Site updated: 2020-01-28 16:35:08
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Jimmy Xiang
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<h3 class="wrapper title" title="飞蟒微课堂Python面试专项课程启动——LeetCode刷题计划">飞蟒微课堂Python面试专项课程启动——LeetCode刷题计划</h3>
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LeetCode刷题计划启动啦
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cs224n解答
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cs224n解答
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飞蟒微课堂正式开班
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166
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166
archives/2020/index.html
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<p>你是否在朋友圈看过Python培训的广告? 你在微博是否刷出过大佬在学Python的新闻？你会惊讶，为什么现在都在大肆宣传Python，今天我就给你答案。</p>
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<p>IT行业发展日新月异，每天你都会听到很多新兴技术和编程语言以及他们的最新进展。</p>
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<p>对于那些对学哪种编程语言更适合，感觉困惑的初学者，其实不用担心，FlyPython为你提供了一个计划。我们不用需要学习三大编程语言，五大框架的谎言来骗你。相反，我们将只关注一种语言，那就是Python。</p>
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<p>让我们从一个有趣的事实开始。在现在流行的编程语言中，Python是最受欢迎。你可以通过在各种榜单上来确认这一事实。</p>
|
||||
<h2 id="为什么要学习Python？"><a href="#为什么要学习Python？" class="headerlink" title="为什么要学习Python？"></a>为什么要学习Python？</h2><p><img src="https://tva1.sinaimg.cn/large/006tNbRwly1gb93c0tlnnj317a0cyjto.jpg" alt></p>
|
||||
<p>你可能会想到的第一个问题是“为什么要专门学习Python？”。嗯，这个问题的答案很简单。</p>
|
||||
<p>考虑一下要包含在编程语言中的因素。</p>
|
||||
<h4 id="1-学习能力"><a href="#1-学习能力" class="headerlink" title="1.学习能力"></a>1.学习能力</h4><p>Python很难吗？一点也不！Python是很多人的第二语言，现在越来越多人开始作为第一语言学习。Python语言旨在简化了复杂的编程，它削减了所有低级任务，并为你执行所需的任何任务提供了高级抽象。Python基础语法非常简单，你可以通过一个月的练习轻松掌握它。</p>
|
||||
<h4 id="2-提高生产力"><a href="#2-提高生产力" class="headerlink" title="2.提高生产力"></a>2.提高生产力</h4><p>学习了编程语言后，打算做什么？你是否要构建应用程序，Web服务，令人兴奋的游戏，自动化重复性任务，执行复杂的科学或数字计算或从某些数据挖掘观点，Python让你无所不能。它是目前最有生产力的语言之一。</p>
|
||||
<h4 id="3-高薪"><a href="#3-高薪" class="headerlink" title="3.高薪"></a>3.高薪</h4><p>学习Python是你今天可以做出的最好的投资。Python开发人员的薪水很高，尤其是在Web开发，机器学习和数据科学领域。薪资范围从10k起，具体取决于地点和你在行业中的经验。IT行业对Python开发人员的需求很大，因此你在市场上找到Python职位不会有任何麻烦。</p>
|
||||
<h2 id="Python应用方向"><a href="#Python应用方向" class="headerlink" title="Python应用方向"></a>Python应用方向</h2><p>使用Python可以做的事情没有限制，但是在这里我们将向你介绍一些最重要的Python实际应用，以提示你可以在哪里实际使用Python编程语言。</p>
|
||||
<p><img src="https://tva1.sinaimg.cn/large/006tNbRwly1gb93c7xhhaj30ma0botam.jpg" alt></p>
|
||||
