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coding-agent


			
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  <h1>3.4 BM25算法简介与应用</h1>

<h2 id="_1">学习目标<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
<ol>
<li>理解BM25算法的基本原理及其在信息检索中的作用。</li>
<li>掌握如何使用BM25进行文本匹配。</li>
<li>学会将BM25算法集成到工程化代码中。</li>
</ol>
<hr />
<h2 id="bm25">一、BM25算法概述<a class="headerlink" href="#bm25" title="Permanent link">&para;</a></h2>
<h3 id="1">1 公式<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>BM25（Best Matching 25）是一种信息检索领域的排名算法，用于计算查询（Query）与文档（Document）之间的相关性得分。它改进了传统的TF-IDF算法，引入文档长度归一化和词频饱和机制，使检索结果更准确。</p>
<div align=center><img src="../img/3-2-1.png" style="zoom:90%" ><img/></div>

<p>其中：</p>
<blockquote>
<ul>
<li>fi 是词项 qi在文档 D中的出现次数（TF），</li>
<li>N是文档总数，</li>
<li>ni是包含词项 qi的文档数，</li>
<li>∣D∣是文档 D的长度，</li>
<li>avgdl 是所有文档的平均长度，</li>
<li>k1 和 b是调整参数，通常设置为 k1=1.2和 b=0.75 。</li>
</ul>
</blockquote>
<h3 id="2">2 简单示例<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>假设我们有以下文档集合：</p>
<ul>
<li>
<p>文档1："我喜欢编程"</p>
</li>
<li>
<p>文档2："编程很有趣"</p>
</li>
<li>查询："他喜欢编程"</li>
</ul>
<p><strong>步骤</strong>：</p>
<ol>
<li>分词：将文档和查询拆分为词。</li>
<li>文档1：["我", "喜欢", "编程"]</li>
<li>文档2：["编程", "很", "有趣"]</li>
<li>查询：["他", "喜欢", "编程"]</li>
<li>计算BM25得分：使用<code>rank_bm25</code>库计算每个文档与查询的相关性。</li>
</ol>
<hr />
<h2 id="_2">二、代码实现<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h2>
<h3 id="1_1">1 整体结构<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
<div class="highlight"><pre><span></span><code>bm25_lesson/
├── retrieval/
│   └── bm25_search.py  # BM25检索模块
├── main.py             # 主程序入口
└── requirements.txt    # 依赖文件
</code></pre></div>
<h3 id="2_1">2 具体模块<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
<h4 id="21-retrievalbm25_searchpy">2.1 检索模块 (<code>retrieval/bm25_search.py</code>)<a class="headerlink" href="#21-retrievalbm25_searchpy" title="Permanent link">&para;</a></h4>
<div class="highlight"><pre><span></span><code><span class="kn">import</span><span class="w"> </span><span class="nn">jieba</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">rank_bm25</span><span class="w"> </span><span class="kn">import</span> <span class="n">BM25L</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">logging</span>

<span class="c1"># 配置日志</span>
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">,</span> <span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(asctime)s</span><span class="s1"> - </span><span class="si">%(levelname)s</span><span class="s1"> - </span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="n">logger</span> <span class="o">=</span> <span class="n">logging</span><span class="o">.</span><span class="n">getLogger</span><span class="p">(</span><span class="vm">__name__</span><span class="p">)</span>

<span class="k">class</span><span class="w"> </span><span class="nc">BM25Search</span><span class="p">:</span>
    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">documents</span><span class="p">):</span>
        <span class="c1"># 初始化文档集合</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">documents</span> <span class="o">=</span> <span class="n">documents</span>
        <span class="c1"># 分词后的文档</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">tokenized_docs</span> <span class="o">=</span> <span class="p">[</span><span class="n">jieba</span><span class="o">.</span><span class="n">lcut</span><span class="p">(</span><span class="n">doc</span><span class="p">)</span> <span class="k">for</span> <span class="n">doc</span> <span class="ow">in</span> <span class="n">documents</span><span class="p">]</span>
        <span class="c1"># 初始化BM25模型</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">bm25</span> <span class="o">=</span> <span class="n">BM25L</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tokenized_docs</span><span class="p">)</span>
        <span class="n">logger</span><span class="o">.</span><span class="n">info</span><span class="p">(</span><span class="s2">&quot;BM25模型初始化完成&quot;</span><span class="p">)</span>

