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sklearn_featureSelection.html
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sklearn_featureSelection.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
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<title>sklearn_featureSelection</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<p>chapter 10 数据表达与特征工程</p>
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<h1 id="%E6%95%B0%E6%8D%AE%E8%A1%A8%E8%BE%BE">数据表达<a class="anchor-link" href="#%E6%95%B0%E6%8D%AE%E8%A1%A8%E8%BE%BE">¶</a></h1>
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<h2 id="%E4%BD%BF%E7%94%A8%E5%93%91%E5%8F%98%E9%87%8F%E8%BD%AC%E5%8C%96%E7%B1%BB%E5%9E%8B%E7%89%B9%E5%BE%81">使用哑变量转化类型特征<a class="anchor-link" href="#%E4%BD%BF%E7%94%A8%E5%93%91%E5%8F%98%E9%87%8F%E8%BD%AC%E5%8C%96%E7%B1%BB%E5%9E%8B%E7%89%B9%E5%BE%81">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 导入 pandas</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="n">fruits</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">({</span><span class="s2">"value"</span><span class="p">:[</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">,</span><span class="mi">9</span><span class="p">],</span>
<span class="s2">"type"</span><span class="p">:[</span><span class="s2">"waterMelon"</span><span class="p">,</span> <span class="s2">"banana"</span><span class="p">,</span> <span class="s2">"orange"</span><span class="p">,</span> <span class="s2">"apple"</span><span class="p">,</span> <span class="s2">"grape"</span><span class="p">]})</span>
<span class="n">display</span><span class="p">(</span><span class="n">fruits</span><span class="p">)</span>
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.dataframe tbody tr th {
vertical-align: top;
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.dataframe thead th {
text-align: right;
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</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>value</th>
<th>type</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>5</td>
<td>waterMelon</td>
</tr>
<tr>
<th>1</th>
<td>6</td>
<td>banana</td>
</tr>
<tr>
<th>2</th>
<td>7</td>
<td>orange</td>
</tr>
<tr>
<th>3</th>
<td>8</td>
<td>apple</td>
</tr>
<tr>
<th>4</th>
<td>9</td>
<td>grape</td>
</tr>
</tbody>
</table>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 转化数据表中的字符串为数值</span>
<span class="n">fruits_dum</span><span class="o">=</span><span class="n">pd</span><span class="o">.</span><span class="n">get_dummies</span><span class="p">(</span><span class="n">fruits</span><span class="p">)</span>
<span class="n">fruits_dum</span>
<span class="c1"># 数值列并没有变化，分类列变成了0-1矩阵</span>
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</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>value</th>
<th>type_apple</th>
<th>type_banana</th>
<th>type_grape</th>
<th>type_orange</th>
<th>type_waterMelon</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>5</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
</tr>
<tr>
<th>1</th>
<td>6</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<th>2</th>
<td>7</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
</tr>
<tr>
<th>3</th>
<td>8</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<th>4</th>
<td>9</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
</tbody>
</table>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 令程序将数值也看做字符串</span>
<span class="n">fruits</span><span class="p">[</span><span class="s2">"value"</span><span class="p">]</span> <span class="o">=</span> <span class="n">fruits</span><span class="p">[</span><span class="s2">"value"</span><span class="p">]</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">str</span><span class="p">)</span> <span class="c1">#先将数值转为字符串，这一句可选，但是推荐加上。</span>
<span class="c1"># 用 get_dummies 转化为字符串</span>
<span class="n">pd</span><span class="o">.</span><span class="n">get_dummies</span><span class="p">(</span><span class="n">fruits</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s2">"value"</span><span class="p">])</span>
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.dataframe tbody tr th:only-of-type {
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.dataframe tbody tr th {
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.dataframe thead th {
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</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>type</th>
<th>value_5</th>
<th>value_6</th>
<th>value_7</th>
<th>value_8</th>
<th>value_9</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>waterMelon</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<th>1</th>
<td>banana</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<th>2</th>
<td>orange</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>0</td>
</tr>
<tr>
<th>3</th>
<td>apple</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
</tr>
<tr>
<th>4</th>
<td>grape</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1</td>
</tr>
</tbody>
</table>
</div>
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<h2 id="%E5%AF%B9%E6%95%B0%E6%8D%AE%E8%BF%9B%E8%A1%8C%E8%A3%85%E7%AE%B1%E5%A4%84%E7%90%86">对数据进行装箱处理<a class="anchor-link" href="#%E5%AF%B9%E6%95%B0%E6%8D%AE%E8%BF%9B%E8%A1%8C%E8%A3%85%E7%AE%B1%E5%A4%84%E7%90%86">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 产生数据</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">rnd</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">38</span><span class="p">)</span>
<span class="n">x</span><span class="o">=</span><span class="n">rnd</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="c1"># 向数据集添加噪音</span>