<h4 id="1-网站开发"><a href="#1-网站开发" class="headerlink" title="1.网站开发"></a>1.网站开发</h4><p>Python是快速开发Web应用程序的理想选择。借助Django，Tornado，Flask等许多框架，Python使你可以快速构建Web应用程序。Python用于Web开发的服务器端，你可以使用Python与数据库进行交互并构建REST API服务。</p>
|
||||
<h4 id="2-数据科学"><a href="#2-数据科学" class="headerlink" title="2.数据科学"></a>2.数据科学</h4><p>早期的Python主要用于构建应用程序和编写脚本以自动执行任务，但是现在，数据科学使Python更加流行。数据科学人员非常依赖Python，因为它的优点包括简单，强大的社区以及轻松计算等功能。在数据科学领域流行的Python库和框架是：</p>
|
||||
<ul>
|
||||
<li>Pandas（数据分析）</li>
|
||||
<li>Numpy（数值和科学计算）</li>
|
||||
<li>Matplotlib，Seaborn（数据可视化）</li>
|
||||
<li>Scikit-learn（机器学习）</li>
|
||||
<li>Tensorflow，Keras，Pytorch（深度学习）</li>
|
||||
</ul>
|
||||
<h4 id="3-人工智能"><a href="#3-人工智能" class="headerlink" title="3.人工智能"></a>3.人工智能</h4><p>不久的将来将是人工智能时代。过去，计算机被用来以很高的速度执行数学计算，但是现在，许多大型组织和研究人员正在致力于构建可以像人类一样执行任务的智能系统。机器在某种程度上足以理解人类的情感及其自然语言。它们可以模仿人类以前无法完成的某些动作。同样，Python在构建AI系统方面很受欢迎。</p>
|
||||
<p>下面列出了一些用于构建智能系统的Python库 ：</p>
|
||||
<ul>
|
||||
<li>NLTK (自然语言工具包)</li>
|
||||
<li>OpenCV (开源计算机视觉库)</li>
|
||||
<li>Rasa （开源聊天机器人库）</li>
|
||||
</ul>
|
||||
<h4 id="4-自动化"><a href="#4-自动化" class="headerlink" title="4.自动化"></a>4.自动化</h4><p>有许多重复性的与业务相关的任务。Python可以通过自动执行任务来简化工作，例如，抓取网站来收集数据，编写测试用例，自动化办公任务。<br>Python可以轻松访问和读取所有类型的文件，这通过自动执行重复任务为节省大量时间提供了机会。用于自动化的框架或库是：</p>
|
||||
<ul>
|
||||
<li>Robot Framework</li>
|
||||
<li>PyTest</li>
|
||||
<li>PyUnit</li>
|
||||
</ul>
|
||||
<p>Python在不同领域中的使用增长非常迅速，并且没有停止的迹象。可以肯定地说，Python将在这个瞬息万变的IT行业中会长期坚持下去。</p>
|
||||
<h4 id="如何学习Python？"><a href="#如何学习Python？" class="headerlink" title="如何学习Python？"></a>如何学习Python？</h4><p><img src="https://tva1.sinaimg.cn/large/006tNbRwly1gb93cfkmq4j30p00bojtb.jpg" alt></p>
|
||||
<p>你很棒已经读到了这里，现在我知道你对编程感到兴奋，并在思考你想使用Python构建什么样程序。让我们再迈出一步，为自己制定一个计划，以有效地学习Python。</p>
|
||||
<p>FlyPython推出了飞蟒微课堂，希望能给学员一些学习Python的路径指导。</p>
|
||||
<p><img src="https://tva1.sinaimg.cn/large/006tNbRwly1gb93cn4we7j30ng0poq4j.jpg" alt></p>
|
||||
<p>你的Python学习之路可以遵从以下7个步骤：</p>
|
||||
<h4 id="步骤1：加强基础"><a href="#步骤1：加强基础" class="headerlink" title="步骤1：加强基础"></a>步骤1：加强基础</h4><p>一切都从头开始，了解与编程相关的术语和概念。因此，请在你的计算机上安装Python，然后开始学习Python编程语言的基本语法，变量和数据类型</p>
|
||||
<h4 id="步骤2：了解决策和控制流程"><a href="#步骤2：了解决策和控制流程" class="headerlink" title="步骤2：了解决策和控制流程"></a>步骤2：了解决策和控制流程</h4><p>熟悉基础知识后，了解了如何使用编程语言进行决策判断。有多种不同的方法，例如if和else语句，可让根据条件进行决策。循环也是所有编程语言的重要组成部分。您可以使用循环轻松地执行重复性任务，并通过实现不同类型的循环（例如For循环，while循环和嵌套循环）来学习概念。</p>
|
||||
<h4 id="步骤3：掌握面向对象的编程"><a href="#步骤3：掌握面向对象的编程" class="headerlink" title="步骤3：掌握面向对象的编程"></a>步骤3：掌握面向对象的编程</h4><p>面向对象编程是一种通过考虑对象和类形式的现实世界实体来解决所有问题的方法。为了成为一名更好的程序员，必须了解面向对象编程的概念和原理。在构建大型应用程序时，，面向对象设计是有益的，它通过重用可用组件来帮助我们编写简洁的代码。它们也易于维护。</p>
