基于BP算法的人脸识别程序（MATLAB）
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人脸库用的事ORL库，本程序用的是matlab写的一个简单的人脸识别程序，在运行程序时，需要更改代码中两个地方，一是BP_Train里面的一个路径，而是Accuracy里的文件路径，需要把两个路径都改为当前存放的路径。参考本程序需要有一定的matlab基础。 <html xmlns="http://www.w3.org/1999/xhtml"><meta charset="utf-8"><meta name="generator" content="pdf2htmlEX"><meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"><link rel="stylesheet" href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css"><link rel="stylesheet" href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css"><link rel="stylesheet" href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/5745099/raw.css"><script src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/js/compatibility.min.js"></script><script src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/js/pdf2htmlEX.min.js"></script><script>try{pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({});}catch(e){}</script><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="/image.php?url=https://csdnimg.cn/release/download_crawler_static/5745099/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">模式识别<span class="ff2"> <span class="_"> </span></span>西安<span class="_ _0"></span>交通大学<span class="_ _0"></span><span class="ff2"> </span></div><div class="t m0 x2 h2 y2 ff2 fs0 fc0 sc0 ls0 ws0">1 </div><div class="t m0 x3 h2 y3 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x4 h3 y4 ff3 fs1 fc0 sc0 ls0 ws0">基于<span class="ff4 ls1">BP</span>神经网<span class="_ _0"></span>络和<span class="ff5">k<span class="_ _0"></span><span class="ff4">-<span class="_ _0"></span><span class="ff3">近邻<span class="_ _0"></span>综合决策<span class="_ _0"></span><span class="ls2">法的<span class="ls0">人脸识<span class="_ _0"></span>别<span class="ff4">ma<span class="_ _0"></span>tlab<span class="_ _0"></span><span class="ff3">实现<span class="_ _0"></span><span class="ff4"> </span></span></span></span></span></span></span></span></div><div class="t m0 x5 h4 y5 ff6 fs2 fc0 sc0 ls0 ws0">高海南<span class="ff7"> <span class="_"> </span>311003801<span class="_ _0"></span>1 </span></div><div class="t m0 x3 h5 y6 ff8 fs1 fc0 sc0 ls0 ws0">1 <span class="_ _1"> </span><span class="ff1 sc1">人脸识别原理</span> </div><div class="t m0 x6 h6 y7 ff1 fs2 fc0 sc0 ls0 ws0">人脸识别是目前模式识别领域中被广泛研究的热门课题，<span class="_ _2"></span>它在安全领域以及</div><div class="t m0 x3 h6 y8 ff1 fs2 fc0 sc0 ls0 ws0">经济领域都有极其广泛的应用前景。<span class="_ _2"></span>人脸识别就是采集人脸图像进行分析和处理<span class="ff9">, </span></div><div class="t m0 x3 h6 y9 ff1 fs2 fc0 sc0 ls0 ws0">从人脸图像中获取有效的识别信息<span class="ff9">, </span>用来进行人脸及身份鉴别的一门技术。<span class="_ _2"></span>本文</div><div class="t m0 x3 h6 ya ff1 fs2 fc0 sc0 ls0 ws0">在<span class="ff9">MATLAB</span>环境下，<span class="_ _3"></span>取<span class="ff9">ORL</span>人脸数据库的部分人脸样本集，<span class="_ _3"></span>基于<span class="ff9">PCA</span>方法提取人脸特</div><div class="t m0 x3 h6 yb ff1 fs2 fc0 sc0 ls0 ws0">征，形成特征脸空间，然后将每个人脸样本投影到该空间得到一投影系<span class="_ _4"></span>数向<span class="_ _4"></span>量<span class="_ _4"></span>，</div><div class="t m0 x3 h6 yc ff1 fs2 fc0 sc0 ls0 ws0">该投影系数向量在一个低维空间表述了一个人脸样本，<span class="_ _2"></span>这样就得到了训练样本集。</div><div class="t m0 x3 h6 yd ff1 fs2 fc0 sc0 ls0 ws0">同时将另一部分<span class="ff9">ORL</span>人脸数据库的人脸作同样处理得到测试样本集。然后基于<span class="ff9">BP</span></div><div class="t m0 x3 h6 ye ff1 fs2 fc0 sc0 ls0 ws0">神经网络算法和<span class="ff9">k-</span>近邻算法进行综合决策对待识别的人脸进行分类。<span class="_ _2"></span>该方法的识</div><div class="t m0 x3 h6 yf ff1 fs2 fc0 sc0 ls0 ws0">别率比单独的<span class="ff9">BP</span>神经网络算法和<span class="ff9">k-</span>近邻法有一定的提高。<span class="ff9"> </span></div><div class="t m0 x3 h7 y10 ffa fs3 fc0 sc0 ls0 ws0">1.1 ORL<span class="_ _5"> </span><span class="ff1 sc1">人脸<span class="_ _4"></span>数<span class="_ _4"></span>据库简介<span class="_ _4"></span><span class="ff9"> </span></span></div><div class="t m0 x7 h6 y11 ff1 fs2 fc0 sc0 ls0 ws0">实验时人脸图像取自英国剑桥大学的<span class="ff9">ORL</span>人脸数据库，<span class="ff9">ORL</span>数据库由<span class="ff9">40</span>个人组</div><div class="t m0 x3 h6 y12 ff1 fs2 fc0 sc0 ls0 ws0">成，每个人有<span class="ff9">10</span>幅不同的图像，每幅图像是一个<span class="ff9">92</span>×<span class="ff9">112</span>像素、<span class="ff9">256</span>级的<span class="_ _4"></span>灰度<span class="_ _4"></span>图<span class="_ _4"></span>，</div><div class="t m0 x3 h6 y13 ff1 fs2 fc0 sc0 ls0 ws0">他们是在不同时间、<span class="_ _6"></span>光照略有变化、<span class="_ _6"></span>不同表情以及不同脸部细节下获取的。<span class="_ _7"></span>如图</div><div class="t m0 x3 h6 y14 ff9 fs2 fc0 sc0 ls0 ws0">1<span class="ff1">所示。</span> </div><div class="t m0 x8 h8 y15 ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x9 h6 y16 ff1 fs2 fc0 sc0 ls0 ws0">图<span class="ff9">1 ORL</span>人脸数据库<span class="ff9"> </span></div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div></html><div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/5745099/bg2.