<span class="n">y_no_noise</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="mi">6</span><span class="o">*</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span><span class="n">x</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">reshape</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">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">y_no_noise</span> <span class="o">+</span> <span class="n">rnd</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span><span class="o">/</span><span class="mi">2</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</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="s1">'o'</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'r'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [5]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 分别使用 MLP 算法和 KNN 算法 对这个数据集进行回归分析</span>
<span class="kn">from</span> <span class="nn">sklearn.neural_network</span> <span class="kn">import</span> <span class="n">MLPRegressor</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">KNeighborsRegressor</span>
<span class="c1"># 生成一个等差数列</span>
<span class="n">line</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</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">mlpr</span><span class="o">=</span><span class="n">MLPRegressor</span><span class="p">()</span><span class="o">.</span><span class="n">fit</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">knr</span><span class="o">=</span><span class="n">KNeighborsRegressor</span><span class="p">()</span><span class="o">.</span><span class="n">fit</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">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">mlpr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">line</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s2">"MLP"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">knr</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">line</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s2">"KNN"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</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="s1">'o'</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'r'</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="n">loc</span><span class="o">=</span><span class="s2">"best"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="c1"># 肉眼可见，MLP更平滑，而KNN覆盖更多的点。</span>
<span class="c1"># 该采用哪一个呢？</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 对数据进行一下“装箱处理”(binning)，也称为“离散化处理”(discretization)</span>
<span class="c1"># 设置箱子个数11</span>
<span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
<span class="c1">#将数据进行装箱处理</span>
<span class="n">target_bin</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">bins</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"装箱范围:</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span><span class="n">bins</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"前10个数据点的特征值:</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">X</span><span class="p">[:</span><span class="mi">10</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"前10个数据点的箱子:</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">target_bin</span><span class="p">[:</span><span class="mi">10</span><span class="p">])</span>
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<pre>装箱范围:
[-5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5.]
前10个数据点的特征值:
[[-1.1522688 ]
[ 3.59707847]
[ 4.44199636]
[ 2.02824894]
[ 1.33634097]
[ 1.05961282]
[-2.99873157]
[-1.12612112]
[-2.41016836]
[-4.25392719]]
前10个数据点的箱子:
[[ 4]
[ 9]
[10]
[ 8]
[ 7]
[ 7]
[ 3]
[ 4]
[ 3]
[ 1]]
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<h3 id="OneHotEncoder">OneHotEncoder<a class="anchor-link" href="#OneHotEncoder">¶</a></h3>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [7]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># sklearn 的 OneHotEncoder 和 pandas 的 get_dummies 功能基本一致，但是 OneHotEncoder 目前只能用于整型数值的类型变量。</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">OneHotEncoder</span>
<span class="n">onehot</span> <span class="o">=</span> <span class="n">OneHotEncoder</span><span class="p">(</span><span class="n">sparse</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">onehot</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">target_bin</span><span class="p">)</span>
<span class="n">X_in_bin</span><span class="o">=</span><span class="n">onehot</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">target_bin</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"装箱前的数据形态:</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">target_bin</span><span class="o">.</span><span class="n">shape</span> <span class="p">)</span> <span class="c1">#50行1列</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"装箱后的数据形态:</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">X_in_bin</span><span class="o">.</span><span class="n">shape</span> <span class="p">)</span> <span class="c1">#50行10列</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"装箱后的前10个数据点:</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">X_in_bin</span><span class="p">[:</span><span class="mi">10</span><span class="p">])</span>
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<pre>装箱前的数据形态:
(50, 1)
装箱后的数据形态:
(50, 10)
装箱后的前10个数据点:
[[0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
[0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
[0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]
[0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
[0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]
[1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]
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<div class="jp-InputPrompt jp-InputArea-prompt">In [8]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 分别使用 MLP 算法和 KNN 算法 对这个新数据集进行回归分析</span>
<span class="c1"># 使用独热编码进行数据表达</span>
<span class="n">line2</span><span class="o">=</span><span class="n">onehot</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">bins</span><span class="p">))</span>
