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<!-- Title -->
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<h1>
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<i class="fa fa-circle-o-notch fa-spin"></i>
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<a href="." >近朱者赤近墨者黑-kNN</a>
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</h1>
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<h1 id="近朱者赤近墨者黑-knn">近朱者赤近墨者黑-kNN</h1>
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<p><strong>kNN算法</strong>其实是众多机器学习算法中最简单的一种，因为该算法的思想完全可以用 8 个字来概括：<strong>“近朱者赤，近墨者黑”</strong>。</p>
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<h2 id="knn算法解决分类问题">kNN算法解决分类问题</h2>
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<p>假设现在有这样的一个样本空间(由样本组成的一个空间)，该样本空间里有宅男和文艺青年这两个类别，其中红圈表示宅男，绿圈表示文艺青年。如下图所示：</p>
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<p><img src="img/8.jpg" alt=""></p>
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<p>其实构建出这样的样本空间的过程就是<strong>kNN算法</strong>的训练过程。可想而知<strong>kNN算法</strong>是没有训练过程的，所以<strong>kNN算法</strong>属于懒惰学习算法。</p>
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<p>假设我在这个样本空间中用黄圈表示，如下图所示：</p>
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<p><img src="img/9.jpg" alt=""></p>
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<p>现在使用<strong>kNN算法</strong>来鉴别一下我是宅男还是文艺青年。首先需要计算我与样本空间中所有样本的距离。假设计算得到的距离表格如下：</p>
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<table>
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<thead>
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<tr>
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<th>样本编号</th>
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<th>1</th>
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<th>2</th>
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<th>...</th>
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<th>13</th>
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<th>14</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>标签</td>
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<td>宅男</td>
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<td>宅男</td>
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<td>...</td>
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<td>文艺青年</td>
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<td>文艺青年</td>
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</tr>
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<tr>
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<td>距离</td>
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<td>11.2</td>
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<td>9.5</td>
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<td>...</td>
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<td>23.3</td>
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<td>37.6</td>
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</tr>
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</tbody>
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</table>
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<p>然后找出与我距离最小的 k 个样本( k 是一个超参数，需要自己设置，一般默认为 5 )，假设与我离得最近的 5 个样本的标签和距离如下：</p>
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<table>
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<thead>
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<tr>
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<th>样本编号</th>
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<th>4</th>
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<th>5</th>
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<th>6</th>
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<th>7</th>
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<th>8</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>标签</td>
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<td>宅男</td>
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<td>宅男</td>
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<td>宅男</td>
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<td>宅男</td>
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<td>文艺青年</td>
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</tr>
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<tr>
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<td>距离</td>
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<td>11.2</td>
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<td>9.5</td>
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<td>7.7</td>
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<td>5.8</td>
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<td>15.2</td>
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</tr>
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</tbody>
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</table>
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<p>最后只需要对这 5 个样本的标签进行统计，并将票数最多的标签作为预测结果即可。如上表中，宅男是 4 票，文艺青年是 1 票，所以我是宅男。</p>
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<p><strong>注意</strong>：有的时候可能会有票数一致的情况，比如 k = 4 时与我离得最近的样本如下：</p>
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<table>
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<thead>
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<tr>
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<th>样本编号</th>
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<th>4</th>
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<th>9</th>
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<th>11</th>
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<th>13</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>标签</td>
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<td>宅男</td>
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<td>宅男</td>
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<td>文艺青年</td>
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<td>文艺青年</td>
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</tr>
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<tr>
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<td>距离</td>
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<td>4.2</td>
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<td>9.5</td>
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<td>7.7</td>
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<td>5.8</td>
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</tr>
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</tbody>
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</table>
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<p>可以看出宅男和文艺青年的比分是 2 : 2 ，那么可以尝试将属于宅男的 2 个样本与我的总距离和属于文艺青年的 2 个样本与我的总距离进行比较。然后选择总距离最小的标签作为预测结果。在这个例子中预测结果为文艺青年(宅男的总距离为 4.2 + 9.5 ，文艺青年的总距离为 7.7 + 5.8 )。</p>
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<h2 id="knn算法解决回归问题">kNN算法解决回归问题</h2>
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<p>很明显，刚刚我们使用<strong>kNN算法</strong>解决了一个分类问题，那<strong>kNN算法</strong>能解决回归问题吗？当然可以！</p>
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<p>在使用<code>kNN</code>算法解决回归问题时的思路和解决分类问题的思路基本一致，只不过预测标签值是多少的的时候是将距离最近的 k 个样本的标签值加起来再算个平均，而不是投票。例如离待预测样本最近的 5 个样本的标签如下：</p>
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<table>
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<thead>
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<tr>
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<th>样本编号</th>
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<th>4</th>
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<th>9</th>
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<th>11</th>
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<th>13</th>
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<th>15</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>标签</td>
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<td>1.2</td>
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<td>1.5</td>
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<td>0.8</td>
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<td>1.33</td>
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<td>1.19</td>
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</tr>
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</tbody>
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</table>
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<p>所以待预测样本的标签为：<code>(1.2+1.5+0.8+1.33+1.19)/5=1.204</code></p>
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