<html xmlns="http://www.w3.org/1999/xhtml"><head><meta charset="utf-8"><meta name="generator" content="pdf2htmlEX"><meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/base.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/10381547/raw.css"><script src="https://csdnimg.cn/release/download_crawler_static/js/compatibility.min.js"></script><script src="https://csdnimg.cn/release/download_crawler_static/js/pdf2htmlEX.min.js"></script><script>try{pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({});}catch(e){}</script><title></title></head><body><div id="sidebar" style="display: none"><div id="outline"></div></div><div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/10381547/bg1.jpg"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">原文地址：<span class="ff2 sc1">https://www<span class="_ _0"></span>.coursera.org/learn/machine-</span></div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc1 ls0 ws0">learning/discussions/weeks/8/threads/XLl24URmEea1pw5frt5ut<span class="_ _1"></span>w<span class="_ _0"></span> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc1 ls1 ws0">Q1<span class="ff1 sc0 ls0">）我们如何知<span class="_ _0"></span>道哪些是最重要的功能<span class="_ _0"></span>要保留？为什么我们只<span class="_ _0"></span>能选择第一个<span class="_ _2"> </span></span><span class="ls0">K<span class="ff1 sc0">？他们不是</span></span></div><div class="t m0 x1 h2 y5 ff1 fs0 fc0 sc0 ls0 ws0">自然地按照意义<span class="_ _0"></span>排序吗？选择<span class="_ _2"> </span><span class="ff2 sc1">K<span class="_ _3"> </span></span>最有影响力的维度<span class="_ _0"></span>不是更有意义吗？<span class="_ _0"></span><span class="ff3 sc1"> </span></div><div class="t m0 x1 h3 y6 ff1 fs0 fc0 sc1 ls0 ws0">吴教授没有深入讨论奇异值分解（<span class="ff3 ls2">SVD</span>）如何工作的细节，但事实证明，<span class="ff3 ls2">SVD<span class="_ _3"> </span></span>的输出正是</div><div class="t m0 x1 h3 y7 ff1 fs0 fc0 sc1 ls0 ws0">我们在<span class="_ _3"> </span><span class="ff3">PCA<span class="_"> </span></span>中所需要的。它对输入矩阵进行<span class="ff4">“</span>谱分解<span class="ff4">”</span>，并以一种明显的形式给出它，这些</div><div class="t m0 x1 h3 y8 ff1 fs0 fc0 sc1 ls0 ws0">是重要的维度。<span class="ff3 ls2">SVD<span class="_ _3"> </span></span>的输出是：<span class="ff3"> </span></div><div class="t m0 x1 h3 y9 ff3 fs0 fc0 sc1 ls3 ws0">[U<span class="ff1 ls0">，<span class="ff3">S</span>，<span class="ff3">V] = svd</span>（<span class="ff3">Sigma</span>）<span class="ff3">; </span></span></div><div class="t m0 x1 h3 ya ff1 fs0 fc0 sc1 ls0 ws0">其中<span class="_ _3"> </span><span class="ff3">Sigma<span class="_"> </span></span>是协方差矩阵。输出值<span class="_ _3"> </span><span class="ff3">U<span class="_ _3"> </span></span>和<span class="_ _2"> </span><span class="ff3">V<span class="_ _3"> </span></span>是酉矩阵，<span class="ff3">U<span class="_ _3"> </span></span>的列是变换的特征向量。<span class="ff3">S<span class="_"> </span></span>是对</div><div class="t m0 x1 h3 yb ff1 fs0 fc0 sc1 ls0 ws0">角矩阵，包含降序的相应特征值。换句话说，<span class="ff3 ls2">SVD<span class="_ _3"> </span></span>已经完成了确定哪些维度最重要的工</div><div class="t m0 x1 h3 yc ff1 fs0 fc0 sc1 ls0 ws0">作，并按照该顺序给出了结果。