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<h1>SVM</h1>
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<h2> Contents </h2>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-will-we-do">What will we do?</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#svms">Когда приенимо SVMs?</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#svm-ml">Сравнение SVM с др. ML моделями:</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#support-vector-machine">Support Vector Machine - описание алгоритма:</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#support-vectors">Опорные вектора - Support Vectors:</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Гиперплоскость:</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#let-s-define-our-loss-function-what-to-minimize-and-our-objective-function-what-to-optimize">Let’s define our loss function (what to minimize) and our objective function (what to optimize)</a><ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#loss-function">Loss function</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#objective-function">Objective Function</a></li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#kernel-svm">Kernel SVM</a></li>
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<article class="bd-article" role="main">
<section class="tex2jax_ignore mathjax_ignore" id="svm">
<h1>SVM<a class="headerlink" href="#svm" title="Permalink to this heading">#</a></h1>
<section id="what-will-we-do">
<h2>What will we do?<a class="headerlink" href="#what-will-we-do" title="Permalink to this heading">#</a></h2>
<p>Мы построим SVM модель, которая найдет оптимальную гиперплоскость, максимизирующую разницу между двумя классами игрушечных данных, используя градиентный спуск.</p>
</section>
<section id="svms">
<h2>Когда приенимо SVMs?<a class="headerlink" href="#svms" title="Permalink to this heading">#</a></h2>
<p>-Классификация, регрессия (прогнозирование временных рядов и т.д.), обнаружение выбросов, кластеризация</p>
</section>
<section id="svm-ml">
<h2>Сравнение SVM с др. ML моделями:<a class="headerlink" href="#svm-ml" title="Permalink to this heading">#</a></h2>
<ul class="simple">
<li><p>Как правило, SVM отлично подходят для относительно небольших наборов данных с меньшим количеством выбросов.</p></li>
<li><p>Другие алгоритмы (случайные леса, глубокие нейронные сети и т.д.) требуют больше данных, но почти всегда дают очень надежные модели.</p></li>
<li><p>Решение о том, какой классификатор использовать, зависит от вашего набора данных и общей сложности задачи.</p></li>
<li><p>“Преждевременная оптимизация - корень всего зла (или, по крайней мере, большей его части) в программировании”. - Дональд Кнут, профессор CS (речь на премии Тьюринга, 1974)</p></li>
</ul>
</section>
<section id="support-vector-machine">
<h2>Support Vector Machine - описание алгоритма:<a class="headerlink" href="#support-vector-machine" title="Permalink to this heading">#</a></h2>
<p>Это контролируемый алгоритм машинного обучения, который может использоваться как для задач классификации, так и для задач регрессии. Но обычно это используется для классификации. Учитывая 2 или более помеченных классов данных, он действует как дискриминирующий классификатор, формально определяемый оптимальной гиперплоскостью, которая разделяет все классы. Новые примеры, которые затем отображаются в том же пространстве, могут быть классифицированы в зависимости от того, по какую сторону разрыва они находятся.</p>
</section>
<section id="support-vectors">
<h2>Опорные вектора - Support Vectors:<a class="headerlink" href="#support-vectors" title="Permalink to this heading">#</a></h2>
<p><img alt="alt text" src="https://www.dtreg.com/uploaded/pageimg/SvmMargin2.jpg" /></p>
