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        <p>学习Apriori算法首先要了解几个概念：项集、支持度、置信度、最小支持度、最小置信度、频繁项集。</p>
<p>项集：顾名思义，即项的集合。eg：牛奶、面包组成一个集合{牛奶、面包}，其中牛奶和面包为项，{牛奶、面包}为项集，称之为2项集。（说白了，其实就是集合）<br>支持度：项集A、B同时发生的概率称之为关联规则的支持度。<br>置信度：项集A发生的情况下，则项集B发生的概率为关联规则的置信度。</p>
<a id="more"></a>
<p>支持度与置信度的概念有些抽象，具体可以看下面的例子：<br><img src="https://tva1.sinaimg.cn/large/008eGmZEly1gnynlcwo3sj307n03rmx3.jpg" alt="这里写图片描述"><br>如图数据为顾客购物情况，每一个id对应的items都是一个项集，现在需要对{milk，diaper}与{beer}关联性进行研究，计算支持度与置信度。<br>计算如下：<br>计算支持度：计算{milk，diaper}{beer}同时发生的概率就相当于计算{milk，diaper，beer}出现的次数所占数据条的比重，即2/5.<br>计算置信度：计算{milk，diaper}发生的情况下，则{beer}发生的概率就相当于计算{milk，diaper，beer}出现的次数所占{milk，diaper}发生次数的比重，即2/3.</p>
<p>最小支持度：最小支持度就是人为按照实际意义规定的阈值，表示项集在统计意义上的最低重要性。<br>最小置信度：最小置信度也是人为按照实际意义规定的阈值，表示关联规则最低可靠性。<br>如果支持度与置信度同时达到最小支持度与最小置信度，则此关联规则为强规则。<br>频繁项集：满足最小支持度的所有项集，称作频繁项集。<br>（频繁项集性质：1、频繁项集的所有非空子集也为频繁项集；2、若A项集不是频繁项集，则其他项集或事务与A项集的并集也不是频繁项集）</p>
<p>了解了以上定义，那么如何从大量的数据中找出不同项的关联规则呢？下面具体看Apriori算法实现过程。<br>Apriori实现过程：首先，找出所有的频繁项集，再从频繁项集中找出符合最小置信度的项集，最终便得到有强规则的项集（即我们所需的项的关联性）。<br>例如：<br>数据如下<br><img src="https://tva1.sinaimg.cn/large/008eGmZEly1gnynlgcyoxj30pe07qjub.jpg" alt="这里写图片描述"><br>算法过程如下<br>首先计算出所有的频繁项集，这里最小支持度为0.2<br><img src="https://tva1.sinaimg.cn/large/008eGmZEly1gnynlk2g29j30ml0ggtem.jpg" alt="这里写图片描述"><br>得出L1、L2、L3的各个项集均为频繁项集，再进行计算每个频繁项集的置信度，其中L1不必计算。计算结果如下<br><img src="https://tva1.sinaimg.cn/large/008eGmZEly1gnynlnscl0j30fw0g5adg.jpg" alt="这里写图片描述"><br>（如果想了解寻找频繁项集的详细过程，可以研读张良均等著《python数据分析与挖掘实战》，里面有详细过程）<br>至此就完成了Apriori算法的全部过程。</p>
<p>接下来python实现Apriori算法</p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">#-*- coding: utf-8 -*-</span></span><br><span class="line"><span class="keyword">from</span> __future__ <span class="keyword">import</span> print_function</span><br><span class="line"><span class="keyword">import</span> pandas <span class="keyword">as</span> pd</span><br><span class="line"></span><br><span class="line"><span class="comment">#自定义连接函数，用于实现L_&#123;k-1&#125;到C_k的连接</span></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">connect_string</span><span class="params">(x, ms)</span>:</span></span><br><span class="line">  x = list(map(<span class="keyword">lambda</span> i:sorted(i.split(ms)), x))</span><br><span class="line">  l = len(x[<span class="number">0</span>])</span><br><span class="line">  r = []</span><br><span class="line">  <span class="keyword">for</span> i <span class="keyword">in</span> range(len(x)):</span><br><span class="line">    <span class="keyword">for</span> j <span class="keyword">in</span> range(i,len(x)):</span><br><span class="line">      <span class="keyword">if</span> x[i][:l<span class="number">-1</span>] == x[j][:l<span class="number">-1</span>] <span class="keyword">and</span> x[i][l<span class="number">-1</span>] != x[j][l<span class="number">-1</span>]:</span><br><span class="line">        r.append(x[i][:l<span class="number">-1</span>]+sorted([x[j][l<span class="number">-1</span>],x[i][l<span class="number">-1</span>]]))</span><br><span class="line">  <span class="keyword">return</span> r</span><br><span class="line"></span><br><span class="line"><span class="comment">#寻找关联规则的函数</span></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">find_rule</span><span class="params">(d, support, confidence, ms = <span class="string">u'--'</span>)</span>:</span></span><br><span class="line">  result = pd.DataFrame(index=[<span class="string">'support'</span>, <span class="string">'confidence'</span>]) <span class="comment">#定义输出结果</span></span><br><span class="line"></span><br><span class="line">  support_series = <span class="number">1.0</span>*d.sum()/len(d) <span class="comment">#支持度序列</span></span><br><span class="line">  column = list(support_series[support_series &gt; support].index) <span class="comment">#初步根据支持度筛选</span></span><br><span class="line">  k = <span class="number">0</span></span><br><span class="line"></span><br><span class="line">  <span class="keyword">while</span> len(column) &gt; <span class="number">1</span>:</span><br><span class="line">    k = k+<span class="number">1</span></span><br><span class="line">    print(<span class="string">u'\n正在进行第%s次搜索...'