
<span class="na">ApplyTo</span><span class="o">=</span><span class="s">LearnOnly</span>
<span class="na">LogSizeRange</span><span class="o">=</span><span class="s">1</span>
<span class="na">LogValueRange</span><span class="o">=</span><span class="s">1</span>
</pre></div>
</div>
<p>The stimuli data reported for the full MNIST learning set will look
like:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">env</span><span class="o">.</span><span class="n">StimuliData</span><span class="o">-</span><span class="n">raw</span> <span class="n">data</span><span class="p">:</span>
<span class="n">Number</span> <span class="n">of</span> <span class="n">stimuli</span><span class="p">:</span> <span class="mi">60000</span>
<span class="n">Data</span> <span class="n">width</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">]</span>
<span class="n">Data</span> <span class="n">height</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">]</span>
<span class="n">Data</span> <span class="n">channels</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">Value</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">255</span><span class="p">]</span>
<span class="n">Value</span> <span class="n">mean</span><span class="p">:</span> <span class="mf">33.3184</span>
<span class="n">Value</span> <span class="n">std</span><span class="o">.</span> <span class="n">dev</span><span class="o">.</span><span class="p">:</span> <span class="mf">78.5675</span>
</pre></div>
</div>
<div class="section" id="zero-mean-and-unity-standard-deviation-normalization">
<h2>Zero-mean and unity standard deviation normalization<a class="headerlink" href="#zero-mean-and-unity-standard-deviation-normalization" title="Permalink to this headline">¶</a></h2>
<p>It it possible to normalize the whole database to have zero mean and
unity standard deviation on the learning set using a
<code class="docutils literal notranslate"><span class="pre">RangeAffineTransformation</span></code> transformation:</p>
<div class="highlight-ini notranslate"><div class="highlight"><pre><span></span><span class="c1">; Stimuli normalization based on learning set global mean and std.dev.</span>
<span class="k">[env.Transformation-normalize]</span>
<span class="na">Type</span><span class="o">=</span><span class="s">RangeAffineTransformation</span>
<span class="na">FirstOperator</span><span class="o">=</span><span class="s">Minus</span>
<span class="na">FirstValue</span><span class="o">=</span><span class="s">[env.StimuliData-raw]_GlobalValue.mean</span>
<span class="na">SecondOperator</span><span class="o">=</span><span class="s">Divides</span>
<span class="na">SecondValue</span><span class="o">=</span><span class="s">[env.StimuliData-raw]_GlobalValue.stdDev</span>
</pre></div>
</div>
<p>The variables <code class="docutils literal notranslate"><span class="pre">_GlobalValue.mean</span></code> and <code class="docutils literal notranslate"><span class="pre">_GlobalValue.stdDev</span></code> are
automatically generated in the <code class="docutils literal notranslate"><span class="pre">[env.StimuliData-raw]</span></code> block. Thanks
to this facility, unknown and arbitrary database can be analysed and
normalized in one single step without requiring any external data
manipulation.</p>
<p>After normalization, the stimuli data reported is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">env</span><span class="o">.</span><span class="n">StimuliData</span><span class="o">-</span><span class="n">normalized</span> <span class="n">data</span><span class="p">:</span>
<span class="n">Number</span> <span class="n">of</span> <span class="n">stimuli</span><span class="p">:</span> <span class="mi">60000</span>
<span class="n">Data</span> <span class="n">width</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">]</span>
<span class="n">Data</span> <span class="n">height</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">]</span>
<span class="n">Data</span> <span class="n">channels</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">Value</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.424074</span><span class="p">,</span> <span class="mf">2.82154</span><span class="p">]</span>
<span class="n">Value</span> <span class="n">mean</span><span class="p">:</span> <span class="mf">2.64796e-07</span>
<span class="n">Value</span> <span class="n">std</span><span class="o">.</span> <span class="n">dev</span><span class="o">.</span><span class="p">:</span> <span class="mi">1</span>
</pre></div>
</div>
<p>Where we can check that the global mean is close to 0 and the standard