<p>Опорные векторы - это точки данных, ближайшие к гиперплоскости, точки набора данных, удаление которых изменило бы положение разделяющей гиперплоскости. Из-за этого их можно считать критическими элементами набора данных, именно они помогают нам создавать нашу SVM.</p>
</section>
<section id="id1">
<h2>Гиперплоскость:<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
<p><img alt="alt text" src="http://slideplayer.com/slide/1579281/5/images/32/Hyperplanes+as+decision+surfaces.jpg" /></p>
<p>Геометрия говорит нам, что гиперплоскость - это подпространство, которое на одно измерение меньше окружающего его пространства. Например, гиперплоскость n-мерного пространства − это плоское подмножество с размерностью n - 1. По своей природе он разделяет пространство на два полупространства.</p>
</section>
<section id="let-s-define-our-loss-function-what-to-minimize-and-our-objective-function-what-to-optimize">
<h2>Let’s define our loss function (what to minimize) and our objective function (what to optimize)<a class="headerlink" href="#let-s-define-our-loss-function-what-to-minimize-and-our-objective-function-what-to-optimize" title="Permalink to this heading">#</a></h2>
<section id="loss-function">
<h3>Loss function<a class="headerlink" href="#loss-function" title="Permalink to this heading">#</a></h3>
<p>Используем Hinge loss. Эта функция потерь, используемая для обучения классификаторов. Hinge loss используется для “maximum-margin” классификации.</p>
<p><img alt="alt text" src="http://i.imgur.com/OzCwzyN.png" /></p>
<p>c - функция потерь, x - выборка, y - истинная метка, f(x) - прогнозируемая метка.</p>
<p><img alt="alt text" src="http://i.imgur.com/FZ7JcG3.png" /></p>
</section>
<section id="objective-function">
<h3>Objective Function<a class="headerlink" href="#objective-function" title="Permalink to this heading">#</a></h3>
<p><img alt="alt text" src="http://i.imgur.com/I5NNu44.png" /></p>
<p>Как вы можете видеть, наша цель SVM состоит из двух терминов. Первый член - это регуляризатор, сердце SVM, второй член - потеря. Регуляризатор балансирует между максимизацией маржи и убытками. Мы хотим найти поверхность принятия решения, которая находится максимально далеко от любых точек данных.</p>
<p>Как нам минимизировать наши потери / оптимизировать для достижения нашей цели (т.е. учиться)?</p>
<p>Мы должны вывести нашу целевую функцию, чтобы получить градиенты! Градиентный спуск ftw. Поскольку у нас есть два члена, мы выведем их отдельно, используя правило суммы при дифференцировании.</p>
<p><img alt="alt text" src="http://i.imgur.com/6uK3BnH.png" /></p>
<p>Это означает, что если у нас неправильно классифицированная выборка, мы обновляем весовой вектор w, используя градиенты обоих терминов, в противном случае, если классифицировано правильно, мы просто обновляем w по градиенту регуляризатора.</p>
<p>Условие неправильной классификации</p>
<p><img alt="alt text" src="http://i.imgur.com/g9QLAyn.png" /></p>
<p>Правило обновления весов (неправильная классификация)</p>
<p><img alt="alt text" src="http://i.imgur.com/rkdPpTZ.png" /></p>
<p>Введем параметр скорости обучения(learning rate) η и регуляризатор λ
параметр скорости обучения - длина шагов, которые алгоритм делает по градиенту на кривой ошибок.</p>
<ul class="simple">
<li><p>Learning rate слишком велик? Алгоритм может перескочить оптимальную точку.</p></li>
<li><p>Learning rate слишком мал? Алгоритм может сходиться в оптимальную точку слишком долго.</p></li>
</ul>
<p>Regularizer это компромисс между низкой training error и низкой testing error - т.е. способность обобщения модели на новые\тестовые данные. Обычно этот параметр выбирают равным обратным количеству эпох.</p>
<ul class="simple">
<li><p>Regularizer слишком велик high? Переобучение (большая testing error)</p></li>
<li><p>Regularizer слишком мал? Переобучение (большая training error)</p></li>
</ul>
<p>Правило обновления весов (правильная классификация)</p>