|
||||
<h4 id="步骤4：使用框架创建Web应用"><a href="#步骤4：使用框架创建Web应用" class="headerlink" title="步骤4：使用框架创建Web应用"></a>步骤4：使用框架创建Web应用</h4><p>在Web开发环境中，Python用于Web应用程序的服务器端编程。我们使用HTML，CSS和JavaScript来定义网站的外观以及过渡效果和动画。这也称为应用程序的前端。应用程序的后端涉及处理来自浏览器或前端的请求，从数据库检索数据并执行操作。Python管理所有这些与服务器端相关的任务。用于Web开发的最受欢迎的Python框架是Django。另一个流行的框架是Flask。这些框架提供了应用程序的快速开发。因此，你可以选择其中任何一个，并通过创建具有基本CRUD操作的Web应用程序来创建一个小项目。</p>
|
||||
<h4 id="步骤5：掌握数据科学的技能"><a href="#步骤5：掌握数据科学的技能" class="headerlink" title="步骤5：掌握数据科学的技能"></a>步骤5：掌握数据科学的技能</h4><p>数据科学和机器学习的世界在很大程度上取决于Python。我们开始介绍机器学习算法的类型，通过实现不同的机器学习模型来练习编程。使用Pandas库分析数据，使用Numpy库执行数值计算，使用scikit-learn构建机器学习模型，并使用matplotlib或seaborn等库可视化数据。</p>
|
||||
<h4 id="步骤6：Python机器学习项目"><a href="#步骤6：Python机器学习项目" class="headerlink" title="步骤6：Python机器学习项目"></a>步骤6：Python机器学习项目</h4><p>环顾四周，思考可以解决哪些问题。创建一个项目构想列表，并从你学到的所有东西中构建出一些东西。通过集成所有内容来进行大型项目。你可以通过向用户提供某种形式的服务来构建机器学习模型并将其与网站集成。</p>
|
||||
<p>准备从头开始创建Python项目：</p>
|
||||
<ul>
|
||||
<li>虚假新闻检测</li>
|
||||
<li>音频情感识别</li>
|
||||
<li>聊天机器人</li>
|
||||
<li>交通标志识别</li>
|
||||
</ul>
|
||||
<p>我们会从最初的数据准备开始，构建机器学习pipeline，教你真正的机器学习项目实战。</p>
|
||||
<h4 id="步骤7：Python面试"><a href="#步骤7：Python面试" class="headerlink" title="步骤7：Python面试"></a>步骤7：Python面试</h4><p>Python面试分为两个部分，第一部分是数据结构算法准备阶段，主要是Leetcode真题解析。第二部分是各大厂面试真题解析，带你实战。</p>
|
||||
<h4 id="飞蟒微课堂更新计划"><a href="#飞蟒微课堂更新计划" class="headerlink" title="飞蟒微课堂更新计划"></a>飞蟒微课堂更新计划</h4><p>微课堂推出7个免费的专项课程来对应上面的7个步骤。照顾到不同的同学基础各不相同，课程之间相互独立，我们会同时更新不同的课程，最后把整个课程体系完善。</p>
|
||||
<p>目前的计划会同时启动Python面试和Python语法课程，请关注公众号FlyPython和飞蟒官网。</p>
|
||||
<h4 id="课程访问资源"><a href="#课程访问资源" class="headerlink" title="课程访问资源"></a>课程访问资源</h4><ul>
|
||||
<li>飞蟒官网: <a href="https://flypython.com" target="_blank" rel="noopener">https://flypython.com</a></li>
|
||||
<li>微课堂课程主页：<a href="http://flypython.com/python" target="_blank" rel="noopener">http://flypython.com/python</a></li>
|
||||
<li>Python日报：<a href="http://flypython.com/flypython_daily" target="_blank" rel="noopener">http://flypython.com/flypython_daily</a></li>
|
||||
<li>LeetCode题解： <a href="http://flypython.com/leetcode" target="_blank" rel="noopener">http://flypython.com/leetcode</a></li>
|
||||
</ul>
|
||||
<p><img src="https://tva1.sinaimg.cn/large/006tNbRwly1gb937qeljej30p00dwq5g.jpg" alt></p>
