wangwei
/
Notes-ML-AndrewNg

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<div  id='write'  class = 'is-node'><div class='md-toc' mdtype='toc'><p class="md-toc-content"><span class="md-toc-item md-toc-h1" data-ref="n2"><a class="md-toc-inner" href="#header-n2">1. 引言(Introduction)</a></span><span class="md-toc-item md-toc-h2" data-ref="n3"><a class="md-toc-inner" href="#header-n3">1.1 Welcome</a></span><span class="md-toc-item md-toc-h2" data-ref="n40"><a class="md-toc-inner" href="#header-n40">1.2 什么是机器学习(What is Machine Learning)</a></span><span class="md-toc-item md-toc-h2" data-ref="n79"><a class="md-toc-inner" href="#header-n79">1.3 监督学习(Supervised Learning)</a></span><span class="md-toc-item md-toc-h2" data-ref="n96"><a class="md-toc-inner" href="#header-n96">1.4 无监督学习(Unsupervised Learning)</a></span><span class="md-toc-item md-toc-h1" data-ref="n130"><a class="md-toc-inner" href="#header-n130">2 单变量线性回归(Linear Regression with One Variable)</a></span><span class="md-toc-item md-toc-h2" data-ref="n131"><a class="md-toc-inner" href="#header-n131">2.1 模型表示(Model Representation)</a></span><span class="md-toc-item md-toc-h2" data-ref="n165"><a class="md-toc-inner" href="#header-n165">2.2 代价函数(Cost Function)</a></span><span class="md-toc-item md-toc-h2" data-ref="n189"><a class="md-toc-inner" href="#header-n189">2.3 代价函数 - 直观理解1(Cost Function - Intuition I)</a></span><span class="md-toc-item md-toc-h2" data-ref="n203"><a class="md-toc-inner" href="#header-n203">2.4 代价函数 - 直观理解2(Cost Function - Intuition II)</a></span><span class="md-toc-item md-toc-h2" data-ref="n216"><a class="md-toc-inner" href="#header-n216">2.5 梯度下降(Gradient Descent)</a></span><span class="md-toc-item md-toc-h2" data-ref="n232"><a class="md-toc-inner" href="#header-n232">2.6 梯度下降直观理解(Gradient Descent Intuition)</a></span><span class="md-toc-item md-toc-h2" data-ref="n254"><a class="md-toc-inner" href="#header-n254">2.7 线性回归中的梯度下降(Gradient Descent For Linear Regression)</a></span><span class="md-toc-item md-toc-h1" data-ref="n279"><a class="md-toc-inner" href="#header-n279">3 Linear Algebra Review</a></span><span class="md-toc-item md-toc-h2" data-ref="n281"><a class="md-toc-inner" href="#header-n281">3.1 Matrices and Vectors</a></span><span class="md-toc-item md-toc-h2" data-ref="n286"><a class="md-toc-inner" href="#header-n286">3.2 Addition and Scalar Multiplication</a></span><span class="md-toc-item md-toc-h2" data-ref="n291"><a class="md-toc-inner" href="#header-n291">3.3 Matrix Vector Multiplication</a></span><span class="md-toc-item md-toc-h2" data-ref="n296"><a class="md-toc-inner" href="#header-n296">3.4 Matrix Matrix Multiplication</a></span><span class="md-toc-item md-toc-h2" data-ref="n301"><a class="md-toc-inner" href="#header-n301">3.5 Matrix Multiplication Properties</a></span><span class="md-toc-item md-toc-h2" data-ref="n306"><a class="md-toc-inner" href="#header-n306">3.6 Inverse and Transpose</a></span></p></div><h1><a name='header-n2' class='md-header-anchor '></a>1. 引言(Introduction)</h1><h2><a name='header-n3' class='md-header-anchor '></a>1.1 Welcome</h2><p>随着互联网数据不断累积，硬件不断升级迭代，在这个信息爆炸的时代，机器学习已被应用在各行各业中，可谓无处不在。</p><p>一些常见的机器学习的应用，例如：</p><ul><li>手写识别</li><li>垃圾邮件分类</li><li>搜索引擎</li><li>图像处理</li><li>…</li></ul><p>使用到机器学习的一些案例：</p><ul><li><p>数据挖掘</p><ul><li>网页点击流数据分析</li></ul></li><li><p>人工无法处理的工作(量大)</p><ul><li>手写识别</li><li>计算机视觉</li></ul></li><li><p>个人定制</p><ul><li>推荐系统</li></ul></li><li><p>研究大脑</p></li><li><p>……</p></li></ul><h2><a name='header-n40' class='md-header-anchor '></a>1.2 什么是机器学习(What is Machine Learning)</h2><ol start='' ><li>机器学习定义