</span> %k)</span><br><span class="line">    column = connect_string(column, ms)</span><br><span class="line">    print(<span class="string">u'数目：%s...'</span> %len(column))</span><br><span class="line">    sf = <span class="keyword">lambda</span> i: d[i].prod(axis=<span class="number">1</span>, numeric_only = <span class="keyword">True</span>) <span class="comment">#新一批支持度的计算函数</span></span><br><span class="line"></span><br><span class="line">    <span class="comment">#创建连接数据，这一步耗时、耗内存最严重。当数据集较大时，可以考虑并行运算优化。</span></span><br><span class="line">    d_2 = pd.DataFrame(list(map(sf,column)), index = [ms.join(i) <span class="keyword">for</span> i <span class="keyword">in</span> column]).T</span><br><span class="line"></span><br><span class="line">    support_series_2 = <span class="number">1.0</span>*d_2[[ms.join(i) <span class="keyword">for</span> i <span class="keyword">in</span> column]].sum()/len(d) <span class="comment">#计算连接后的支持度</span></span><br><span class="line">    column = list(support_series_2[support_series_2 &gt; support].index) <span class="comment">#新一轮支持度筛选</span></span><br><span class="line">    support_series = support_series.append(support_series_2)</span><br><span class="line">    column2 = []</span><br><span class="line"></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> column: <span class="comment">#遍历可能的推理，如&#123;A,B,C&#125;究竟是A+B--&gt;C还是B+C--&gt;A还是C+A--&gt;B？</span></span><br><span class="line">      i = i.split(ms)</span><br><span class="line">      <span class="keyword">for</span> j <span class="keyword">in</span> range(len(i)):</span><br><span class="line">        column2.append(i[:j]+i[j+<span class="number">1</span>:]+i[j:j+<span class="number">1</span>])</span><br><span class="line"></span><br><span class="line">    cofidence_series = pd.Series(index=[ms.join(i) <span class="keyword">for</span> i <span class="keyword">in</span> column2]) <span class="comment">#定义置信度序列</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> column2: <span class="comment">#计算置信度序列</span></span><br><span class="line">      cofidence_series[ms.join(i)] = support_series[ms.join(sorted(i))]/support_series[ms.join(i[:len(i)<span class="number">-1</span>])]</span><br><span class="line"></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> cofidence_series[cofidence_series &gt; confidence].index: <span class="comment">#置信度筛选</span></span><br><span class="line">      result[i] = <span class="number">0.0</span></span><br><span class="line">      result[i][<span class="string">'confidence'</span>] = cofidence_series[i]</span><br><span class="line">      result[i][<span class="string">'support'</span>] = support_series[ms.join(sorted(i.split(ms)))]</span><br><span class="line"></span><br><span class="line">  result = result.T.sort_values([<span class="string">'confidence'</span>,<span class="string">'support'</span>], ascending = <span class="keyword">False</span>) <span class="comment">#结果整理，输出</span></span><br><span class="line">  print(<span class="string">u'\n结果为：'</span>)</span><br><span class="line">  print(result)</span><br><span class="line"></span><br><span class="line">  <span class="keyword">return</span> result</span><br></pre></td></tr></table></figure>