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<span>Author：</span><span>flypython</span> | <span>Date: </span><span>2020-01-02</span> | <span>Category：</span><span><a href="/fly/飞蟒微课堂/" title="飞蟒微课堂">飞蟒微课堂</a><a href="/fly/飞蟒微课堂/LeetCode/" title="LeetCode">LeetCode</a></span>
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||||
<h2 id="LeetCode刷题计划"><a href="#LeetCode刷题计划" class="headerlink" title="LeetCode刷题计划"></a>LeetCode刷题计划</h2><p>我至今面试过几百人，发现很多候选人基础确实有不少的问题，尤其是转专业的同学。</p>
|
||||
<p>大多数的公司面试工程师时都会考察这几个方面，</p>
|
||||
<ul>
|
||||
<li>数据结构与算法，一般为leetcode题目</li>
|
||||
<li>简历上的项目探讨与深入研究</li>
|
||||
<li>业务场景设计题</li>
|
||||
</ul>
|
||||
<p>按照不同的职位，会增加相应的内容。比如算法工程师，会问机器学习与深度学习算法，如果有paper和比赛，也会问一些。但是一般前两轮都是数据结构和算法，所以数据结构与算法是敲门砖，希望同学们能在这方面多下些功夫。</p>
|
||||
<p>Python面试专项课程分为两部分，一是刷leetcode，二是公司面试真题。完整的题解目录请在FlyPython公众号菜单上查看，这次主要介绍leetcode，面试真题后面会有具体的介绍。</p>
|
||||
<p>那怎么刷LeetCode呢？你可以根据自己的实际情况来决定，如果时间充裕可以通过题型来分类，每个题型都刷10题左右。如果时间紧张，建议刷热门题和公司题库，提高命中率。你也可以每周参加leetcode的周赛，来维持手感。</p>
|
||||
<p>真正做到bug free，确实很难，有的时候刷2-3遍也不行，得多做变型题，多想多总结，不断积累基础就变扎实了。难度以中等为主，兼顾hard。</p>
|
||||
<p>这次的LeetCode刷题计划，是以leetcode中文站的精选TOP面试题为基础的，题目共145道，希望对同学们有帮助。</p>
|
||||
<ul>
|
||||
<li>题目链接： <a href="https://leetcode-cn.com/problemset/top/" target="_blank" rel="noopener">https://leetcode-cn.com/problemset/top/</a></li>
|
||||
<li>题解总目录： <a href="http://flypython.com/leetcode/" target="_blank" rel="noopener">http://flypython.com/leetcode/</a> </li>
|
||||
<li>leetcode主页: <a href="https://leetcode-cn.com/u/flypython/" target="_blank" rel="noopener">https://leetcode-cn.com/u/flypython/</a></li>
|
||||
</ul>
|
||||
<h2 id="附：LeetCode练手题"><a href="#附：LeetCode练手题" class="headerlink" title="附：LeetCode练手题"></a>附：LeetCode练手题</h2><p>还没有注册LeetCode的同学，先去注册一个并完成下面的的练手题。还没有关注FlyPython的同学长按最后的二维码关注我吧。</p>
|
||||
<h4 id="LCP-1-猜数字"><a href="#LCP-1-猜数字" class="headerlink" title="LCP 1. 猜数字"></a>LCP 1. 猜数字</h4><p>链接：<a href="https://leetcode-cn.com/problems/guess-numbers/" target="_blank" rel="noopener">https://leetcode-cn.com/problems/guess-numbers/</a><br>难度：简单</p>
|
||||
<h4 id="题目"><a href="#题目" class="headerlink" title="题目"></a>题目</h4><blockquote>
|
||||
<p>小A 和 小B 在玩猜数字。小B 每次从 1, 2, 3 中随机选择一个，小A 每次也从 1, 2, 3 中选择一个猜。他们一共进行三次这个游戏，请返回 小A 猜对了几次？</p>
|
||||
<p>输入的guess数组为 小A 每次的猜测，answer数组为 小B 每次的选择。guess和answer的长度都等于3。</p>
|
||||
<p>示例 1：</p>
|
||||
<p>输入：guess = [1,2,3], answer = [1,2,3]<br>输出：3<br>解释：小A 每次都猜对了。</p>
|
||||
<p>示例 2：</p>
|
||||
<p>输入：guess = [2,2,3], answer = [3,2,1]<br>输出：1<br>解释：小A 只猜对了第二次。</p>
|
||||
<p>限制：</p>
|
||||