<span class="ff3 ls4">Ng<span class="_"> </span></span>教授在<span class="_ _3"> </span><span class="ff3">7<span class="_ _3"> </span></span>点左右的标题为<span class="ff4">“</span>选择数量或主要部分<span class="ff4">”</span>的视频</div><div class="t m0 x1 h3 yd ff1 fs0 fc0 sc1 ls0 ws0">中进行了讨论。网络上有许多优秀的文章可以提供有关<span class="_ _3"> </span><span class="ff3">SVD<span class="_"> </span></span>的更多信息：<span class="ff3"> </span></div><div class="t m0 x1 h3 ye ff3 fs0 fc1 sc1 ls0 ws0">http://mathworld.wolfram.com/SingularValueDecomposition.html<span class="fc0"> </span></div><div class="t m0 x1 h3 yf ff3 fs0 fc1 sc1 ls0 ws0">https://en.wikipedia.org/wiki/Singular_value_decomposition<span class="fc0"> </span></div><div class="t m0 x1 h3 y10 ff1 fs0 fc0 sc1 ls0 ws0">这里是<span class="_ _3"> </span><span class="ff3 ls2">SVD<span class="_"> </span></span>的<span class="_ _3"> </span><span class="ff3">MATLAB<span class="_ _3"> </span></span>文档：<span class="ff3"> </span></div><div class="t m0 x1 h3 y11 ff3 fs0 fc1 sc1 ls0 ws0">http://www.mathworks.com/help/matlab/ref/svd.html<span class="fc0"> </span></div><div class="t m0 x1 h2 y12 ff2 fs0 fc0 sc1 ls1 ws0">Q2<span class="ff1 sc0 ls0">）为什么我们<span class="_ _0"></span>不需要计算<span class="_ _2"> </span></span><span class="ls0">U<span class="_ _3"> </span><span class="ff1 sc0">的矩阵逆以恢复原始维<span class="_ _0"></span>度中的数据？</span><span class="ff3"> </span></span></div><div class="t m0 x1 h3 y13 ff1 fs0 fc0 sc1 ls0 ws0">请看看上面有关奇异值分解的参考资料。事实证明，返回的<span class="_ _3"> </span><span class="ff3">U<span class="_"> </span></span>矩阵具有它是酉矩阵的特殊</div><div class="t m0 x1 h3 y14 ff1 fs0 fc0 sc1 ls0 ws0">性质。酉矩阵的一个特殊性质是：<span class="ff3"> </span></div><div class="t m0 x2 h3 y15 ff3 fs0 fc0 sc1 ls0 ws0"> <span class="_ _3"> </span> <span class="ff1">其中<span class="ff4">“*”</span>表示<span class="ff4">“</span>共轭转置<span class="ff4">”</span>。</span> </div><div class="t m0 x1 h3 y16 ff1 fs0 fc0 sc1 ls0 ws0">由于我们在这里处理实数，这相当于：<span class="ff3"> </span></div><div class="t m0 x3 h3 y17 ff1 fs0 fc0 sc1 ls0 ws0">所以我们可以计算逆并使用它，但这会浪费能量和计算周期。<span class="ff3"> </span></div><div class="t m0 x1 h2 y18 ff2 fs0 fc0 sc1 ls1 ws0">Q3<span class="ff1 sc0 ls5">）从视频</span><span class="ff5 ls0">“<span class="ff1 sc0 ls5">应用<span class="_ _3"> </span></span><span class="ff2">PCA<span class="_"> </span><span class="ff1 sc0 ls5">的建议</span></span>”<span class="_ _1"></span><span class="ff1 sc0">：为什么我们只在<span class="_ _0"></span>训练集上使用<span class="_ _2"> </span><span class="ff2 sc1">PCA</span>？<span class="ff3 sc1"> </span></span></span></div><div class="t m0 x1 h3 y19 ff1 fs0 fc0 sc1 ls0 ws0">如果将<span class="_ _3"> </span><span class="ff3">PCA<span class="_"> </span></span>应用于整个数据集，然后将该组分解为训练集，验证集和测试集，那么原始</div><div class="t m0 x1 h3 y1a ff1 fs0 fc0 sc1 ls0 ws0">测试集中的数据将对缩减的训练集产生影响。<span class="ff3"> </span></div><div class="t m0 x1 h3 y1b ff1 fs0 fc0 sc1 ls0 ws0">这会导致过度配合。<span class="ff3"> </span></div></div><a class="l"><div class="d m1"></div></a><a class="l"><div class="d m1"></div></a><a class="l"><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div></body></html>
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