<p><img alt="alt text" src="http://i.imgur.com/xTKbvZ6.png" /></p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">url</span> <span class="o">=</span> <span class="s1">'https://raw.githubusercontent.com/melwinlobo18/K-Nearest-Neighbors/master/Dataset/data.csv'</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">url</span><span class="p">)</span> <span class="c1"># Dataset - Breast Cancer Wisconsin Data</span>
<span class="n">df</span><span class="p">[</span><span class="s1">'diagnosis'</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s1">'diagnosis'</span><span class="p">]</span><span class="o">.</span><span class="n">map</span><span class="p">({</span>
<span class="s1">'M'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
<span class="s1">'B'</span><span class="p">:</span> <span class="mi">2</span>
<span class="p">})</span> <span class="c1"># Label values - 1 for Malignant and 2 for Benign</span>
<span class="n">labels</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s1">'diagnosis'</span><span class="p">]</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<span class="n">df</span><span class="p">[</span><span class="s1">'Class'</span><span class="p">]</span> <span class="o">=</span> <span class="n">labels</span> <span class="c1">#Cpying values of diagnosis to newly clreated labels column</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">drop</span><span class="p">([</span><span class="s1">'id'</span><span class="p">,</span> <span class="s1">'Unnamed: 32'</span><span class="p">,</span> <span class="s1">'diagnosis'</span><span class="p">],</span>
<span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="c1">#Dropping unncessary columns</span>
<span class="n">df</span><span class="o">.</span><span class="n">head</span><span class="p">()</span> <span class="c1">#Displaying first five rows of the dataset</span>
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<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>radius_mean</th>
<th>texture_mean</th>
<th>perimeter_mean</th>
<th>area_mean</th>
<th>smoothness_mean</th>
<th>compactness_mean</th>
<th>concavity_mean</th>
<th>concave points_mean</th>
<th>symmetry_mean</th>
<th>fractal_dimension_mean</th>
<th>...</th>
<th>texture_worst</th>
<th>perimeter_worst</th>
<th>area_worst</th>
<th>smoothness_worst</th>
<th>compactness_worst</th>
<th>concavity_worst</th>
<th>concave points_worst</th>
<th>symmetry_worst</th>
<th>fractal_dimension_worst</th>
<th>Class</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>17.99</td>
<td>10.38</td>
<td>122.80</td>
<td>1001.0</td>
<td>0.11840</td>
<td>0.27760</td>
<td>0.3001</td>
<td>0.14710</td>
<td>0.2419</td>
<td>0.07871</td>
<td>...</td>
<td>17.33</td>
<td>184.60</td>
<td>2019.0</td>
<td>0.1622</td>
<td>0.6656</td>
<td>0.7119</td>
<td>0.2654</td>
<td>0.4601</td>
<td>0.11890</td>
<td>1</td>
</tr>
<tr>
<th>1</th>
<td>20.57</td>
<td>17.77</td>
<td>132.90</td>
<td>1326.0</td>
<td>0.08474</td>
<td>0.07864</td>
<td>0.0869</td>
<td>0.07017</td>
<td>0.1812</td>
<td>0.05667</td>
<td>...</td>
<td>23.41</td>
<td>158.80</td>
<td>1956.0</td>
<td>0.1238</td>
<td>0.1866</td>
<td>0.2416</td>
<td>0.1860</td>
<td>0.2750</td>
<td>0.08902</td>
<td>1</td>
</tr>
<tr>
<th>2</th>
<td>19.69</td>
<td>21.25</td>
<td>130.00</td>
<td>1203.0</td>
<td>0.10960</td>
<td>0.15990</td>
<td>0.1974</td>
<td>0.12790</td>
<td>0.2069</td>
<td>0.05999</td>
<td>...</td>
<td>25.53</td>
<td>152.50</td>
<td>1709.0</td>
<td>0.1444</td>
<td>0.4245</td>
<td>0.4504</td>
<td>0.2430</td>
<td>0.3613</td>
<td>0.08758</td>
<td>1</td>
</tr>
<tr>
<th>3</th>
<td>11.42</td>
<td>20.38</td>
<td>77.58</td>
<td>386.1</td>
<td>0.14250</td>
<td>0.28390</td>
<td>0.2414</td>
<td>0.10520</td>
<td>0.2597</td>
<td>0.09744</td>
<td>...</td>
<td>26.50</td>
<td>98.87</td>
<td>567.7</td>
<td>0.2098</td>
<td>0.8663</td>
<td>0.6869</td>
<td>0.2575</td>