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">模式识别<span class="ff2"> <span class="_"> </span></span>西安<span class="_ _0"></span>交通大学<span class="_ _0"></span><span class="ff2"> </span></div><div class="t m0 x2 h2 y2 ff2 fs0 fc0 sc0 ls0 ws0">2 </div><div class="t m0 x3 h2 y3 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h7 y4 ffa fs3 fc0 sc0 ls0 ws0">1.2 <span class="_ _5"> </span><span class="ff1 sc1 ls3">基于<span class="_ _5"> </span></span>PCA<span class="_ _5"> </span><span class="ff1 sc1">的<span class="_ _4"></span>人脸图像<span class="_ _4"></span>的特征<span class="_ _4"></span>提取</span> </div><div class="t m0 x6 h6 y17 ff9 fs2 fc0 sc0 ls0 ws0">PCA<span class="ff1">法是模式识别中的一种行之有效的特征提取方法。在人脸识别研究中</span>, </div><div class="t m0 x3 h6 y18 ff1 fs2 fc0 sc0 ls0 ws0">可以将该方法用于人脸图像的特征提取。<span class="ff9"> </span></div><div class="t m0 x7 h6 y19 ff1 fs2 fc0 sc0 ls0 ws0">一个<span class="_ _8"> </span><span class="ff9">m</span>×<span class="ff9">n<span class="_ _8"> </span></span>的二维脸部图片将其按列首位相连，<span class="_ _9"></span>可以看成是<span class="_ _8"> </span><span class="ff9">m</span>×<span class="ff9">n<span class="_ _8"> </span></span>的一个一维向</div><div class="t m0 x3 h6 y1a ff1 fs2 fc0 sc0 ls0 ws0">量。<span class="_ _7"></span><span class="ff9">ORL<span class="_ _8"> </span><span class="ff1">人脸数据库中每张人脸图片大小是<span class="_ _8"> </span></span>92<span class="ff1">×</span>112<span class="ff1">，<span class="_ _6"></span>它可以看成是一个<span class="_ _8"> </span><span class="ff9">10304<span class="_ _8"> </span></span>维</span></span></div><div class="t m0 x3 h6 y1b ff1 fs2 fc0 sc0 ls0 ws0">的向量，<span class="_ _2"></span>也可以看成是一个<span class="_ _8"> </span><span class="ff9">10304<span class="_ _8"> </span></span>维空间中一<span class="_ _4"></span>点。<span class="_ _2"></span>图<span class="_ _4"></span>片映射到这个巨大的空间后，</div><div class="t m0 x3 h6 y1c ff1 fs2 fc0 sc0 ls0 ws0">由于人脸的构造<span class="_ _4"></span>相对<span class="_ _4"></span>来说比较接近<span class="_ _4"></span>，因此<span class="_ _4"></span>可以<span class="_ _4"></span>用一个相应的低<span class="_ _4"></span>维子空间来<span class="_ _4"></span>表示。</div><div class="t m0 x3 h6 y1d ff1 fs2 fc0 sc0 ls0 ws0">我们把这个子空间叫做“脸空间”<span class="_ _a"></span>。<span class="ff9">PCA<span class="_ _8"> </span></span>的主要思想就是找到能够最好地说明图片</div><div class="t m0 x3 h6 y1e ff1 fs2 fc0 sc0 ls0 ws0">在图片空间中的分布情况的那些向量，<span class="_ _b"></span>这些向量能够定义<span class="_ _b"></span>“脸空间”<span class="_ _a"></span>。<span class="_ _b"></span>每个向量的</div><div class="t m0 x3 h6 y1f ff1 fs2 fc0 sc0 ls0 ws0">长度为<span class="_ _c"> </span><span class="ff9">m</span>×<span class="ff9">n</span>，描述一张<span class="_ _c"> </span><span class="ff9">m</span>×<span class="ff9">n<span class="_ _c"> </span></span>的图片，并且是原始脸部图片的一个线性组合，称</div><div class="t m0 x3 h6 y20 ff1 fs2 fc0 sc0 ls0 ws0">为“特征脸”<span class="_ _a"></span>。对于一副<span class="_ _8"> </span><span class="ff9">m</span>×<span class="ff9">n<span class="_ _8"> </span></span>的人脸图像，将<span class="_ _4"></span>其每列相连构成一个大小为<span class="_ _8"> </span><span class="ff9">D=m</span>×<span class="ff9">n</span></div><div class="t m0 x3 h6 y21 ff1 fs2 fc0 sc0 ls0 ws0">维的列向量。<span class="ff9">D<span class="_ _c"> </span></span>就是人脸图像的维数，也即是图像空间的维数。设<span class="_ _c"> </span><span class="ff9">N<span class="_ _c"> </span></span>是训练样本</div><div class="t m0 x3 h6 y22 ff1 fs2 fc0 sc0 ls0 ws0">的数目；</div><div class="c xa y23 w2 h9"><div class="t m1 xb ha y24 ffb fs4 fc0 sc0 ls0 ws0">j</div><div class="t m1 xc hb y25 ffb fs5 fc0 sc0 ls0 ws0">x</div></div><div class="t m0 xd h6 y22 ff1 fs2 fc0 sc0 ls0 ws0">表示第<span class="_ _8"> </span><span class="ff9">j<span class="_ _8"> </span></span>幅人脸图像形成的人脸向量；</div><div class="c xe y26 w3 hc"><div class="t m2 xf hd y27 ffb fs6 fc0 sc0 ls0 ws0">u</div></div><div class="t m0 x10 h6 y22 ff1 fs2 fc0 sc0 ls0 ws0">为训练样本的平均图像向量，</div><div class="t m0 x3 h6 y28 ff1 fs2 fc0 sc0 ls0 ws0">则所需样本的协方差矩阵为：<span class="ff9"> </span></div><div class="t m0 x3 h8 y29 ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x11 y2a w4 he"><div class="t m3 x12 hf y2b ffc fs7 fc0 sc0 ls0 ws0">1</div><div class="t m3 x13 h10 y2c ffc fs8 fc0 sc0 ls0 ws0">(<span class="_ _d"> </span>)(<span class="_ _e"> </span>)</div><div class="t m3 x14 h11 y2d ffb fs7 fc0 sc0 ls0 ws0">N</div><div class="t m3 x15 h11 y2e ffb fs7 fc0 sc0 ls0 ws0">T</div><div class="t m3 x16 h11 y2f ffb fs7 fc0 sc0 ls0 ws0">r<span class="_ _f"> </span>j<span class="_ _10"> </span>i</div><div class="t m3 x17 h11 y2b ffb fs7 fc0 sc0 ls0 ws0">j</div><div class="t m3 xf h12 y2c ffb fs8 fc0 sc0 ls0 ws0">S<span class="_ _11"> </span>x<span class="_ _12"> </span>u<span class="_ _13"> </span>x<span class="_ _14"> </span>u</div><div class="t