谱分类MATLAB程序

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十几个程序,谱聚类的完整例子,有详细的例子,绝对物有所值,包括花朵分类,核函数等,MATLAB程序,下载绝对值得!包括研究生写论文,也是值得参考
project.rar
  • unmixing_code.m
    1.6KB
  • projectmainIris(Daniel).m
    1.7KB
  • projectmainIris.m
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  • ringdataset.m
    702B
  • ndimweightmatrix.m
    480B
  • projectmainRing.m
    1.6KB
  • projectmain.m
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  • ndimALTweightmatrix.m
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  • randomdiskpoint.m
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  • Peter Rizzi - Project 6 Home.pdf
    360.3KB
内容介绍
<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://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62844e033b39c07824499b55/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/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://static.pudn.com/prod/directory_preview_static/62844e033b39c07824499b55/bg1.jpg"><div class="c x1 y1 w2 h2"><div class="t m0 x2 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">Project 6 - Spectral Clustering</div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls0 ws0">By: Daniel Jacobson, Austin Alderete, Peter Rizzi</div><div class="t m0 x3 h4 y4 ff1 fs1 fc0 sc0 ls0 ws0">Description (http://math.gmu.edu/~tsauer/class/447/proj/chap12proj.pdf)</div><div class="t m0 x2 h3 y5 ff1 fs0 fc0 sc0 ls0 ws0">Introduction to Connected Components and the Project</div><div class="t m0 x2 h5 y6 ff1 fs2 fc0 sc0 ls0 ws0">What it means to be connected</div><div class="t m0 x2 h4 y7 ff1 fs1 fc0 sc0 ls0 ws0">Spectral clustering is a method of clustering data that relies on eigenvalues to clump data into sets. We,</div><div class="t m0 x2 h4 y8 ff1 fs1 fc0 sc0 ls0 ws0">naturally<span class="_ _0"></span>, have an inutition for what it means for a set of objects to be clustered. Our visual processing has</div><div class="t m0 x2 h4 y9 ff1 fs1 fc0 sc0 ls0 ws0">evolved to search for patterns and separate sets of data. However<span class="_ _0"></span>, there is no universal, intuitive</div><div class="t m0 x2 h4 ya ff1 fs1 fc0 sc0 ls0 ws0">algorithm for data sorting. In spectral clustering, a similarity matrix is first defined. A similarity matrix A has</div><div class="t m0 x2 h4 yb ff1 fs1 fc0 sc0 ls0 ws0">the property that <span class="_ _1"> </span> contains information regarding how ``similar'' points <span class="_ _2"> </span> and <span class="_ _3"> </span> are. From this matrix,</div><div class="t m0 x2 h4 yc ff1 fs1 fc0 sc0 ls0 ws0">what is known as a Laplacian matrix is constructed. A Laplacian matrix is a matrix representation of a</div><div class="t m0 x2 h4 yd ff1 fs1 fc0 sc0 ls0 ws0">graph. Wikipedia (http://en.wikipedia.org/wiki/Laplacian_matrix#Symmetric_normalized_Laplacian) gives</div><div class="t m0 x2 h4 ye ff1 fs1 fc0 sc0 ls0 ws0">an excellent example of a graph, its degree matrix, its adjacency matrix (similarity matrix), and its</div><div class="t m0 x2 h4 yf ff1 fs1 fc0 sc0 ls0 ws0">Laplacian matrix. The eigenvectors and eigenvalues for this Lapalcian matrix are then found. Partitioning</div><div class="t m0 x2 h4 y10 ff1 fs1 fc0 sc0 ls0 ws0">of the points is then performed based on the eigenvectors and values.</div><div class="t m0 x2 h4 y11 ff1 fs1 fc0 sc0 ls0 ws0">An example method of partitioning is as follows: consider the second-smallest eigenvalue of the</div><div class="t m0 x2 h4 y12 ff1 fs1 fc0 sc0 ls0 ws0">Laplacian matrix and its corresponding eigenvector; for all points with a component in said eigenvector</div><div class="t m0 x2 h4 y13 ff1 fs1 fc0 sc0 ls0 ws0">less than the value of the eigenvalue, place the points in one set; then place all other points in a separate</div><div class="t m0 x2 h4 y14 ff1 fs1 fc0 sc0 ls0 ws0">set; additional partitions may be applied on this next set with respect to the next eigenvalue. There are</div><div class="t m0 x2 h4 y15 ff1 fs1 fc0 sc0 ls0 ws0">many methods of spectral clustering, but this is simply one example. The graph Laplacians used</div><div class="t m0 x2 h4 y16 ff1 fs1 fc0 sc0 ls0 ws0">throughout this project differ<span class="_ _0"></span>, and are each covered in turn.