<p>guess的长度 = 3<br>answer的长度 = 3<br>guess的元素取值为 {1, 2, 3} 之一。<br>answer的元素取值为 {1, 2, 3} 之一。</p>
|
||||
</blockquote>
|
||||
<h4 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h4><p>leetcode最简单的练手题，可以循环比较计数，也可以直接三个元素比较。</p>
|
||||
<h4 id="解法"><a href="#解法" class="headerlink" title="解法"></a>解法</h4><p><img src="https://tva1.sinaimg.cn/large/006tNbRwly1gb1xh2ta3wg313q0hu7s8.gif" alt></p>
|
||||
<p><img src="https://tva1.sinaimg.cn/large/006tNbRwly1gb937qeljej30p00dwq5g.jpg" alt></p>
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<h2 class="wrapper title">cs224n 解答拾遗： 为何word2vec 训练的时候每个词有两个不同的向量</h2>
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<div class="wrapper tips">
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<span>Author：</span><span>flypython</span> | <span>Date: </span><span>2020-01-01</span> | <span>Category：</span><span><a href="/fly/自然语言处理/" title="自然语言处理">自然语言处理</a><a href="/fly/自然语言处理/cs224n/" title="cs224n">cs224n</a></span>
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<h3 id="1-前言：为何一个词有2个向量"><a href="#1-前言：为何一个词有2个向量" class="headerlink" title="1.前言：为何一个词有2个向量"></a>1.前言：为何一个词有2个向量</h3><blockquote>
|
||||
<p>在cs224n 2019课程中的L1和L2中，我们详细论述了word2vec skip-gram 模型，相信大家都已经掌握了。</p>
|
||||
</blockquote>
|
||||
<p>但这里有一个细节，肯定让不少同学非常疑惑。<br>视频中提到，一个词有2个向量，总参数是2d*V。</p>
|
||||
<p><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/2vec_20200114150901.png" alt></p>
|
||||
<p>（Lecture 01 Introduction and Word Vectors，ppt第23页)提到了use two vectors per word</p>
|
||||
<p><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/2vec_20200114145552.png" alt></p>
|
||||
<p>（Lecture 01 Introduction and Word Vectors，ppt第27页）</p>
|
||||
<p>如上图示，在训练过程中是存在2个词向量的。这怎么理解？明明一个词最终输出的时候，只有一个词向量呀。</p>
|
||||
<h3 id="2-word2vec回顾"><a href="#2-word2vec回顾" class="headerlink" title="2.word2vec回顾"></a>2.word2vec回顾</h3><p>在视频中，Manning教授简单提了一嘴，我们这里详细说明一下,word2vec为什么要在训练的时候使用2个词向量，这2个词向量是什么关系，最终输出的是什么词向量。</p>
|
||||
<p>这2个词向量一个是词$w$的word representations （$v_w$） 在下图中表示为V，一个是该词w的context representations （$u_w$）在下图中表示为U。</p>
|
||||
<p><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/2vec_20200114145755.png" alt></p>
|
||||
<p>（Lecture 02 Word Vectors 2 and Word Senses ppt第4页）</p>
|
||||
<p>在我们训练词向量的时候，对于训练语料，使得P(o|c)的概率最大，也就是<br>J=-logP(o|c)最小（如果没有负号则是求最大，cs224n视频的ppt就没有负号）。</p>
|
||||
<p>我们是怎么定义P(o|c)的呢？</p>
|
||||
<p>定义如下：</p>
|
||||
<p>$P(o|c)={exp(u_o^Tv_c)}/{\sum_{w=1}^V exp(u_w^Tv_c)}$</p>
|
||||
