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<div class=" highlight hl-ipython2"><pre><span class="o">%</span><span class="k">matplotlib</span> inline
<span class="kn">import</span> <span class="nn">seaborn</span> <span class="c"># import before other plotting libraries</span>
<span class="kn">import</span> <span class="nn">numpy</span><span class="o">,</span> <span class="nn">scipy</span><span class="o">,</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span><span class="o">,</span> <span class="nn">librosa</span><span class="o">,</span> <span class="nn">sklearn</span><span class="o">,</span> <span class="nn">urllib</span><span class="o">,</span> <span class="nn">IPython.display</span><span class="o">,</span> <span class="nn">stanford_mir</span>
<span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s">'figure.figsize'</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">14</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
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<h1 id="Basic-Feature-Extraction">Basic Feature Extraction<a class="anchor-link" href="#Basic-Feature-Extraction">¶</a></h1>
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<p>Somehow, we must extract the characteristics of our audio signal that are most relevant to the problem we are trying to solve. For example, if we want to classify instruments by timbre, we will want features that distinguish sounds by their timbre and not their pitch. If we want to perform pitch detection, we want features that distinguish pitch and not timbre.</p>
<p>This process is known as feature extraction.</p>
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<p>Let's begin with twenty audio files: ten kick drum samples, and ten snare drum samples. Each audio file contains one drum hit.</p>
<p>For convenience, we will use <code>stanford_mir.download_samples</code> to download this data set at once.</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">kick_filepaths</span><span class="p">,</span> <span class="n">snare_filepaths</span> <span class="o">=</span> <span class="n">stanford_mir</span><span class="o">.</span><span class="n">download_samples</span><span class="p">(</span><span class="n">collection</span><span class="o">=</span><span class="s">"drum_samples_train"</span><span class="p">)</span>
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<p>Read and store each signal:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">kick_signals</span> <span class="o">=</span> <span class="p">[</span>
<span class="n">librosa</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">p</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">kick_filepaths</span>
<span class="p">]</span>
<span class="n">snare_signals</span> <span class="o">=</span> <span class="p">[</span>
<span class="n">librosa</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">p</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">snare_filepaths</span>
<span class="p">]</span>
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<p>Display the kick drum signals:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">kick_signals</span><span class="p">):</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">librosa</span><span class="o">.</span><span class="n">display</span><span class="o">.</span><span class="n">waveplot</span><span class="p">(</span><span class="n">x</span><span class="p">[:</span><span class="mi">10000</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
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"
>
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<div class="prompt input_prompt">
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<div class="text_cell_render border-box-sizing rendered_html">
<p>Display the snare drum signals:</p>
</div>
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<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In [5]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">snare_signals</span><span class="p">):</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">librosa</span><span class="o">.</span><span class="n">display</span><span class="o">.</span><span class="n">waveplot</span><span class="p">(</span><span class="n">x</span><span class="p">[:</span><span class="mi">10000</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
</pre></div>
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<h2 id="Constructing-a-Feature-Vector">Constructing a Feature Vector<a class="anchor-link" href="#Constructing-a-Feature-Vector">¶</a></h2>
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<p>A <em>feature vector</em> is simply a collection of features. Here is a simple function that constructs a two-dimensional feature vector from a signal:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">extract_features</span><span class="p">(</span><span class="n">signal</span><span class="p">):</span>
<span class="k">return</span> <span class="p">[</span>
<span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">zero_crossing_rate</span><span class="p">(</span><span class="n">signal</span><span class="p">)[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">librosa</span><span class="o">.</span><span class="n">feature</span><span class="o">.</span><span class="n">spectral_centroid</span><span class="p">(</span><span class="n">signal</span><span class="p">)[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
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<p>If we want to aggregate all of the feature vectors among signals in a collection, we can use a list comprehension as follows:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">kick_features</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">extract_features</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">kick_signals</span><span class="p">])</span>
<span class="n">snare_features</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">extract_features</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">snare_signals</span><span class="p">])</span>
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<p>Visualize the differences in features by plotting separate histograms for each of the classes:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">kick_features</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'b'</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">snare_features</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'r'</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">((</span><span class="s">'kicks'</span><span class="p">,</span> <span class="s">'snares'</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'Zero Crossing Rate'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'Count'</span><span class="p">)</span>
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<pre><matplotlib.text.Text at 0x109d3c310></pre>
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<div class="input">
<div class="prompt input_prompt">In [9]:</div>
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<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">kick_features</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'b'</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4000</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">snare_features</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'r'</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4000</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">40</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">((</span><span class="s">'kicks'</span><span class="p">,</span> <span class="s">'snares'</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'Spectral Centroid (frqeuency bin)'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'Count'</span><span class="p">)</span>
</pre></div>
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<div class="output">
<div class="output_area"><div class="prompt output_prompt">Out[9]:</div>
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<pre><matplotlib.text.Text at 0x109ae6990></pre>
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<h2 id="Feature-Scaling">Feature Scaling<a class="anchor-link" href="#Feature-Scaling">¶</a></h2>
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<p>The features that we used in the previous example included zero crossing rate and spectral centroid. These two features are expressed using different units. This discrepancy can pose problems when performing classification later. Therefore, we will normalize each feature vector to a common range and store the normalization parameters for later use.</p>
<p>Many techniques exist for scaling your features. For now, we'll use <a href="http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.MinMaxScaler.html"><code>sklearn.preprocessing.MinMaxScaler</code></a>. <code>MinMaxScaler</code> returns an array of scaled values such that each feature dimension is in the range -1 to 1.</p>
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<p>Let's concatenate all of our feature vectors into one <em>feature table</em>:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">feature_table</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">kick_features</span><span class="p">,</span> <span class="n">snare_features</span><span class="p">))</span>
<span class="k">print</span> <span class="n">feature_table</span><span class="o">.</span><span class="n">shape</span>
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<pre>(20, 2)
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<p>Scale each feature dimension to be in the range -1 to 1:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">scaler</span> <span class="o">=</span> <span class="n">sklearn</span><span class="o">.</span><span class="n">preprocessing</span><span class="o">.</span><span class="n">MinMaxScaler</span><span class="p">(</span><span class="n">feature_range</span><span class="o">=</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="n">training_features</span> <span class="o">=</span> <span class="n">scaler</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">feature_table</span><span class="p">)</span>
<span class="k">print</span> <span class="n">training_features</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="k">print</span> <span class="n">training_features</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<pre>[-1. -1.]
[ 1. 1.]
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<p>Plot the scaled features:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">training_features</span><span class="p">[:</span><span class="mi">10</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">training_features</span><span class="p">[:</span><span class="mi">10</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s">'b'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">training_features</span><span class="p">[</span><span class="mi">10</span><span class="p">:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">training_features</span><span class="p">[</span><span class="mi">10</span><span class="p">:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s">'r'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'Zero Crossing Rate'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'Spectral Centroid'</span><span class="p">)</span>
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<pre><matplotlib.text.Text at 0x10970ee50></pre>
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