m3 x18 h13 y2b ffd fs7 fc0 sc0 ls0 ws0"></div><div class="t m3 x19 h14 y2c ffd fs8 fc0 sc0 ls0 ws0"><span class="_ _15"> </span><span class="_ _16"> </span></div><div class="t m3 x1a h15 y30 ffd fs9 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x1b h8 y29 ff9 fs2 fc0 sc0 ls0 ws0"> (1) </div><div class="t m0 x1c h8 y31 ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x1d y32 w5 he"><div class="t m4 x1e hf y2b ffc fs7 fc0 sc0 ls0 ws0">1</div><div class="t m4 x1f h10 y33 ffc fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x20 h11 y2d ffb fs7 fc0 sc0 ls0 ws0">N</div><div class="t m4 x21 h11 y2f ffb fs7 fc0 sc0 ls0 ws0">j</div><div class="t m4 x22 h11 y2b ffb fs7 fc0 sc0 ls0 ws0">j</div><div class="t m4 xf h12 y2c ffb fs8 fc0 sc0 ls4 ws0">ux</div><div class="t m4 x23 h12 y34 ffb fs8 fc0 sc0 ls0 ws0">N</div><div class="t m4 x13 h13 y2b ffd fs7 fc0 sc0 ls0 ws0"></div><div class="t m4 x24 h14 y2c ffd fs8 fc0 sc0 ls0 ws0"></div><div class="t m4 x12 h15 y30 ffd fs9 fc0 sc0 ls0 ws0"></div></div><div class="t m0 x25 h8 y31 ff9 fs2 fc0 sc0 ls0 ws0"> (2) </div><div class="t m0 x3 h6 y35 ff9 fs2 fc0 sc0 ls0 ws0"> <span class="ff1">令</span></div><div class="c x7 y36 w6 h16"><div class="t m5 x1f h17 y37 ffd fsa fc0 sc0 ls0 ws0"><span class="_ _17"> </span></div><div class="t m6 x26 h18 y38 ffb fsb fc0 sc0 ls0 ws0">u<span class="_ _18"></span>x<span class="_ _19"></span>u<span class="_ _1a"></span>x<span class="_ _1b"></span>u<span class="_ _1c"></span>x</div><div class="t m6 x27 h19 y39 ffb fsc fc0 sc0 ls0 ws0">N</div><div class="t m6 x28 h1a y38 ffd fsb fc0 sc0 ls0 ws0"><span class="_ _1d"></span><span class="_ _1e"></span><span class="_ _1f"></span><span class="_ _20"> </span><span class="ffe"></span></div><div class="t m6 x29 h1b y39 ffc fsc fc0 sc0 ls0 ws0">2<span class="_ _21"></span>1</div><div class="t m6 xf h1c y38 ffc fsb fc0 sc0 ls0 ws0">A</div></div><div class="t m0 x2a h6 y35 ff9 fs2 fc0 sc0 ls0 ws0">,<span class="ff1">则有</span></div><div class="c x2b y3a w7 h16"><div class="t m7 x2c h19 y3b ffb fsc fc0 sc0 ls0 ws0">T</div><div class="t m7 x16 h19 y3c ffb fsc fc0 sc0 ls0 ws0">r</div><div class="t m7 x2d h18 y3d ffb fsb fc0 sc0 ls5 ws0">AA<span class="_ _22"></span><span class="ls0">S<span class="_ _23"> </span><span class="ffd"></span></span></div></div><div class="t m0 xe h6 y35 ff9 fs2 fc0 sc0 ls0 ws0">,<span class="ff1">其维数为<span class="_ _8"> </span></span>D*D<span class="ff1">。</span> </div><div class="t m0 x6 h6 y3e ff1 fs2 fc0 sc0 ls0 ws0">根据<span class="_ _24"> </span><span class="ff9">K-L<span class="_ _24"> </span></span>变换原理，需要求得的新坐标系由矩阵</div><div class="c x2e y3f w8 h1d"><div class="t m8 x2f h1e y40 ffb fsd fc0 sc0 ls0 ws0">T</div><div class="t m8 xc h1f y41 ffb fse fc0 sc0 ls6 ws0">AA</div></div><div class="t m0 x30 h6 y3e ff1 fs2 fc0 sc0 ls0 ws0">的非零特征值所对应得</div><div class="t m0 x3 h6 y42 ff1 fs2 fc0 sc0 ls0 ws0">特征向量组成。<span class="_ _b"></span>直接计算的计算量比较大，<span class="_ _25"></span>所以采用奇异值分解<span class="_ _25"></span>（<span class="ff9">SVD</span>）<span class="_ _25"></span>定理，<span class="_ _b"></span>通</div><div class="t m0 x3 h6 y43 ff1 fs2 fc0 sc0 ls0 ws0">过求解</div><div class="c x31 y44 w9 h20"><div class="t m9 x32 h21 y45 ffb fsf fc0 sc0 ls0 ws0">A<span class="_ _26"></span>A</div><div class="t m9 xb h22 y46 ffb fs10 fc0 sc0 ls0 ws0">T</div></div><div class="t m0 x33 h6 y43 ff1 fs2 fc0 sc0 ls0 ws0">的特征值和特征向量来获得</div><div class="c x2 y44 w8 h20"><div class="t ma x2f h22 y46 ffb fs10 fc0 sc0 ls0 ws0">T</div><div class="t ma xc h21 y45 ffb fsf fc0 sc0 ls7 ws0">AA</div></div><div class="t m0 x34 h6 y43 ff1 fs2 fc0 sc0 ls0 ws0">的特征值和特征向量。<span class="_ _2"></span>依据<span class="_ _8"> </span><span class="ff9">SVD<span class="_ _8"> </span></span>定理，</div><div class="t m0 x3 h6 y47 ff1 fs2 fc0 sc0 ls0 ws0">令</div><div class="c x4 y48 wa h16"><div class="t mb x35 h23 y49 ffb fs11 fc0 sc0 ls0 ws0">i</div><div class="t mb xf h24 y4a ffb fs12 fc0 sc0 ls0 ws0">l</div></div><div class="t m0 x36 h8 y47 ff9 fs2 fc0 sc0 ls0 ws0"> (</div><div class="c x37 y4b wb h25"><div class="t mc x38 h26 y4c ffb fs13 fc0 sc0 ls0 ws0">r<span class="_ _27"></span>i<span class="_ _28"> </span><span class="ffc">,<span class="_ _29"></span>,<span class="_ _2a"></span>2<span class="_ _2b"></span>,<span class="_ _2c"></span>1<span class="_ _2d"> </span><span class="ffe"><span class="_ _2e"></span><span class="ffd"></span></span></span></div></div><div class="t m0 x39 h6 y47 ff9 fs2 fc0 sc0 ls0 ws0">)<span class="ff1">为矩阵</span></div><div class="c x3a y4d w8 h20"><div class="t ma x2f h22 y46 ffb fs10 fc0 sc0 ls0 ws0">T</div><div class="t ma xc h21 y45 ffb fsf fc0 sc0 ls7 ws0">AA</div></div><div class="t m0 x3b h6 y47 ff1 fs2 fc0 sc0 ls0 ws0">的<span class="_ _8"> </span><span class="ff9">r<span class="_ _8"> </span></span>个非零特征值，</div><div class="c x3c y48 wc h16"><div class="t md x3d h19 y39 ffb fsc fc0 sc0 ls0 ws0">i</div><div class="t md xf h18 y38 ffb fsb fc0 sc0 ls0 ws0">v</div></div><div class="t m0 x3e h6 y47 ff1 fs2 fc0 sc0 ls0 ws0">为</div><div class="c x3f y4d w9 h20"><div class="t m9 x32 h21 y45 ffb fsf fc0 sc0 ls0 ws0">A<span class="_ _26"></span>A</div><div class="t m9 xb h22 y46 ffb fs10 fc0 sc0 ls0 ws0">T</div></div><div class="t m0 x40 h6 y47 ff1 fs2 fc0 sc0 ls0 ws0">对应于</div><div class="c x41 y48 wa h16"><div class="t mb x35 h23 y49 ffb fs11 fc0 sc0 ls0 ws0">i</div><div class="t mb xf h24 y4a ffb fs12 fc0 sc0 ls0 ws0">l</div></div><div class="t m0 x42 h6 y47 ff1 fs2 fc0 sc0 ls0 ws0">的特征向量。</div><div class="t m0 x3 h6 y4e ff1 fs2 fc0 sc0 ls0 ws0">由于特征值越大<span class="_ _4"></span>，与<span class="_ _4"></span>之对应的特征<span class="_ _4"></span>向量对图像<span class="_ _4"></span>识别的贡<span class="_ _4"></span>献越大，为<span class="_ _4"></span>此将特<span class="_ _4"></span>征值按</div><div class="t m0 x3 h6 y4f ff1 fs2 fc0 sc0 ls0 ws0">大小排列，依照公式<span class="ff9"> </span></div><div class="t m0 x37 h8 y50 ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x43 y51 wd h27"><div class="t me x44 h28 y52 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x44 h28 y53 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x44 h28 y54 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x44 h28 y55 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x44 h28 y56 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x44 h28 y57 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x44 h28 y58 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x2c h28 y52 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x2c h28 y53 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x2c h28 y54 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x2c h28 y55 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x2c h28 y56 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x2c h28 y57 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x2c h28 y58 ffd fs14 fc0 sc0 ls0 ws0"></div><div class="t me x45 h28 y59 ffd fs14 fc0 sc0 ls0 ws0"><span class="_ _19"></span><span class="_ _2f"></span></div><div class="t me x46 h29 y5a ffd fs15 fc0 sc0 ls0 ws0"></div><div class="t me x46 h29 y5b ffd fs15 fc0 sc0 ls0 ws0"></div><div class="t me x47 h2a y5c ffd fs16 fc0 sc0 ls0 ws0"></div><div class="t me x47 h2a y5d ffd fs16 fc0 sc0 ls0 ws0"></div><div class="t me x48 h2b y59 ffb fs14 fc0 sc0 ls0 ws0">r<span class="_ _1b"></span>k</div><div class="t me x49 h2b y5e ffb fs14 fc0 sc0 ls0 ws0">l</div><div class="t me x49 h2b y5f ffb fs14 fc0 sc0 ls0 ws0">l</div><div class="t me x4a h2b y59 ffb fs14 fc0 sc0 ls0 ws0">p</div><div class="t me x47 h2c y60 ffb fs16 fc0 sc0 ls0 ws0">r</div><div class="t me x4b h2c y5c ffb fs16 fc0 sc0 ls0 ws0">i</div><div class="t me x4c h2c y61 ffb fs16 fc0 sc0 ls0 ws0">i</div><div class="t me x47 h2c y62 ffb fs16 fc0 sc0 ls0 ws0">k</div><div class="t me x4b h2c y5d ffb fs16 fc0 sc0 ls0 ws0">i</div><div class="t me x4c h2c y63 ffb fs16 fc0 sc0 ls0 ws0">i</div><div class="t me x18 h2c y64 ffb fs16 fc0 sc0 ls0 ws0">k</div><div class="t me x4d h2d y59 ffc fs14 fc0 sc0 ls0 ws0">,<span class="_ _2a"></span>9<span class="_ _2a"></span>.<span class="_ _2a"></span>0<span class="_ _30"></span>m<span class="_ _4"></span>i<span class="_ _b"></span>n</div><div class="t me x4e h2e y5c ffc fs16 fc0 sc0 ls0 ws0">1</div><div class="t me x4e h2e y5d ffc fs16 fc0 sc0 ls0 ws0">1</div></div><div class="t m0 x4f h8 y50 ff9 fs2 fc0 sc0 ls0 ws0"> (3) </div><div class="t m0 x6 h6 y65 ff1 fs2 fc0 sc0 ls0 ws0">选取前</div><div class="c x26 y66 we h2f"><div class="t mf x4a h30 y67 ffb fs17 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 x50 h6 y65 ff1 fs2 fc0 sc0 ls0 ws0">个特征值对应的特征向量，<span class="_ _2"></span>构成了降维后的特征脸子空间。<span class="_ _31"></span>则</div><div class="c x51 y68 w8 h1d"><div class="t m8 x2f h31 y40 ffb fs18 fc0 sc0 ls0 ws0">T</div><div class="t m8 xc h1f y41 ffb fse fc0 sc0 ls8 ws0">AA</div></div><div class="t m0 x52 h6 y65 ff1 fs2 fc0 sc0 ls0 ws0">的</div><div class="t m0 x3 h6 y69 ff1 fs2 fc0 sc0 ls0 ws0">正交归一特征向量</div><div class="c x53 y6a we h16"><div class="t m10 x54 h32 y6b ffb fs19 fc0 sc0 ls0 ws0">i</div><div class="t m10 xf h24 y4a ffb fs12 fc0 sc0 ls0 ws0">u</div></div><div class="t m0 x55 h6 y69 ff1 fs2 fc0 sc0 ls0 ws0">为：<span class="ff9"> </span></div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div><div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/5745099/bg3.