<td>0.6638</td>
<td>0.17300</td>
<td>1</td>
</tr>
<tr>
<th>4</th>
<td>20.29</td>
<td>14.34</td>
<td>135.10</td>
<td>1297.0</td>
<td>0.10030</td>
<td>0.13280</td>
<td>0.1980</td>
<td>0.10430</td>
<td>0.1809</td>
<td>0.05883</td>
<td>...</td>
<td>16.67</td>
<td>152.20</td>
<td>1575.0</td>
<td>0.1374</td>
<td>0.2050</td>
<td>0.4000</td>
<td>0.1625</td>
<td>0.2364</td>
<td>0.07678</td>
<td>1</td>
</tr>
</tbody>
</table>
<p>5 rows × 31 columns</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">target_names</span> <span class="o">=</span> <span class="p">[</span><span class="s1">''</span><span class="p">,</span> <span class="s1">'M'</span><span class="p">,</span> <span class="s1">'B'</span><span class="p">]</span>
<span class="n">df</span><span class="p">[</span><span class="s1">'attack_type'</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">Class</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">target_names</span><span class="p">[</span><span class="n">x</span><span class="p">])</span>
<span class="n">df</span><span class="o">.</span><span class="n">head</span><span class="p">()</span>
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<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>radius_mean</th>
<th>texture_mean</th>
<th>perimeter_mean</th>
<th>area_mean</th>
<th>smoothness_mean</th>
<th>compactness_mean</th>
<th>concavity_mean</th>
<th>concave points_mean</th>
<th>symmetry_mean</th>
<th>fractal_dimension_mean</th>
<th>...</th>
<th>perimeter_worst</th>
<th>area_worst</th>
<th>smoothness_worst</th>
<th>compactness_worst</th>
<th>concavity_worst</th>
<th>concave points_worst</th>
<th>symmetry_worst</th>
<th>fractal_dimension_worst</th>
<th>Class</th>
<th>attack_type</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>17.99</td>
<td>10.38</td>
<td>122.80</td>
<td>1001.0</td>
<td>0.11840</td>
<td>0.27760</td>
<td>0.3001</td>
<td>0.14710</td>
<td>0.2419</td>
<td>0.07871</td>
<td>...</td>
<td>184.60</td>
<td>2019.0</td>
<td>0.1622</td>
<td>0.6656</td>
<td>0.7119</td>
<td>0.2654</td>
<td>0.4601</td>
<td>0.11890</td>
<td>1</td>
<td>M</td>
</tr>
<tr>
<th>1</th>
<td>20.57</td>
<td>17.77</td>
<td>132.90</td>
<td>1326.0</td>
<td>0.08474</td>
<td>0.07864</td>
<td>0.0869</td>
<td>0.07017</td>
<td>0.1812</td>
<td>0.05667</td>
<td>...</td>
<td>158.80</td>
<td>1956.0</td>
<td>0.1238</td>
<td>0.1866</td>
<td>0.2416</td>
<td>0.1860</td>
<td>0.2750</td>
<td>0.08902</td>
<td>1</td>
<td>M</td>
</tr>
<tr>
<th>2</th>
<td>19.69</td>
<td>21.25</td>
<td>130.00</td>
<td>1203.0</td>
<td>0.10960</td>
<td>0.15990</td>
<td>0.1974</td>
<td>0.12790</td>
<td>0.2069</td>
<td>0.05999</td>
<td>...</td>
<td>152.50</td>
<td>1709.0</td>
<td>0.1444</td>
<td>0.4245</td>
<td>0.4504</td>
<td>0.2430</td>
<td>0.3613</td>
<td>0.08758</td>
<td>1</td>
<td>M</td>
</tr>
<tr>
<th>3</th>
<td>11.42</td>
<td>20.38</td>
<td>77.58</td>
<td>386.1</td>
<td>0.14250</td>
<td>0.28390</td>
<td>0.2414</td>
<td>0.10520</td>
<td>0.2597</td>
<td>0.09744</td>
<td>...</td>
<td>98.87</td>
<td>567.7</td>
<td>0.2098</td>
<td>0.8663</td>
<td>0.6869</td>
<td>0.2575</td>
<td>0.6638</td>
<td>0.17300</td>
<td>1</td>
<td>M</td>
</tr>
<tr>
<th>4</th>
<td>20.29</td>
<td>14.34</td>
<td>135.10</td>
<td>1297.0</td>
<td>0.10030</td>
<td>0.13280</td>
<td>0.1980</td>
<td>0.10430</td>
<td>0.1809</td>
<td>0.05883</td>
<td>...</td>
<td>152.20</td>
<td>1575.0</td>
<td>0.1374</td>
<td>0.2050</td>
<td>0.4000</td>
<td>0.1625</td>
<td>0.2364</td>
<td>0.07678</td>
<td>1</td>
<td>M</td>
</tr>
</tbody>
</table>
<p>5 rows × 32 columns</p>
