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<li><a class="reference internal" href="#">7. Multi-label data stratification</a></li>
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<div class="section" id="Multi-label-data-stratification">
<h1>7. Multi-label data stratification<a class="headerlink" href="#Multi-label-data-stratification" title="Permalink to this headline">¶</a></h1>
<p>With the development of more complex multi-label transformation methods
the community realizes how much the quality of classification depends on
how the data is split into train/test sets or into folds for parameter
estimation. More questions appear on stackoverflow or
<a class="reference external" href="https://datascience.stackexchange.com/questions/33076/how-can-i-perform-stratified-sampling-for-multi-label-multi-class-classification">crossvalidated</a>
concerning methods for multi-label stratification.</p>
<p>For many reasons, described
<a class="reference external" href="http://lpis.csd.auth.gr/publications/sechidis-ecmlpkdd-2011.pdf">here</a>
and <a class="reference external" href="http://proceedings.mlr.press/v74/szyma%C5%84ski17a.html">here</a>
traditional single-label approaches to stratifying data fail to provide
balanced data set divisions which prevents classifiers from generalizing
information.</p>
<p>Some train/test splits don’t include evidence for a given label at all
in the train set. others disproportionately put even as much as 70% of
label pair evidence in the test set, leaving the train set without
proper evidence for generalizing conditional probabilities for label
relations.</p>
<p>You can also watch a great video presentation from ECML 2011 which
explains this in depth:</p>
<blockquote>
On the Stratification of Multi-Label Data Grigorios Tsoumakas</blockquote><p>Scikit-multilearn provides an implementation of iterative stratification
which aims to provide well-balanced distribution of evidence of label
relations up to a given order. To see what it means, let’s load up some
data. We’ll be using the scene data set, both in divided and undivided
variants, to illustrate the problem.</p>
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<span></span>In [263]:
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<div class="input_area highlight-ipython2 notranslate"><div class="highlight"><pre>
<span></span><span class="kn">from</span> <span class="nn">skmultilearn.dataset</span> <span class="kn">import</span> <span class="n">load_dataset</span>
<span class="n">X</span><span class="p">,</span><span class="n">y</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">load_dataset</span><span class="p">(</span><span class="s1">'scene'</span><span class="p">,</span> <span class="s1">'undivided'</span><span class="p">)</span>
</pre></div>
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scene:undivided - exists, not redownloading
</pre></div></div>
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<p>Let’s look at how many examples are available per label combination:</p>
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<span></span><span class="kn">from</span> <span class="nn">skmultilearn.model_selection.measures</span> <span class="kn">import</span> <span class="n">get_combination_wise_output_matrix</span>
</pre></div>
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<span></span><span class="n">Counter</span><span class="p">(</span><span class="n">combination</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">get_combination_wise_output_matrix</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">combination</span> <span class="ow">in</span> <span class="n">row</span><span class="p">)</span>
</pre></div>
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<span></span>Counter({(0, 0): 427,
(0, 3): 1,
(0, 4): 38,
(0, 5): 19,
(1, 1): 364,
(2, 2): 397,
(2, 3): 24,
(2, 4): 14,
(3, 3): 433,
(3, 4): 76,
(3, 5): 6,
(4, 4): 533,
(4, 5): 1,
(5, 5): 431})
</pre></div>
</div>
</div>
<p>Let’s load up the original division, to see how the set was split into
train/test data in 2004, before multi-label stratification methods
appeared.</p>
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<span></span><span class="n">_</span><span class="p">,</span> <span class="n">original_y_train</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">load_dataset</span><span class="p">(</span><span class="s1">'scene'</span><span class="p">,</span> <span class="s1">'train'</span><span class="p">)</span>
<span class="n">_</span><span class="p">,</span> <span class="n">original_y_test</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">load_dataset</span><span class="p">(</span><span class="s1">'scene'</span><span class="p">,</span> <span class="s1">'test'</span><span class="p">)</span>
</pre></div>
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scene:train - exists, not redownloading
scene:test - exists, not redownloading
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<span></span>In [267]:
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<span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
</pre></div>
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<span></span><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">({</span>