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">模式识别<span class="ff2"> <span class="_"> </span></span>西安<span class="_ _0"></span>交通大学<span class="_ _25"></span><span class="ff2"> </span></div><div class="t m0 x2 h2 y2 ff2 fs0 fc0 sc0 ls0 ws0">3 </div><div class="t m0 x3 h2 y3 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 xa h8 y6c ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x56 y6d wf h33"><div class="t m11 x14 h34 y6e ffc fs1a fc0 sc0 ls0 ws0">1</div><div class="t m11 x54 h35 y6f ffb fs1b fc0 sc0 ls9 ws0">ii</div><div class="t m11 x57 h35 y70 ffb fs1b fc0 sc0 ls0 ws0">i</div><div class="t m11 xf h36 y71 ffb fs1a fc0 sc0 ls0 ws0">u<span class="_ _32"> </span>Av</div><div class="t m11 x58 h36 y72 ffb fs1a fc0 sc0 ls0 ws0">l</div><div class="t m11 x59 h37 y71 ffd fs1a fc0 sc0 ls0 ws0"></div></div><div class="t m0 x5a h8 y73 ff9 fs2 fc0 sc0 ls0 ws0">(</div><div class="c x5b y74 w10 h38"><div class="t m12 x19 h39 y75 ffc fs1c fc0 sc0 ls0 ws0">1<span class="_ _7"></span>,<span class="_ _33"></span>2<span class="_ _25"></span>,<span class="_ _34"> </span>,<span class="_ _35"></span><span class="ffb lsa">ip<span class="_ _36"></span><span class="ffd ls0"><span class="_ _37"> </span><span class="fff"></span></span></span></div></div><div class="t m0 x1b h8 y73 ff9 fs2 fc0 sc0 ls0 ws0">) (4) </div><div class="t m0 x7 h6 y76 ff1 fs2 fc0 sc0 ls0 ws0">则特征脸空间为：<span class="ff9"> </span></div><div class="t m0 xa h8 y77 ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="c x1d y78 w11 h3a"><div class="t m13 x57 h3b y79 ffc fs1d fc0 sc0 lsb ws0">12</div><div class="t m13 x1a h3c y7a ffc fs1e fc0 sc0 ls0 ws0">[<span class="_ _13"> </span>,<span class="_ _38"> </span>,<span class="_ _39"> </span>,<span class="_ _34"> </span>]</div><div class="t m13 x5c h3d y79 ffb fs1d fc0 sc0 ls0 ws0">p</div><div class="t m13 x5d h3e y7a ffb fs1e fc0 sc0 ls0 ws0">u<span class="_ _3a"> </span>u<span class="_ _3b"> </span>u<span class="_ _3c"></span><span class="ffd"><span class="_ _26"></span><span class="ff10">W<span class="_ _3d"> </span><span class="fff"></span></span></span></div></div><div class="t m0 x5e h8 y7b ff9 fs2 fc0 sc0 ls0 ws0"> (5) </div><div class="t m0 x7 h6 y7c ff1 fs2 fc0 sc0 ls0 ws0">将训练样本</div><div class="c x5f y7d w12 h2f"><div class="t m14 xf h3f y7e ff10 fs1f fc0 sc0 ls0 ws0">y</div></div><div class="t m0 x60 h6 y7c ff1 fs2 fc0 sc0 ls0 ws0">投影到<span class="_ _b"></span>“特征脸”<span class="_ _25"></span>空间</div><div class="c x61 y7f w13 h40"><div class="t m15 xf h41 y80 ff10 fs20 fc0 sc0 ls0 ws0">W</div></div><div class="t m0 x62 h6 y7c ff1 fs2 fc0 sc0 ls0 ws0">，<span class="_ _b"></span>得到一组投影向量</div><div class="c x63 y7d w14 h16"><div class="t m16 x57 h32 y81 ffb fs19 fc0 sc0 ls0 ws0">T</div><div class="t m16 x59 h42 y82 ffd fs12 fc0 sc0 ls0 ws0"><span class="_ _3e"></span><span class="ff10">Y<span class="_ _3f"> </span>W<span class="_ _c"> </span>y</span></div></div><div class="t m0 x64 h6 y7c ff1 fs2 fc0 sc0 ls0 ws0">，<span class="_ _b"></span>构成</div><div class="t m0 x3 h6 y83 ff1 fs2 fc0 sc0 ls0 ws0">人脸识别的训练样本数据库。<span class="ff9"> </span></div><div class="t m0 x3 h7 y84 ffa fs3 fc0 sc0 ls0 ws0">1.3 k-<span class="ff1 sc1 ls3">近邻算法</span> </div><div class="t m0 x6 h6 y85 ff1 fs2 fc0 sc0 ls0 ws0">在识别时，<span class="_ _6"></span>先将每一幅待识别的人脸图像投影到<span class="_ _6"></span>“特征脸”空间，<span class="_ _6"></span>再利用<span class="ff9">k-</span></div><div class="t m0 x3 h6 y86 ff1 fs2 fc0 sc0 ls0 ws0">近邻分类器，比较其与库中<span class="ff9">k</span>个人脸的位置，从而识别出该图像是库中那个人的</div><div class="t m0 x3 h6 y87 ff1 fs2 fc0 sc0 ls0 ws0">人脸。<span class="_ _7"></span>本实验令<span class="ff9">k=3</span>，<span class="_ _7"></span>如果判断得到最短三个距离对应了三个类别<span class="_ _b"></span>（三个人）<span class="_ _a"></span>，<span class="_ _7"></span>则</div><div class="t m0 x3 h6 y88 ff1 fs2 fc0 sc0 ls0 ws0">取该人脸属于距离最短对应的人脸类别，<span class="_ _3"></span>此时相当于最近邻算法；<span class="_ _3"></span>其他情况按投</div><div class="t m0 x3 h6 y89 ff1 fs2 fc0 sc0 ls0 ws0">票法判别，相当于<span class="ff9">k-</span>近邻算法。<span class="ff9"> </span></div><div class="t m0 x3 h7 y8a ffa fs3 fc0 sc0 ls0 ws0">1.4 <span class="lsc">BP<span class="_"> </span></span><span class="ff1 sc1">神<span class="_ _4"></span>经<span class="_ _4"></span>网络法</span> </div><div class="t m0 x6 h6 y8b ff9 fs2 fc0 sc0 ls0 ws0">BP<span class="ff1">神经网络的算法又称为误差反向传播算法</span>, BP <span class="ff1">神经网络具有良好的自适</span></div><div class="t m0 x3 h6 y8c ff1 fs2 fc0 sc0 ls0 ws0">应性和分类识别等能力。<span class="ff9">BP</span>神经网络模型的结构如图<span class="ff9">2</span>所示。它是由输入层、隐</div><div class="t m0 x3 h6 y8d ff1 fs2 fc0 sc0 ls0 ws0">层和输出层所组成的。