</div></div></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">df1</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="n">df</span><span class="o">.</span><span class="n">Class</span> <span class="o">==</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">df2</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="n">df</span><span class="o">.</span><span class="n">Class</span> <span class="o">==</span> <span class="mi">2</span><span class="p">]</span>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'radius_mean'</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="s1">'texture_mean'</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">df1</span><span class="p">[</span><span class="s1">'radius_mean'</span><span class="p">],</span> <span class="n">df1</span><span class="p">[</span><span class="s1">'texture_mean'</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s1">'green'</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">'+'</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">df2</span><span class="p">[</span><span class="s1">'radius_mean'</span><span class="p">],</span> <span class="n">df2</span><span class="p">[</span><span class="s1">'texture_mean'</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s1">'blue'</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">'.'</span><span class="p">)</span>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x7f7b59d689a0>
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<img alt="_images/d69c5c418b299a0a3371a22846139fe735a5ac900723ac72275a948a7c259f91.png" src="_images/d69c5c418b299a0a3371a22846139fe735a5ac900723ac72275a948a7c259f91.png" />
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">X</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">drop</span><span class="p">([</span><span class="s1">'Class'</span><span class="p">,</span> <span class="s1">'attack_type'</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="s1">'columns'</span><span class="p">)</span>
<span class="n">X</span><span class="o">.</span><span class="n">head</span><span class="p">()</span>
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<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>radius_mean</th>
<th>texture_mean</th>
<th>perimeter_mean</th>
<th>area_mean</th>
<th>smoothness_mean</th>
<th>compactness_mean</th>
<th>concavity_mean</th>
<th>concave points_mean</th>
<th>symmetry_mean</th>
<th>fractal_dimension_mean</th>
<th>...</th>
<th>radius_worst</th>
<th>texture_worst</th>
<th>perimeter_worst</th>
<th>area_worst</th>
<th>smoothness_worst</th>
<th>compactness_worst</th>
<th>concavity_worst</th>
<th>concave points_worst</th>
<th>symmetry_worst</th>
<th>fractal_dimension_worst</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>17.99</td>
<td>10.38</td>
<td>122.80</td>
<td>1001.0</td>
<td>0.11840</td>
<td>0.27760</td>
<td>0.3001</td>
<td>0.14710</td>
<td>0.2419</td>
<td>0.07871</td>
<td>...</td>
<td>25.38</td>
<td>17.33</td>
<td>184.60</td>
<td>2019.0</td>
<td>0.1622</td>
<td>0.6656</td>
<td>0.7119</td>
<td>0.2654</td>
<td>0.4601</td>
<td>0.11890</td>
</tr>
<tr>
<th>1</th>
<td>20.57</td>
<td>17.77</td>
<td>132.90</td>
<td>1326.0</td>
<td>0.08474</td>
<td>0.07864</td>
<td>0.0869</td>
<td>0.07017</td>
<td>0.1812</td>
<td>0.05667</td>
<td>...</td>
<td>24.99</td>
<td>23.41</td>
<td>158.80</td>
<td>1956.0</td>
<td>0.1238</td>
<td>0.1866</td>
<td>0.2416</td>
<td>0.1860</td>
<td>0.2750</td>
<td>0.08902</td>
</tr>
<tr>
<th>2</th>
<td>19.69</td>
<td>21.25</td>
<td>130.00</td>
<td>1203.0</td>
<td>0.10960</td>
<td>0.15990</td>
<td>0.1974</td>
<td>0.12790</td>
<td>0.2069</td>
<td>0.05999</td>
<td>...</td>
<td>23.57</td>
<td>25.53</td>
<td>152.50</td>
<td>1709.0</td>
<td>0.1444</td>
<td>0.4245</td>
<td>0.4504</td>
<td>0.2430</td>
<td>0.3613</td>
<td>0.08758</td>
</tr>
<tr>
<th>3</th>
<td>11.42</td>
<td>20.38</td>
<td>77.58</td>
<td>386.1</td>
<td>0.14250</td>
<td>0.28390</td>
<td>0.2414</td>
<td>0.10520</td>
<td>0.2597</td>
<td>0.09744</td>
<td>...</td>
<td>14.91</td>
<td>26.50</td>
<td>98.87</td>
<td>567.7</td>
<td>0.2098</td>
<td>0.8663</td>
<td>0.6869</td>
<td>0.2575</td>
<td>0.6638</td>
<td>0.17300</td>
</tr>
<tr>