<p>可以看到，这个条件概率是中心词和上下文词2个词向量的点乘，再取e的指数，并除以所有词的词向量和中心词的点乘取e的指数之和，公式的本质是一个向量点乘+softmax。</p>
|
||||
<p>这里当w是o 中心词的时候，使用词的word representations，而w是c上下文词的时候，使用词的context representations。</p>
|
||||
<h3 id="3-问：为什么要这么做呢，为什么不都使用同一个词向量呢？"><a href="#3-问：为什么要这么做呢，为什么不都使用同一个词向量呢？" class="headerlink" title="3.问：为什么要这么做呢，为什么不都使用同一个词向量呢？"></a>3.问：为什么要这么做呢，为什么不都使用同一个词向量呢？</h3><p>答：使用2个词向量的目的是，训练时我们需要让具有相同上下文的词的词向量相互接近，但我们不希望这些词的上下文的词也相互接近。</p>
|
||||
<p>以下面2句话的例子讲解一下：</p>
|
||||
<p>the <strong>dog</strong> has a tail</p>
|
||||
<p>the <strong>cat</strong> has a tail</p>
|
||||
<p>这里采用word2vec skip-gram ,naive softmax 模型，窗口大小采用k=1。</p>
|
||||
<p>对于中心词dog来说，需要计算：</p>
|
||||
<p>P(dog|has) </p>
|
||||
<p>P(dog|the) </p>
|
||||
<p>对于中心词cat来说，需要计算：</p>
|
||||
<p>P(cat|has)</p>
|
||||
<p>P(cat|the)</p>
|
||||
<p>这里的条件概率公式是上面的：<br>$P(o|c)={exp(u_o^Tv_c)}/{\sum_{w=1}^V exp(u_w^Tv_c)}$</p>
|
||||
<p>分别把中心词dog/cat 和上下文词has/the带入，就可求出概率。<br>对于目标函数J=-logP(o|c)，我们要求其最小值，那么在word2vec算法中，需要做梯度下降算法。这里使用sgd，只需要对每个样本进行梯度下降，如下公式：</p>
|
||||
<p>$u_o(new)=u_o(old)-\alpha \partial J/(\partial u_o)$</p>
|
||||
<p>$v_c(new)=v_c(old)-\alpha \partial J/(\partial v_c)$</p>
|
||||
<p>多次迭代sgd后，会使得J变小，而$u_o$和$v_c$的点乘会变大，进而使得两者余弦距离接近。那么如果dog/cat 分别和has/the 接近了，dog和cat的词余弦距离就会接近。</p>
|
||||
<p>假设这里$u_o$和$v_c$都是同一种向量，那么不光dog和cat的词余弦距离接近，cat和has也会相近，连has和the都会相近。</p>
|
||||
<p>但是我们希望最后输出的词向量，dog和cat相近，但不希望cat和has相近，也不希望has和the相近。如果都相近，词就没有区分度了。</p>
|
||||
<p>所以我们对于每个词采用双词向量，对于dog 这个词，有一个word representations （$v_c$） 用来作为中心词时计算，有一个context representations （$u_o$）作为上下文词时进行计算。</p>
|
||||
<p>context representations训练为了使得中心词word representations相近，context representations作为中间结果不输出，而word representations作为最终结果输出。这样就避免了所有中心词的词向量都接近的困境了。</p>
|
||||
<p>最终，我们保存中心词的word representations，既公式中的$v_c$ 。</p>
|
||||
<h3 id="4-考古"><a href="#4-考古" class="headerlink" title="4.考古"></a>4.考古</h3><p>解释清楚这个问题以后，我们知道最早的算法是否使用2个vec的。</p>
|
||||
<p>在word2vec提出者，Tomas Mikolov 的论文Distributed Representations of Words and Phrases and their Compositionality<br>和他提供的word2vec.c代码里，训练过程中，每个word都存在2个词向量。</p>
|
||||
<p>如下图<br><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/2vec_20200114150350.png" alt><br>论文Distributed Representations of Words and Phrases and their Compositionality 中截图</p>
|
||||
<p><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/2vec_20200114150726.png" alt><br>word2vec.c代码截图</p>
|
||||
<p>所以我们清楚了，最早的word2vec算法确实在训练的时候是存在2个vec的。</p>
|
||||