<span class="ff9"> </span></div><div class="t m0 x65 h8 y8e ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3b h6 y8f ff1 fs2 fc0 sc0 ls0 ws0">图<span class="ff9">2 BP</span>网络结构图<span class="ff9"> </span></div><div class="t m0 x7 h6 y90 ff1 fs2 fc0 sc0 ls0 ws0">对于</div><div class="c x27 y91 we h2f"><div class="t mf x4a h30 y67 ffb fs17 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 x66 h6 y90 ff1 fs2 fc0 sc0 ls0 ws0">维投影系数，<span class="_ _3"></span>则<span class="ff9"> BP</span>网络的输入层需要</div><div class="c x67 y91 we h2f"><div class="t mf x4a h30 y67 ffb fs17 fc0 sc0 ls0 ws0">p</div></div><div class="t m0 x68 h6 y90 ff1 fs2 fc0 sc0 ls0 ws0">个节点，<span class="_ _3"></span>每一个投影系数对应</div><div class="t m0 x3 h6 y92 ff9 fs2 fc0 sc0 ls0 ws0">40<span class="ff1">个人中某一个，若对应第</span></div><div class="c x69 y93 w15 h43"><div class="t m17 xf h44 y94 ffb fs21 fc0 sc0 ls0 ws0">i</div></div><div class="t m0 x6a h6 y92 ff1 fs2 fc0 sc0 ls0 ws0">个人，则期望输出向量定义为<span class="ff9"> </span></div><div class="c x50 y95 w16 h45"><div class="t m18 x12 h46 y96 ffd fs22 fc0 sc0 ls0 ws0"><span class="_ _40"> </span></div><div class="t m19 x55 h47 y97 ffb fs23 fc0 sc0 ls0 ws0">T</div><div class="t m19 x6b h48 y98 ffc fs24 fc0 sc0 ls0 ws0">1<span class="_ _2a"></span>.<span class="_ _41"></span>0<span class="_ _42"></span>1<span class="_ _2a"></span>.<span class="_ _41"></span>0<span class="_ _43"></span>9<span class="_ _2a"></span>.<span class="_ _41"></span>0<span class="_ _26"></span>1<span class="_ _44"></span>.<span class="_ _44"></span>0<span class="_ _42"></span>1<span class="_ _44"></span>.<span class="_ _44"></span>0</div><div class="t m19 x2f h49 y99 ffc fs23 fc0 sc0 ls0 ws0">1<span class="_ _45"></span><span class="lsd">40</span></div><div class="t m19 x6c h4a y98 ffe fs24 fc0 sc0 ls0 ws0"><span class="_ _46"></span><span class="_ _1e"></span><span class="ffd"></span></div><div class="t m19 x59 h4b y99 ffd fs23 fc0 sc0 ls0 ws0"></div><div class="t m19 xf h4c y98 ff10 fs24 fc0 sc0 ls0 ws0">t</div></div><div class="t m0 x6d h6 y9a ff1 fs2 fc0 sc0 ls0 ws0">，</div><div class="c x6e y9b w17 h25"><div class="t m1a x6f h4d y4c ffc fs13 fc0 sc0 ls0 ws0">9<span class="_ _2b"></span>.<span class="_ _2a"></span>0<span class="_ _47"></span>]<span class="_ _2b"></span>1<span class="_ _2c"></span>,<span class="_ _48"></span>[<span class="_ _49"> </span><span class="ffd"><span class="_ _4a"></span><span class="ffb">i<span class="_ _4b"></span><span class="ff10">t</span></span></span></div></div><div class="t m0 x41 h8 y9a ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x6 h6 y9c ff1 fs2 fc0 sc0 ls0 ws0">即第</div><div class="c x70 y9d w15 h43"><div class="t m17 xf h44 y94 ffb fs21 fc0 sc0 ls0 ws0">i</div></div><div class="t m0 x71 h6 y9c ff1 fs2 fc0 sc0 ls0 ws0">行为<span class="ff9">0.9</span>，其他均为<span class="ff9">0.1</span>，故输出层需要<span class="ff9">40</span>个节点，隐层结点个数可根</div><div class="t m0 x3 h6 y9e ff1 fs2 fc0 sc0 ls0 ws0">据经验公式获得。<span class="_ _3"></span>将测试样本输入该网络训练，<span class="_ _3"></span>得到训练好的网络后可将测试样</div><div class="t m0 x3 h6 y65 ff1 fs2 fc0 sc0 ls0 ws0">本输入网络得到输出值进行判断。<span class="ff9"> </span></div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div><div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/5745099/bg4.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">模式识别<span class="ff2"> <span class="_"> </span></span>西安<span class="_ _0"></span>交通大学<span class="_ _25"></span><span class="ff2"> </span></div><div class="t m0 x2 h2 y2 ff2 fs0 fc0 sc0 ls0 ws0">4 </div><div class="t m0 x3 h2 y3 ff2 fs0 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h7 y4 ffa fs3 fc0 sc0 ls0 ws0">1.5<span class="_"> </span><span class="ff1 sc1 ls3">基于<span class="_ _5"> </span></span><span class="lsc">BP<span class="_ _5"> </span></span><span class="ff1 sc1">神经网<span class="_ _4"></span>络法和<span class="_ _1"> </span></span>k-<span class="ff1 sc1">近邻法的<span class="_ _4"></span>综合<span class="_ _4"></span>决策<span class="ls3">分类</span></span> </div><div class="t m0 x72 h6 y17 ff9 fs2 fc0 sc0 ls0 ws0">k-<span class="ff1">近邻法分类是选择测试样本与样本空间最近的</span>k<span class="ff1">个样本的类别而决策分类</span></div><div class="t m0 x3 h6 y18 ff1 fs2 fc0 sc0 ls0 ws0">的；<span class="_ _2"></span>而<span class="ff9">BP</span>神经网络法本质上是根据输入输出关系通过学习而确定一个非线性空间</div><div class="t m0 x3 h6 y19 ff1 fs2 fc0 sc0 ls0 ws0">映射关系，<span class="_ _3"></span>在此映射关系下对于每个输入得到一个输出，<span class="_ _3"></span>此输出根据网络输出的</div><div class="t m0 x3 h6 y1a ff1 fs2 fc0 sc0 ls0 ws0">定义而确定类别。因此考虑将两种方法综合起来进行决策分类。<span class="ff9"> </span></div><div class="t m0 x72 h6 y1b ff1 fs2 fc0 sc0 ls0 ws0">实际的实验过程中，<span class="_ _4c"></span><span class="ff9">k-<span class="ff1">近邻法得到的结果稳定，<span class="_ _4c"></span>而<span class="ff9">BP</span>网络法是一种次优算法，</span></span></div><div class="t m0 x3 h6 y1c ff1 fs2 fc0 sc0 ls0 ws0">需要根据经验确定隐层数目、<span class="_ _3"></span>训练算法。