deviation is 1 on the whole dataset. The result of the transformation on
the first images of the set can be checked in the generated <em>frames</em>
folder, as shown in figure [fig:frame0Mean1StdDev].</p>
<div class="figure align-default" id="id1">
<img alt="Image of the set after normalization." src="_images/frame0Mean1StdDev.png" />
<p class="caption"><span class="caption-text">Image of the set after normalization.</span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
</div>
<div class="section" id="substracting-the-mean-image-of-the-set">
<h2>Substracting the mean image of the set<a class="headerlink" href="#substracting-the-mean-image-of-the-set" title="Permalink to this headline">¶</a></h2>
<p>Using the <code class="docutils literal notranslate"><span class="pre">StimuliData</span></code> object followed with an
<code class="docutils literal notranslate"><span class="pre">AffineTransformation</span></code>, it is also possible to use the mean image of
the dataset to normalize the data:</p>
<div class="highlight-ini notranslate"><div class="highlight"><pre><span></span><span class="k">[env.StimuliData-meanData]</span>
<span class="na">ApplyTo</span><span class="o">=</span><span class="s">LearnOnly</span>
<span class="na">MeanData</span><span class="o">=</span><span class="s">1 ; Provides the _MeanData parameter used in the transformation</span>
<span class="k">[env.Transformation]</span>
<span class="na">Type</span><span class="o">=</span><span class="s">AffineTransformation</span>
<span class="na">FirstOperator</span><span class="o">=</span><span class="s">Minus</span>
<span class="na">FirstValue</span><span class="o">=</span><span class="s">[env.StimuliData-meanData]_MeanData</span>
</pre></div>
</div>
<p>The resulting global mean image can be visualized in
<em>env.StimuliData-meanData/meanData.bin.png</em> an is shown in figure
[fig:meanData].</p>
<div class="figure align-default" id="id2">
<img alt="Global mean image generated by ``StimuliData`` with the ``MeanData`` parameter enabled." src="_images/meanData.png" />
<p class="caption"><span class="caption-text">Global mean image generated by <code class="docutils literal notranslate"><span class="pre">StimuliData</span></code> with the <code class="docutils literal notranslate"><span class="pre">MeanData</span></code>
parameter enabled.</span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
</div>
<p>After this transformation, the reported stimuli data becomes:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">env</span><span class="o">.</span><span class="n">StimuliData</span><span class="o">-</span><span class="n">processed</span> <span class="n">data</span><span class="p">:</span>
<span class="n">Number</span> <span class="n">of</span> <span class="n">stimuli</span><span class="p">:</span> <span class="mi">60000</span>
<span class="n">Data</span> <span class="n">width</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">]</span>
<span class="n">Data</span> <span class="n">height</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">28</span><span class="p">,</span> <span class="mi">28</span><span class="p">]</span>
<span class="n">Data</span> <span class="n">channels</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">Value</span> <span class="nb">range</span><span class="p">:</span> <span class="p">[</span><span class="o">-</span><span class="mf">139.554</span><span class="p">,</span> <span class="mf">254.979</span><span class="p">]</span>
<span class="n">Value</span> <span class="n">mean</span><span class="p">:</span> <span class="o">-</span><span class="mf">3.45583e-08</span>
<span class="n">Value</span> <span class="n">std</span><span class="o">.</span> <span class="n">dev</span><span class="o">.</span><span class="p">:</span> <span class="mf">66.1288</span>
</pre></div>
</div>
<p>The result of the transformation on the first images of the set can be
checked in the generated <em>frames</em> folder, as shown in figure
[fig:frameMinusMean].</p>
<div class="figure align-default" id="id3">
<img alt="Image of the set after the ``AffineTransformation`` substracting the global mean image (keep in mind that the original image value range is [0, 255])." src="_images/frameMinusMean.png" />
<p class="caption"><span class="caption-text">Image of the set after the <code class="docutils literal notranslate"><span class="pre">AffineTransformation</span></code> substracting the
global mean image (keep in mind that the original image value range
is [0, 255]).</span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p>
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