<h3 id="5-参考文献："><a href="#5-参考文献：" class="headerlink" title="5.参考文献："></a>5.参考文献：</h3><p><a href="https://www.quora.com/Why-does-word2vec-have-two-different-representation-for-words" target="_blank" rel="noopener">https://www.quora.com/Why-does-word2vec-have-two-different-representation-for-words</a></p>
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<p>论文：Distributed Representations of Words and Phrases<br>and their Compositionality</p>
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<span>Author：</span><span>flypython</span> | <span>Date: </span><span>2020-01-02</span> | <span>Category：</span><span><a href="/fly/自然语言处理/" title="自然语言处理">自然语言处理</a><a href="/fly/自然语言处理/cs224n/" title="cs224n">cs224n</a></span>
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<blockquote>
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<p>老师，请问共现矩阵奇异值分解后为什么是用U的行来做word embedding呢?</p>
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</blockquote>
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<p>cs224n课程第一周里，提到了2种生成word embedding的方法。<br>一种是基于word2vec的神经网络生成词向量的方法。<br>另一种是基于统计的词向量生成的方法：使用共现矩阵，再进行SVD分解。</p>
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<p><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/count_based.png" alt></p>
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<p>首先要说明，这2种方法输出的word embedding 都是distributed representation(稠密表达)。</p>
|
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<p>其次值得说的是，这2种方法各有优缺点（可能面试里会问），在glove方法中，综合进行了两种算法，达到最优的效果。</p>
|
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<p>那么，我们这里详细探讨一下利用SVD生成词向量的过程，解答上面提到的问题。</p>
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<blockquote>
|
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<p>共现矩阵奇异值分解后为什么是用U的行来做word embedding</p>
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</blockquote>
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<h3 id="1-生成共现矩阵（Window-based-Co-occurrence-Matrix）"><a href="#1-生成共现矩阵（Window-based-Co-occurrence-Matrix）" class="headerlink" title="1.生成共现矩阵（Window based Co-occurrence Matrix）"></a>1.生成共现矩阵（Window based Co-occurrence Matrix）</h3><p>构造一个矩阵X，这个矩阵的大小是 $V*V$ ，这里V是词表的长度。这个矩阵称之为共现矩阵。</p>
|
||||
<p>我们要统计，每个中心词在左右k个窗口的范围内，上下文词出现的词频。于是这里的共现矩阵，第一个维度（列），代表这个中心词，第二个维度（行）代表这个中心词对应的上下文词。<br>$X={x_{ij}}$为第i个词作为中心词时，对应第j个词作为其上下文词时候的词频。</p>
|
||||
<p>我们还是用课上的例子，有3句话：</p>
|
||||
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">I enjoy flying。</span><br><span class="line">I like NLP。</span><br><span class="line">I like deep learning。</span><br></pre></td></tr></table></figure>