<span class="_ _3"></span>当网络比较小时尚可通过不断的实验得</div><div class="t m0 x3 h6 y1d ff1 fs2 fc0 sc0 ls0 ws0">到一个较好的结果，<span class="_ _4d"></span>而当如本实验的网络，<span class="_ _4d"></span>其输<span class="_ _0"></span>入层节点<span class="ff9">p=71</span>，<span class="_ _4d"></span>输出层节点<span class="ff9">c=40</span>，</div><div class="t m0 x3 h6 y1e ff1 fs2 fc0 sc0 ls0 ws0">隐层节点数至少要几十上百个才能得到比较好的结果，<span class="_ _3"></span>因此不适合用试凑法；<span class="_ _3"></span>而</div><div class="t m0 x3 h6 y1f ff1 fs2 fc0 sc0 ls0 ws0">直接根据经验公式并不能得到满意的网络，<span class="_ _2"></span>有时网络的识别率甚至不及<span class="ff9">k-</span>近邻分</div><div class="t m0 x3 h6 y9f ff1 fs2 fc0 sc0 ls0 ws0">类法的识别率。<span class="_ _25"></span>经过分析<span class="ff9">BP</span>网络法得到的输出结果我们发现，<span class="_ _0"></span>当输出向量</div><div class="c x73 ya0 w18 h16"><div class="t m1b x32 h1b y39 ffc fsc fc0 sc0 ls0 ws0">1<span class="_ _4e"></span><span class="lse">40<span class="ffd ls0"></span></span></div><div class="t m1b xf h4e y38 ff10 fsb fc0 sc0 ls0 ws0">t</div></div><div class="t m0 x74 h4f y9f ff1 fs25 fc0 sc0 ls0 ws0">满</div><div class="t m0 x3 h4f ya1 ff1 fs25 fc0 sc0 ls0 ws0">足</div><div class="c x75 ya2 w19 h50"><div class="t m1c x1f h51 ya3 ffd fs26 fc0 sc0 ls0 ws0"><span class="_ _4f"> </span></div><div class="t m1d x76 h52 ya4 ffd fs27 fc0 sc0 ls0 ws0"></div><div class="t m1e x4e h53 ya4 ffd fs28 fc0 sc0 ls0 ws0"><span class="_ _3e"></span><span class="ffc">)<span class="_ _2b"></span>1<span class="_ _41"></span>,<span class="_ _48"></span>(<span class="_ _50"></span>m<span class="_ _6"></span>ax<span class="_ _51"> </span><span class="ffb">i<span class="_ _52"></span><span class="ff10">t</span></span></span></div></div><div class="t m0 x77 h6 ya1 ff1 fs2 fc0 sc0 ls0 ws0">时，分类正确无误；而</div><div class="c x78 ya2 w1a h50"><div class="t m1f x1f h54 ya3 ffd fs29 fc0 sc0 ls0 ws0"><span class="_ _53"> </span></div><div class="t m20 x76 h55 ya4 ffd fs2a fc0 sc0 ls0 ws0"></div><div class="t m21 x4e h53 ya4 ffd fs28 fc0 sc0 ls0 ws0"><span class="_ _3e"></span><span class="ffc">)<span class="_ _2b"></span>1<span class="_ _41"></span>,<span class="_ _48"></span>(<span class="_ _50"></span>m<span class="_ _6"></span>ax<span class="_ _51"> </span><span class="ffb">i<span class="_ _52"></span><span class="ff10">t</span></span></span></div></div><div class="t m0 x79 h6 ya1 ff1 fs2 fc0 sc0 ls0 ws0">时，分类会出现错误。我</div><div class="t m0 x3 h6 ya5 ff1 fs2 fc0 sc0 ls0 ws0">们对出现</div><div class="c x70 ya6 w1a h50"><div class="t m1f x1f h54 ya3 ffd fs29 fc0 sc0 ls0 ws0"><span class="_ _53"> </span></div><div class="t m20 x76 h55 ya4 ffd fs2a fc0 sc0 ls0 ws0"></div><div class="t m21 x4e h53 ya4 ffd fs28 fc0 sc0 ls0 ws0"><span class="_ _3e"></span><span class="ffc">)<span class="_ _2b"></span>1<span class="_ _41"></span>,<span class="_ _48"></span>(<span class="_ _50"></span>m<span class="_ _6"></span>ax<span class="_ _51"> </span><span class="ffb">i<span class="_ _52"></span><span class="ff10">t</span></span></span></div></div><div class="t m0 x7a h6 ya5 ff1 fs2 fc0 sc0 ls0 ws0">的所有样本使用<span class="ff9">k-</span>近邻算法辅助分类，综合得到的结果</div><div class="t m0 x3 h6 ya7 ff1 fs2 fc0 sc0 ls0 ws0">为最终分类的结果。<span class="_ _4d"></span>经实验<span class="_ _4"></span>，<span class="_ _4d"></span>该方法分类正确率高于单一的<span class="ff9">k-</span>近邻法和<span class="ff9">BP</span>网络法，</div><div class="t m0 x3 h6 ya8 ff1 fs2 fc0 sc0 ls0 ws0">且结果比较稳定。<span class="ff9"> </span></div><div class="t m0 x3 h5 ya9 ff8 fs1 fc0 sc0 lsf ws0">2 <span class="_ _1"> </span><span class="ff1 sc1 ls0">算法流程</span><span class="ls0"> </span></div><div class="t m0 x7 h6 yaa ff1 fs2 fc0 sc0 ls0 ws0">根据上述实验原理分析，该算法流程如下：<span class="ff9"> </span></div><div class="t m0 x3 h6 yab ff1 fs2 fc0 sc0 ls0 ws0">（<span class="ff9">1</span>）<span class="ff9"> </span>读入人脸库<span class="ff9"> </span></div><div class="t m0 x31 h6 y3f ff1 fs2 fc0 sc0 ls0 ws0">每个人取前<span class="ff9">5</span>张作为训练样本，<span class="_ _6"></span>后<span class="ff9">5</span>张为测试样本，<span class="_ _6"></span>共<span class="ff9">40</span>人，<span class="_ _6"></span>则训练样本和</div><div class="t m0 x31 h6 yac ff1 fs2 fc0 sc0 ls0 ws0">测试样本数分别</div><div class="c x7b yad w1b h40"><div class="t m22 x7c h56 y80 ffc fs20 fc0 sc0 ls10 ws0">200<span class="_ _54"></span><span class="ffd ls0"><span class="_ _29"></span><span class="ffb">N</span></span></div></div><div class="t m0 x7d h6 yac ff1 fs2 fc0 sc0 ls0 ws0">为。人脸图像为<span class="ff9">92</span>×<span class="ff9">112</span>维，按列相连就构成</div><div class="t m0 x31 h6 yae ff9 fs2 fc0 sc0 ls0 ws0">N=10304<span class="ff1">维矢量</span></div><div class="c x7e yaf w2 h3a"><div class="t m23 xb h57 yb0 ffb fs2b fc0 sc0 ls0 ws0">j</div><div class="t m23 xc h58 yb1 ffb fs2c fc0 sc0 ls0 ws0">x</div></div><div class="t m0 x7f h6 yae ff1 fs2 fc0 sc0 ls0 ws0">，</div><div class="c x80 yaf w2 h3a"><div class="t m23 xb h57 yb0 ffb fs2b fc0 sc0 ls0 ws0">j</div><div class="t m23 xc h58 yb1 ffb fs2c fc0 sc0 ls0 ws0">x</div></div><div class="t m0 x81 h6 yae ff1 fs2 fc0 sc0 ls0 ws0">可视为<span class="ff9">N</span>维空间中的一个点。