这里主要有两种定义：</li></ol><ul><li><p>Arthur Samuel (1959). Machine Learning: Field of study that gives computers the ability to learn without being explicitly programmed.</p><p>这个定义有点不正式但提出的时间最早，来自于一个懂得计算机编程的下棋菜鸟。他编写了一个程序，但没有显式地编程每一步该怎么走，而是让计算机自己和自己对弈，并不断地计算布局的好坏，来判断什么情况下获胜的概率高，从而积累经验，好似学习，最后，这个计算机程序成为了一个比他自己还厉害的棋手。</p></li><li><p>Tom Mitchell (1998) Well-posed Learning Problem: A computer program is said to learn from experience E with respect to some <strong>task T</strong> and some <strong>performance measure P</strong>, if its performance on T, as measured by P, improves with <strong>experience E</strong>. </p><p>Tom Mitchell 的定义更为现代和正式。在过滤垃圾邮件这个例子中，电子邮件系统会根据用户对电子邮件的标记（是/不是垃圾邮件）不断学习，从而提升过滤垃圾邮件的准确率，定义中的三个字母分别代表：</p><ul><li>T(Task): 过滤垃圾邮件任务。</li><li>P(Performance): 电子邮件系统过滤垃圾邮件的准确率。</li><li>E(Experience): 用户对电子邮件的标记。</li></ul></li></ul><ol start='2' ><li><p>机器学习算法</p><p>主要有两种机器学习的算法分类</p><ol start='' ><li>监督学习</li><li>无监督学习</li></ol><p>两者的区别为<strong>是否需要人工参与数据结果的标注</strong>。这两部分的内容占比很大，并且很重要，掌握好了可以在以后的应用中节省大把大把的时间~</p><p>还有一些算法也属于机器学习领域，诸如：</p><ul><li>半监督学习: 介于监督学习于无监督学习之间</li><li>推荐算法: 没错，就是那些个买完某商品后还推荐同款的某购物网站所用的算法。</li><li>强化学习: 通过观察来学习如何做出动作，每个动作都会对环境有所影响，而环境的反馈又可以引导该学习算法。</li><li>迁移学习</li></ul></li></ol><h2><a name='header-n79' class='md-header-anchor '></a>1.3 监督学习(Supervised Learning)</h2><p>监督学习，即为教计算机如何去完成预测任务（有反馈），预先给一定数据量的输入<strong>和对应的结果</strong>即训练集，建模拟合，最后让计算机预测未知数据的结果。</p><p>监督学习一般有两种：</p><ol start='' ><li><p>回归问题(Regression)</p><p>回归问题即为预测一系列的<strong>连续值</strong>。</p><p>在房屋价格预测的例子中，给出了一系列的房屋面基数据，根据这些数据来预测任意面积的房屋价格。给出照片-年龄数据集，预测给定照片的年龄。</p><p><img src='images/20180105_194712.png' alt='' referrerPolicy='no-referrer' /></p></li><li><p>分类问题(Classification)</p><p>分类问题即为预测一系列的<strong>离散值</strong>。</p><p>即根据数据预测被预测对象属于哪个分类。</p><p>视频中举了癌症肿瘤这个例子，针对诊断结果，分别分类为良性或恶性。还例如垃圾邮件分类问题，也同样属于监督学习中的分类问题。</p><p><img src='images/20180105_194839.png' alt='' referrerPolicy='no-referrer' /></p></li></ol><p>视频中提到<strong>支持向量机</strong>这个算法，旨在解决当特征量很大的时候(特征即如癌症例子中的肿块大小，颜色，气味等各种特征)，计算机内存一定会不够用的情况。<strong>支持向量机能让计算机处理无限多个特征。</strong></p><h2><a name='header-n96' class='md-header-anchor '></a>1.4 无监督学习(Unsupervised Learning)</h2><p>相对于监督学习，训练集不会有人为标注的结果（无反馈），我们<strong>不会给出</strong>结果或<strong>无法得知</strong>训练集的结果是什么样，而是单纯由计算机通过无监督学习算法自行分析，从而“得出结果”。计算机可能会把特定的数据集归为几个不同的簇，故叫做聚类算法。</p><p>无监督学习一般分为两种：</p><ol start='' ><li><p>聚类(Clustering)</p><ul><li>新闻聚合</li><li>DNA 个体聚类</li><li>天文数据分析</li><li>市场细分</li><li>社交网络分析</li></ul></li><li><p>非聚类(Non-clustering)</p><ul><li>鸡尾酒问题</li></ul></li></ol><p><strong>新闻聚合</strong></p><p>在例如谷歌新闻这样的网站中，每天后台都会收集成千上万的新闻，然后将这些新闻分组成一个个的新闻专题，这样一个又一个聚类，就是应用了无监督学习的结果。</p><p><strong>鸡尾酒问题</strong></p><p><img src='images/20180105_201639.png' alt='' referrerPolicy='no-referrer' /></p><p>在鸡尾酒会上，大家说话声音彼此重叠，几乎很难分辨出面前的人说了什么。我们很难对于这个问题进行数据标注，而这里的通过机器学习的无监督学习算法，就可以将说话者的声音同背景音乐分离出来，看视频，效果还不错呢~~。</p><p>嗯，这块是打打鸡血的，只需要一行代码就解决了问题，就是这么简单！当然，我没复现过 <sup>_</sup>……</p><p>神奇的一行代码：
<code>[W,s,v] = svd((repmat(sum(x.*x,1),size(x,1),1).*x)*x&#39;);</code></p><p><strong>编程语言建议</strong></p><p>在机器学习刚开始时，<strong>推荐使用 Octave 类的工程计算编程软件</strong>，因为在 C++ 或 Java 等编程语言中，编写对应的代码需要用到复杂的库以及要写大量的冗余代码，比较耗费时间，建议可以在学习过后再考虑使用其他语言来构建系统。