<span class="n">mlpr2</span><span class="o">=</span><span class="n">MLPRegressor</span><span class="p">(</span><span class="n">max_iter</span><span class="o">=</span><span class="mi">500</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_in_bin</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">knr2</span><span class="o">=</span><span class="n">KNeighborsRegressor</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_in_bin</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">mlpr2</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">line2</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s2">"MLP"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">knr2</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">line2</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s2">"KNN"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</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="s1">'o'</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'r'</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="n">loc</span><span class="o">=</span><span class="s2">"best"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"OneHotEncode"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="c1"># 在x>0部分，2个拟合几乎完全重合。</span>
<span class="c1"># 对比 OneHotEncode 编码前，MLP回归模型变得更复杂；而KNN模型变得更简单。</span>
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<p>装箱的好处：可以纠正模型过拟合或者欠拟合的问题。</p>
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<li>尤其是对大规模高纬度的数据集使用线性模型的时候，装箱处理可以大幅提高线性模型的预测准确度。</li>
<li>装箱对于决策树算法没有太多作用，因为这类算法本身就是不停地拆分样本的特征数据，所以不需要再使用装箱操作。 </li>
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<h1 id="%E6%95%B0%E6%8D%AE%E2%80%9C%E5%8D%87%E7%BB%B4%E2%80%9D">数据“升维”<a class="anchor-link" href="#%E6%95%B0%E6%8D%AE%E2%80%9C%E5%8D%87%E7%BB%B4%E2%80%9D">¶</a></h1>
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<p>交叉式特征（Interaction Features）和多项式特征(Polynomial Features)</p>
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<h2 id="%E4%BA%A4%E5%8F%89%E5%BC%8F%E7%89%B9%E5%BE%81%EF%BC%88Interaction-Features%EF%BC%89">交叉式特征（Interaction Features）<a class="anchor-link" href="#%E4%BA%A4%E5%8F%89%E5%BC%8F%E7%89%B9%E5%BE%81%EF%BC%88Interaction-Features%EF%BC%89">¶</a></h2>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 交叉式特征（Interaction Features） 就是在原始特征中添加交互项。</span>
<span class="c1"># 测试 np.hstack() 函数</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">arr1</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span>
<span class="n">arr2</span><span class="o">=</span><span class="p">[</span><span class="mi">10</span><span class="p">,</span><span class="mi">30</span><span class="p">,</span><span class="mi">40</span><span class="p">,</span><span class="mi">50</span><span class="p">]</span>
<span class="n">arr3</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">(</span> <span class="p">[</span><span class="n">arr1</span><span class="p">,</span> <span class="n">arr2</span><span class="p">]</span> <span class="p">)</span>
<span class="n">arr3</span>
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<pre>array([ 1, 2, 3, 4, 10, 30, 40, 50])</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 把原始数据和装箱后的数据堆叠</span>
<span class="c1"># 产生数据</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">rnd</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">38</span><span class="p">)</span>
<span class="n">x</span><span class="o">=</span><span class="n">rnd</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="c1"># 向数据集添加噪音</span>
<span class="n">y_no_noise</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="mi">6</span><span class="o">*</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span><span class="n">x</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">reshape</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">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">y_no_noise</span> <span class="o">+</span> <span class="n">rnd</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span><span class="o">/</span><span class="mi">2</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"X</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span><span class="n">X</span><span class="p">[:</span><span class="mi">3</span><span class="p">])</span>
<span class="c1"># 对数据进行一下“装箱处理”(binning)，也称为“离散化处理”(discretization)</span>
<span class="c1"># 设置箱子个数11</span>
<span class="n">bins</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
<span class="c1"># 将数据进行装箱处理</span>
<span class="n">target_bin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">bins</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2">target_bin</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span><span class="n">target_bin</span><span class="p">[:</span><span class="mi">3</span><span class="p">])</span>
<span class="c1"># OneHotEncoder 只能输入整型</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">OneHotEncoder</span>
<span class="n">onehot</span> <span class="o">=</span> <span class="n">OneHotEncoder</span><span class="p">(</span><span class="n">sparse</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">onehot</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">target_bin</span><span class="p">)</span>
<span class="n">X_in_bin</span><span class="o">=</span><span class="n">onehot</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">target_bin</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2">X_in_bin</span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">X_in_bin</span><span class="p">[:</span><span class="mi">3</span><span class="p">])</span>
<span class="c1"># 按列拼接</span>
<span class="n">X_stack</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">X_in_bin</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">X_stack</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="c1">#(50, 1) (50, 11) 由1列，变为11列。后10列是编码后的。</span>
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<pre>X
[[-1.1522688 ]
[ 3.59707847]
[ 4.44199636]]
target_bin
[[ 4]
[ 9]
[10]]
X_in_bin
[[0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]