<span class="ff9"> </span></div><div class="t m0 x3 h6 yb2 ff1 fs2 fc0 sc0 ls0 ws0">（<span class="ff9">2</span>）<span class="ff9"> </span>构造平均脸和偏差矩阵<span class="ff9"> </span></div><div class="t m0 x31 h6 yb3 ff1 fs2 fc0 sc0 ls0 ws0">平均脸</div><div class="c x50 yb4 w10 h59"><div class="t m24 x1e h5a yb5 ffc fs2d fc0 sc0 ls0 ws0">1</div><div class="t m24 x1f h5b yb6 ffc fs2e fc0 sc0 ls0 ws0">1</div><div class="t m24 x20 h5c yb7 ffb fs2d fc0 sc0 ls0 ws0">N</div><div class="t m24 x4e h5c yb8 ffb fs2d fc0 sc0 ls0 ws0">j</div><div class="t m24 x22 h5c yb5 ffb fs2d fc0 sc0 ls0 ws0">j</div><div class="t m24 x23 h5d yb9 ffb fs2e fc0 sc0 ls0 ws0">N</div><div class="t m24 x13 h5e yb5 ffd fs2d fc0 sc0 ls0 ws0"></div><div class="t m24 x24 h5f yba ffd fs2e fc0 sc0 ls0 ws0"></div><div class="t m24 x12 h60 ybb ffd fs2f fc0 sc0 ls0 ws0"></div><div class="t m24 xf h61 yba ff10 fs2e fc0 sc0 ls11 ws0">ux</div></div><div class="t m0 x82 h8 yb3 ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x31 h6 ybc ff1 fs2 fc0 sc0 ls0 ws0">偏差矩阵</div><div class="c x83 ybd w1c h59"><div class="t m25 x12 h5a yb5 ffc fs2d fc0 sc0 ls0 ws0">1</div><div class="t m25 x13 h5b yba ffc fs2e fc0 sc0 ls0 ws0">(<span class="_ _16"> </span>)(<span class="_ _e"> </span>)</div><div class="t m25 x14 h5c yb7 ffb fs2d fc0 sc0 ls0 ws0">N</div><div class="t m25 x7 h5c ybe ffb fs2d fc0 sc0 ls12 ws0">TT</div><div class="t m25 x16 h5c yb8 ffb fs2d fc0 sc0 ls0 ws0">r<span class="_ _55"> </span>j<span class="_ _10"> </span>i</div><div class="t m25 x17 h5c yb5 ffb fs2d fc0 sc0 ls0 ws0">j</div><div class="t m25 xf h5d yba ffb fs2e fc0 sc0 ls0 ws0">S<span class="_ _11"> </span>x<span class="_ _56"> </span>u<span class="_ _13"> </span>x<span class="_ _14"> </span>u<span class="_ _57"> </span>AA</div><div class="t m25 x5d h5e yb5 ffd fs2d fc0 sc0 ls0 ws0"></div><div class="t m25 x19 h5f yba ffd fs2e fc0 sc0 ls0 ws0"><span class="_ _15"> </span><span class="_ _58"> </span><span class="_ _59"> </span></div><div class="t m25 x7c h60 ybb ffd fs2f fc0 sc0 ls0 ws0"></div></div><div class="t m0 x84 h8 ybc ff9 fs2 fc0 sc0 ls0 ws0">,</div><div class="c x85 ybf w1d h16"><div class="t m26 x23 h17 y37 ffd fsa fc0 sc0 ls0 ws0"><span class="_ _5a"> </span></div><div class="t m27 xd h18 y38 ffb fsb fc0 sc0 ls0 ws0">u<span class="_ _18"></span>x<span class="_ _5b"></span>u<span class="_ _1a"></span>x<span class="_ _5c"></span>u<span class="_ _1c"></span>x<span class="_ _54"></span>A</div><div class="t m27 x86 h19 y39 ffb fsc fc0 sc0 ls0 ws0">N</div><div class="t m27 x87 h1a y38 ffd fsb fc0 sc0 ls0 ws0"><span class="_ _2f"></span><span class="_ _1e"></span><span class="_ _5d"></span><span class="_ _5e"> </span><span class="ffe"></span></div><div class="t m27 x88 h1b y39 ffc fsc fc0 sc0 ls0 ws0">2<span class="_ _5f"></span>1</div></div><div class="t m0 x89 h8 ybc ff9 fs2 fc0 sc0 ls0 ws0"> </div><div class="t m0 x3 h6 yc0 ff1 fs2 fc0 sc0 ls0 ws0">（<span class="ff9">3</span>）<span class="ff9"> </span>计算通过<span class="ff9">K-L</span>变换的特征脸子空间<span class="ff9"> </span></div><div class="c x6 yc1 we h2f"><div class="t mf xc h30 yc2 ffb fs17 fc0 sc0 ls0 ws0">A</div></div><div class="t m0 x31 h6 yc3 ff1 fs25 fc0 sc0 ls0 ws0">为<span class="_ _24"> </span><span class="ff9 fs2">10304<span class="_ _4"></span><span class="ff1">×</span>200<span class="_ _60"> </span><span class="ff1">矩阵，其自相关矩阵</span></span></div><div class="c x8a yc4 w1e h3a"><div class="t m28 x49 h62 yc5 ffb fs1e fc0 sc0 ls0 ws0">A<span class="_ _26"></span>A<span class="_ _61"></span>R</div><div class="t m28 x4e h57 yc6 ffb fs2b fc0 sc0 ls0 ws0">T</div><div class="t m28 x13 h63 yc5 ffd fs1e fc0 sc0 ls0 ws0"></div><div class="t m28 x8b h64 yc7 ffd fs2b fc0 sc0 ls0 ws0"><span class="ffc ls13">200<span class="_ _62"></span>200</span></div></div><div class="t m0 x8c h6 yc3 ff9 fs2 fc0 sc0 ls0 ws0">,<span class="ff1">计算得到矩阵的特征值</span></div><div class="c x3 yc8 wa h16"><div class="t mb x35 h23 y49 ffb fs11 fc0 sc0 ls0 ws0">i</div><div class="t mb xf h24 y4a ffb fs12 fc0 sc0 ls0 ws0">l</div></div><div class="t m0 x8d h6 yc9 ff9 fs2 fc0 sc0 ls0 ws0"> <span class="ff1">，对应于</span></div><div class="c x8e yc8 w1f h16"><div class="t m29 x35 h23 y49 ffb fs11 fc0 sc0 ls0 ws0">i</div><div class="t m29 xf h24 y4a ffb fs12 fc0 sc0 ls0 ws0">l</div></div><div class="t m0 x50 h6 yc9 ff1 fs2 fc0 sc0 ls0 ws0">的特征向量为</div><div class="c x69 yc8 wc h16"><div class="t md x3d h19 y39 ffb fsc fc0 sc0 ls0 ws0">i</div><div class="t md xf h18 y38 ffb fsb fc0 sc0 ls0 ws0">v</div></div><div class="t m0 x81 h6 yc9 ff1 fs2 fc0 sc0 ls0 ws0">，为。对特征值按大小降序排列，依照公式<span class="ff9"> </span></div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div>