    <span class="k">def</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">query</span><span class="p">):</span>
        <span class="c1"># 分词查询</span>
        <span class="n">tokenized_query</span> <span class="o">=</span> <span class="n">jieba</span><span class="o">.</span><span class="n">lcut</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
        <span class="k">try</span><span class="p">:</span>
            <span class="c1"># 计算每个文档的BM25得分</span>
            <span class="n">scores</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bm25</span><span class="o">.</span><span class="n">get_scores</span><span class="p">(</span><span class="n">tokenized_query</span><span class="p">)</span>
            <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;scores--》</span><span class="si">{</span><span class="n">scores</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
            <span class="c1"># 获取最高得分的文档索引</span>
            <span class="n">best_idx</span> <span class="o">=</span> <span class="n">scores</span><span class="o">.</span><span class="n">argmax</span><span class="p">()</span>
            <span class="n">best_score</span> <span class="o">=</span> <span class="n">scores</span><span class="p">[</span><span class="n">best_idx</span><span class="p">]</span>
            <span class="n">best_doc</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">documents</span><span class="p">[</span><span class="n">best_idx</span><span class="p">]</span>
            <span class="n">logger</span><span class="o">.</span><span class="n">info</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;查询: </span><span class="si">{</span><span class="n">query</span><span class="si">}</span><span class="s2">, 最佳匹配: </span><span class="si">{</span><span class="n">best_doc</span><span class="si">}</span><span class="s2">, 得分: </span><span class="si">{</span><span class="n">best_score</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
            <span class="k">return</span> <span class="n">best_doc</span><span class="p">,</span> <span class="n">best_score</span>
        <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
            <span class="n">logger</span><span class="o">.</span><span class="n">error</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;检索失败: </span><span class="si">{</span><span class="n">e</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
            <span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="mf">0.0</span>
</code></pre></div>
<h4 id="22-mainpy">2.2 主程序 (<code>main.py</code>)<a class="headerlink" href="#22-mainpy" title="Permanent link">&para;</a></h4>
<div class="highlight"><pre><span></span><code><span class="kn">from</span><span class="w"> </span><span class="nn">retrieval.bm25_search</span><span class="w"> </span><span class="kn">import</span> <span class="n">BM25Search</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">logging</span>

<span class="c1"># 配置日志</span>
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span><span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">,</span> <span class="nb">format</span><span class="o">=</span><span class="s1">&#39;</span><span class="si">%(asctime)s</span><span class="s1"> - </span><span class="si">%(levelname)s</span><span class="s1"> - </span><span class="si">%(message)s</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="n">logger</span> <span class="o">=</span> <span class="n">logging</span><span class="o">.</span><span class="n">getLogger</span><span class="p">(</span><span class="vm">__name__</span><span class="p">)</span>

<span class="k">def</span><span class="w"> </span><span class="nf">main</span><span class="p">():</span>
    <span class="c1"># 示例文档集合</span>
    <span class="n">documents</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot;我喜欢编程&quot;</span><span class="p">,</span> <span class="s2">&quot;编程很有趣&quot;</span><span class="p">]</span>
    <span class="c1"># 初始化BM25检索器</span>
    <span class="n">bm25_search</span> <span class="o">=</span> <span class="n">BM25Search</span><span class="p">(</span><span class="n">documents</span><span class="p">)</span>
    <span class="c1"># 示例查询</span>
    <span class="n">query</span> <span class="o">=</span> <span class="s2">&quot;他喜欢编程&quot;</span>
    <span class="c1"># 执行检索</span>
    <span class="n">result</span><span class="p">,</span> <span class="n">score</span> <span class="o">=</span> <span class="n">bm25_search</span><span class="o">.</span><span class="n">search</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">result</span><span class="p">:</span>
        <span class="n">logger</span><span class="o">.</span><span class="n">info</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;查询结果: </span><span class="si">{</span><span class="n">result</span><span class="si">}</span><span class="s2">, 得分: </span><span class="si">{</span><span class="n">score</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
    <span class="k">else</span><span class="p">:</span>
        <span class="n">logger</span><span class="o">.</span><span class="n">info</span><span class="p">(</span><span class="s2">&quot;未找到匹配结果&quot;</span><span class="p">)</span>

<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s2">&quot;__main__&quot;</span><span class="p">:</span>
    <span class="n">main</span><span class="p">()</span>
</code></pre></div>
<h4 id="23-requirementstxt">2.3 依赖文件 (<code>requirements.txt</code>)<a class="headerlink" href="#23-requirementstxt" title="Permanent link">&para;</a></h4>
<div class="highlight"><pre><span></span><code>jieba
rank_bm25
</code></pre></div>
<hr />
<h2 id="_3">三、示例运行结果<a class="headerlink" href="#_3" title="Permanent link">&para;</a></h2>
<p>运行<code>main.py</code>，输出如下：
<div class="highlight"><pre><span></span><code>2025-04-02 19:01:27,463 - INFO - BM25模型初始化完成
2025-04-02 19:01:27,464 - INFO - 查询: 他喜欢编程, 最佳匹配: 我喜欢编程, 得分: 1.094
2025-04-02 19:01:27,464 - INFO - 查询结果: 我喜欢编程, 得分: 1.094
</code></pre></div></p>
<p>分析：</p>
<ul>
<li>"编程很有趣"得分高于"我喜欢编程"，因为前者词频更高且文档较短。</li>
<li>BM25通过长度归一化避免了长文档的过度优势。</li>
</ul>
<hr />
<h2 id="_4">本章小结<a class="headerlink" href="#_4" title="Permanent link">&para;</a></h2>
<p>本节主要介绍了BM25算法的原理和应用：</p>
<ul>
<li>
<p><strong>原理</strong>：结合TF、IDF、长度归一化和词频饱和。</p>
</li>
<li>
<p><strong>应用</strong>：通过<code>rank_bm25</code>库实现文本检索。</p>
</li>
</ul>
<hr />


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