[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]
(50, 1) (50, 11)
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 分别使用 MLP 算法和 KNN 算法 对这个数据集进行回归分析</span>
<span class="kn">from</span> <span class="nn">sklearn.neural_network</span> <span class="kn">import</span> <span class="n">MLPRegressor</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">KNeighborsRegressor</span>
<span class="c1"># 生成一个等差数列</span>
<span class="n">line</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</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="c1"># 使用独热编码进行数据表达</span>
<span class="n">line2</span><span class="o">=</span><span class="n">onehot</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span> <span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">bins</span><span class="p">)</span> <span class="p">)</span>
<span class="c1">#将数据进行堆叠</span>
<span class="n">line_stack</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">(</span> <span class="p">[</span><span class="n">line</span><span class="p">,</span> <span class="n">line2</span><span class="p">]</span> <span class="p">)</span>
<span class="c1"># 训练数据</span>
<span class="n">mlpr3</span><span class="o">=</span><span class="n">MLPRegressor</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_stack</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">knr3</span><span class="o">=</span><span class="n">KNeighborsRegressor</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_stack</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="c1"># 绘图</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">mlpr3</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">line_stack</span><span class="p">),</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"MLP"</span><span class="p">)</span>
<span class="c1">#plt.plot(line, knr3.predict(line_stack), label="KNN")</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">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="k">for</span> <span class="n">vline</span> <span class="ow">in</span> <span class="n">bins</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">vline</span><span class="p">,</span> <span class="n">vline</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="s2">":"</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</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="n">loc</span><span class="o">=</span><span class="s2">"best"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</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="s1">'o'</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'r'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"After adding interaction"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="c1"># 每个数据所在的箱体中，MLP增加了斜率。</span>
<span class="c1"># 模型复杂度提高了。</span>
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<h3 id="%E4%BA%A4%E5%8F%89%E7%9B%B8">交叉相<a class="anchor-link" href="#%E4%BA%A4%E5%8F%89%E7%9B%B8">¶</a></h3>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [4]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 每个箱体中的斜率基本一致了，但是这不是我们需要的。我们希望每个箱体都有各自的截距和斜率。</span>
<span class="n">X_multi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">([</span><span class="n">X_in_bin</span><span class="p">,</span> <span class="n">X</span><span class="o">*</span><span class="n">X_in_bin</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">X_in_bin</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X_multi</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="c1">#(50, 20)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">X_multi</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
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<pre>(50, 1) (50, 10)
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<div class="jp-InputPrompt jp-InputArea-prompt">In [5]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># 每个箱子内都有自己的斜率</span>
<span class="c1"># 训练数据</span>
<span class="n">mlpr4</span><span class="o">=</span><span class="n">MLPRegressor</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_multi</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">knr4</span><span class="o">=</span><span class="n">KNeighborsRegressor</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_multi</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="c1">#将数据进行堆叠</span>
<span class="n">line_multi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">(</span> <span class="p">[</span><span class="n">line2</span><span class="p">,</span> <span class="n">line</span> <span class="o">*</span> <span class="n">line2</span><span class="p">]</span> <span class="p">)</span>
<span class="c1"># 绘图</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">mlpr4</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">line_multi</span><span class="p">),</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"MLP"</span><span class="p">)</span>
<span class="c1">#plt.plot(line, knr3.predict(line_stack), label="KNN")</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">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="k">for</span> <span class="n">vline</span> <span class="ow">in</span> <span class="n">bins</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">vline</span><span class="p">,</span> <span class="n">vline</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="s2">":"</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'grey'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</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="s1">'o'</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'r'</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="n">loc</span><span class="o">=</span><span class="s2">"lower right"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Adding multiply"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="c1"># 线性模型在低维度表现不好，在高纬度表现良好。所以可以升维后使用glm模型。</span>
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