<p>Apriori算法调用，进行关联性分析<br>数据如下<br><img src="https://tva1.sinaimg.cn/large/008eGmZEly1gnynmc9a5dj308905r3yb.jpg" alt="这里写图片描述"><br>代码如下</p>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">#-*- coding: utf-8 -*-</span></span><br><span class="line"><span class="comment">#使用Apriori算法挖掘菜品订单关联规则</span></span><br><span class="line"><span class="keyword">from</span> __future__ <span class="keyword">import</span> print_function</span><br><span class="line"><span class="keyword">import</span> pandas <span class="keyword">as</span> pd</span><br><span class="line"><span class="keyword">from</span> apriori <span class="keyword">import</span> * <span class="comment">#导入自行编写的apriori函数</span></span><br><span class="line"></span><br><span class="line">inputfile = <span class="string">'../data/menu_orders.xls'</span></span><br><span class="line">outputfile = <span class="string">'../tmp/apriori_rules.xls'</span> <span class="comment">#结果文件</span></span><br><span class="line">data = pd.read_excel(inputfile, header = <span class="keyword">None</span>)</span><br><span class="line"></span><br><span class="line">print(<span class="string">u'\n转换原始数据至0-1矩阵...'</span>)</span><br><span class="line">ct = <span class="keyword">lambda</span> x : pd.Series(<span class="number">1</span>, index = x[pd.notnull(x)]) <span class="comment">#转换0-1矩阵的过渡函数</span></span><br><span class="line">b = map(ct, data.as_matrix()) <span class="comment">#用map方式执行</span></span><br><span class="line">data = pd.DataFrame(list(b)).fillna(<span class="number">0</span>) <span class="comment">#实现矩阵转换，空值用0填充</span></span><br><span class="line">print(<span class="string">u'\n转换完毕。'</span>)</span><br><span class="line"><span class="keyword">del</span> b <span class="comment">#删除中间变量b，节省内存</span></span><br><span class="line"></span><br><span class="line">support = <span class="number">0.2</span> <span class="comment">#最小支持度</span></span><br><span class="line">confidence = <span class="number">0.5</span> <span class="comment">#最小置信度</span></span><br><span class="line">ms = <span class="string">'---'</span> <span class="comment">#连接符，默认'--'，用来区分不同元素，如A--B。需要保证原始表格中不含有该字符</span></span><br><span class="line"></span><br><span class="line">find_rule(data, support, confidence, ms).to_excel(outputfile) <span class="comment">#保存结果</span></span><br></pre></td></tr></table></figure>
<p>结果如下<br>support confidence<br>e—a 0.3 1.000000<br>e—c 0.3 1.000000<br>c—e—a 0.3 1.000000<br>a—e—c 0.3 1.000000<br>c—a 0.5 0.714286<br>a—c 0.5 0.714286<br>a—b 0.5 0.714286<br>c—b 0.5 0.714286<br>b—a 0.5 0.625000<br>b—c 0.5 0.625000<br>a—c—e 0.3 0.600000<br>b—c—a 0.3 0.600000<br>a—c—b 0.3 0.600000<br>a—b—c 0.3 0.600000</p>
<p>本文主要参考书籍张良均等著《python数据分析与挖掘实战》<br>本文主要参考博客<span class="exturl" data-url="aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2JhaW1hZnVqaW5qaS9hcnRpY2xlL2RldGFpbHMvNTM0NTY5MzE=" title="https://blog.csdn.net/baimafujinji/article/details/53456931">https://blog.csdn.net/baimafujinji/article/details/53456931<i class="fa fa-external-link"></i></span></p>
<p><span class="exturl" data-url="aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2xid2Vpd2FuL2FydGljbGUvZGV0YWlscy84MjcyNTQ2Nj9kaXN0X3JlcXVlc3RfaWQ9MDc1MzQxOTgtZmJiZS00ODI1LTliZmYtMjFmYmQ4YjcyYTFkJmFtcDtkZXB0aF8xLQ==" title="https://blog.csdn.net/lbweiwan/article/details/82725466?dist_request_id=07534198-fbbe-4825-9bff-21fbd8b72a1d&amp;depth_1-">转载地址<i class="fa fa-external-link"></i></span></p>


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