|
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||||
<p>假设这里k=1，统计的共现矩阵X为：<br><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/Window_based_Co-occurrence_Matrix1.png" alt></p>
|
||||
<p>可以看出，这里的共现矩阵X为对称矩阵，也就是对中心词like，enjoy的出现次数是等于对于中心词enjoy，like的出现次数。</p>
|
||||
<h3 id="2-SVD分解的过程"><a href="#2-SVD分解的过程" class="headerlink" title="2.SVD分解的过程"></a>2.SVD分解的过程</h3><p>假设X的size是$V<em>V$,那么U的矩阵是$V</em>K$,奇异值矩阵S是$K<em>K$,而$V^T$的矩阵size 是$K</em>V$.<br>这里V是词表长度，上面解释了，K是指最后需要输出的词向量维度，一般我们取100-300之间的一个值。</p>
|
||||
<p>SVD分解公式可以写作<br>$X=USV^T$<br>写成分量式为：</p>
|
||||
<p>$x_{ij}= \sum_{k=1}^n u_{ij}s_kv_{jk}$</p>
|
||||
<p>那么从这个公式看出，对于每个样本word $x_{ij}$ 与$u_{ij}$是对于的，而不是与$v^T_j$对应，$v^T_j$与每个维度对应。<br><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/svd1.png" alt></p>
|
||||
<h4 id="这里需要解释一下我们是如何得到SVD分解公式的："><a href="#这里需要解释一下我们是如何得到SVD分解公式的：" class="headerlink" title="这里需要解释一下我们是如何得到SVD分解公式的："></a>这里需要解释一下我们是如何得到SVD分解公式的：</h4><p>由线性代数基本知识可知，对于任意矩阵X（size $V*V$ ）来说，我们可以进行奇异值分解，</p>
|
||||
<p>$X=U \Lambda V^T$，</p>
|
||||
<p>这里， $U, V, \Lambda$都是size $V*V$ 的对角矩阵，并且每个值都是非负实数，按大小从大到小排列。</p>
|
||||
<p><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/svd2.png" alt></p>
|
||||
<p>那么我们对$\Lambda$进行降维，只保留前K个值，这样U和V也会跟着变，从维度上看，矩阵U去掉了后面的一些列，变成了$V<em>K$;矩阵$V^T$，去掉了前面的一些行，变成了$K</em>V$（实质上做了空间变换，而不是简单的去除一些数据）。也就是上面的图：<br><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/svd1.png" alt></p>
|
||||
<p>这里就解释了，为什么是用U的行来做word embedding。</p>
|
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<h3 id="3-如果U对应的词向量，那么V对应的是什么呢？"><a href="#3-如果U对应的词向量，那么V对应的是什么呢？" class="headerlink" title="3.如果U对应的词向量，那么V对应的是什么呢？"></a>3.如果U对应的词向量，那么V对应的是什么呢？</h3><p>还有一个问题，如果U对应的词向量，那么V对应的是什么呢？对于词共现矩阵来说，V的意义还不是很清晰，我们考虑这样一个矩阵：</p>
|
||||
<p>词-文档矩阵 Word-Document Matrix，行是所有的词，维度为V，列是每个文档，维度为M。</p>
|
||||
<p>对这样一个矩阵进行SVD分解，并降维到K个奇异值上取值，</p>
|
||||
<p><img src="https://raw.githubusercontent.com/jcjview/jcjview.github.io/master/img/lsa1.png" alt></p>
|
||||
<p>SVD分解公式可以写作<br>$X=U\Sigma V^T$</p>
|
||||
<p>U的矩阵size$V*K$,</p>
|
||||
<p>$V^T$的矩阵size 是$K*V$</p>
|
||||
<p>写成分量式为：</p>
|
||||
<p>$x_{ij}= \sum_{k=1}^n u_{ij}\sigma_kv_{jk}$</p>
|
||||
<p>$u_{ij}$ 对应的第i个词和第j个主题的相关度，$u_{i}是词的主题向量$。</p>
|
||||
<p>$v_{jk}$ 对应第j个文档和第k个主题的相关度，<strong>所以$v_j$是第j个文档的文档向量。</strong></p>
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<p>这样就说明了V在SVD分解的意义。</p>
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