<span class="s1">'train'</span><span class="p">:</span> <span class="n">Counter</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">combination</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">get_combination_wise_output_matrix</span><span class="p">(</span><span class="n">original_y_train</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">combination</span> <span class="ow">in</span> <span class="n">row</span><span class="p">),</span>
<span class="s1">'test'</span> <span class="p">:</span> <span class="n">Counter</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">combination</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">get_combination_wise_output_matrix</span><span class="p">(</span><span class="n">original_y_test</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">combination</span> <span class="ow">in</span> <span class="n">row</span><span class="p">)</span>
<span class="p">})</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">fillna</span><span class="p">(</span><span class="mf">0.0</span><span class="p">)</span>
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<th>test</th>
<td>200.0</td>
<td>1.0</td>
<td>17.0</td>
<td>7.0</td>
<td>199.0</td>
<td>200.0</td>
<td>16.0</td>
<td>8.0</td>
<td>237.0</td>
<td>49.0</td>
<td>5.0</td>
<td>256.0</td>
<td>0.0</td>
<td>207.0</td>
</tr>
<tr>
<th>train</th>
<td>227.0</td>
<td>0.0</td>
<td>21.0</td>
<td>12.0</td>
<td>165.0</td>
<td>197.0</td>
<td>8.0</td>
<td>6.0</td>
<td>196.0</td>
<td>27.0</td>
<td>1.0</td>
<td>277.0</td>
<td>1.0</td>
<td>224.0</td>
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<span></span><span class="n">original_y_train</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">original_y_test</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
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<span></span>(1211, 1196)
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<p>We can see that the split size is nearly identical, yet some label
combination evidence is well balanced between the splits. While this is
a toy case on a small data set, such phenomena are common in larger
datasets. We would like to fix this.</p>
<p>Let’s load the iterative stratifier and divided the set again.</p>
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<span></span><span class="kn">from</span> <span class="nn">skmultilearn.model_selection</span> <span class="kn">import</span> <span class="n">iterative_train_test_split</span>
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<span></span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">iterative_train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">test_size</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">)</span>
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<span></span><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">({</span>
<span class="s1">'train'</span><span class="p">:</span> <span class="n">Counter</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">combination</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">get_combination_wise_output_matrix</span><span class="p">(</span><span class="n">y_train</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">combination</span> <span class="ow">in</span> <span class="n">row</span><span class="p">),</span>
<span class="s1">'test'</span> <span class="p">:</span> <span class="n">Counter</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">combination</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">get_combination_wise_output_matrix</span><span class="p">(</span><span class="n">y_test</span><span class="o">.</span><span class="n">A</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span> <span class="k">for</span> <span class="n">combination</span> <span class="ow">in</span> <span class="n">row</span><span class="p">)</span>
<span class="p">})</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">fillna</span><span class="p">(</span><span class="mf">0.0</span><span class="p">)</span>
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<th>test</th>
<td>213.0</td>
<td>0.0</td>
<td>19.0</td>
<td>9.0</td>
<td>182.0</td>
<td>199.0</td>
<td>12.0</td>
<td>7.0</td>
<td>217.0</td>
<td>38.0</td>
<td>3.0</td>
<td>267.0</td>
<td>1.0</td>
<td>215.0</td>
</tr>
<tr>
<th>train</th>
<td>214.0</td>
<td>1.0</td>
<td>19.0</td>
<td>10.0</td>
<td>182.0</td>
<td>198.0</td>
<td>12.0</td>
<td>7.0</td>
<td>216.0</td>
<td>38.0</td>
<td>3.0</td>
<td>266.0</td>
<td>0.0</td>
<td>216.0</td>
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<p>We can see that the new division is much more balanced.</p>
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@ARTICLE{2017arXiv170201460S,
author = {{Szyma{\'n}ski}, P. and {Kajdanowicz}, T.},
title = "{A scikit-based Python environment for performing multi-label classification}",
journal = {ArXiv e-prints},
archivePrefix = "arXiv",
eprint = {1702.01460},
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keywords = {Computer Science - Learning, Computer Science - Mathematical Software},
year = 2017,
month = feb,
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