</div><div class="t m0 x2 h5 y17 ff1 fs2 fc0 sc0 ls0 ws0">The Project</div><div class="t m0 x2 h4 y18 ff1 fs1 fc0 sc0 ls0 ws0">We begin with a union of connected components in <span class="_ _4"> </span> and fix an <span class="_ _5"> </span>. Then our initial weight matrix </div><div class="t m0 x4 h4 y19 ff1 fs1 fc0 sc0 ls0 ws0"> is defined as <span class="_ _6"> </span> and 0 otherwise for all paris of points <span class="_ _7"> </span> and</div><div class="t m0 x2 h4 y1a ff1 fs1 fc0 sc0 ls0 ws0">implemented in ndimweightmatrix.m (../code/ndimweightmatrix.m). We also occasionally use an alternate</div><div class="t m0 x2 h4 y1b ff1 fs1 fc0 sc0 ls0 ws0">weight matrix that is defined as <span class="_ _8"> </span>. Then <span class="_ _9"> </span> is defined as the diagonal matrix of the</div><div class="t m0 x2 h4 y1c ff1 fs1 fc0 sc0 ls0 ws0">row sums of <span class="_ _a"> </span>.</div><div class="t m0 x2 h4 y1d ff1 fs1 fc0 sc0 ls0 ws0">Then we have our choice of a graph Laplacian from the following list:</div><div class="t m0 x5 h4 y1e ff1 fs1 fc0 sc0 ls0 ws0">1<span class="_ _0"></span>. <span class="_ _b"></span>Unnormalized: </div><div class="t m0 x5 h4 y1f ff1 fs1 fc0 sc0 ls0 ws0">2<span class="_ _0"></span>. <span class="_ _b"></span>Symmetric: </div><div class="t m0 x5 h4 y20 ff1 fs1 fc0 sc0 ls0 ws0">3<span class="_ _0"></span>. <span class="_ _b"></span>Random W<span class="_ _c"></span>alk: </div><div class="t m0 x2 h4 y21 ff1 fs1 fc0 sc0 ls0 ws0">Using MA<span class="_ _0"></span>TLAB's <span class="_"> </span><span class="ff2 fs3">[V, D] = eig( A )<span class="_ _d"> </span></span> command we may find the eigenvalues and corresponding right</div><div class="t m0 x2 h4 y22 ff1 fs1 fc0 sc0 ls0 ws0">eigenvectors of our chosen Lapalcian. Our graph Laplacian is symmetric with nonegative eigenvalues</div><div class="t m0 x2 h4 y23 ff1 fs1 fc0 sc0 ls0 ws0">and the eigenspace corresponding to <span class="_ _e"> </span> is spanned by the vectors <span class="_ _f"> </span>, where <span class="_ _10"> </span> is an</div><div class="t m0 x2 h4 y24 ff1 fs1 fc0 sc0 ls0 ws0">indicator function. Since the <span class="_"> </span><span class="ff2 fs3">eig<span class="_ _d"> </span></span> command returns some orthogonal basis for the eigenspace, we must</div><div class="t m0 x2 h4 y25 ff1 fs1 fc0 sc0 ls0 ws0">"unmix" the eigenvectors to obtain the appropriate indicator functions.</div><div class="t m0 x2 h4 y26 ff1 fs1 fc0 sc0 ls0 ws0">In order to unmix the eigenvectors, we let <span class="_ _11"> </span> be the <span class="_ _12"> </span> matrix of eigenvectors returned where <span class="_ _13"> </span> is</div><div class="t m0 x2 h4 y27 ff1 fs1 fc0 sc0 ls0 ws0">the number of data points and <span class="_ _3"> </span> is the number of clusters. We then apply the <span class="_ _14"> </span> factorization to </div><div class="t m0 x3 h4 y28 ff1 fs1 fc0 sc0 ls0 ws0"> and define <span class="_ _15"> </span> as the <span class="_ _12"> </span> matrix formed by the top <span class="_ _3"> </span> rows ot <span class="_ _16"> </span>. Then the columns of </div><div class="t m0 x2 h4 y29 ff1 fs1 fc0 sc0 ls0 ws0">serve as the indicator functions for the clusters. A MA<span class="_ _0"></span>TLAB implementation is as follows:</div></div><div class="c x1 y2a w2 h6"><div class="t m0 x6 h7 y2b ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">a</span></div></div><div class="c x1 y2c w2 h8"><div class="t m0 x7 h9 y2d ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span><span class="fc1 sc0">j</span></div></div><div class="c x1 y2e w2 ha"><div class="t m0 x8 h7 y2f ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span></div></div><div class="c x1 y30 w2 hb"><div class="t m0 x9 h7 y31 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">j</span></div></div><div class="c x1 y32 w2 ha"><div class="t m0 xa h7 y33 ff4 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">R</span></div></div><div class="c x1 y34 w2 h8"><div class="t m0 xb h9 y35 ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">n</span></div></div><div class="c x1 y36 w2 h8"><div class="t m0 xc h7 y37 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#1013;</span></div><div class="t m0 xd h7 y37 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&gt;</span><span class="_ _17"> </span><span class="fc1 sc0">0</span></div></div><div class="c x1 y38 w2 hc"><div class="t m0 x2 h7 y39 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">W</span></div></div><div class="c x1 y3a w2 hd"><div class="t m0 xe h7 y3b ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span><span class="_ _17"> </span><span class="fc1 sc0">1</span><span class="fc1 sc0"> </span><span class="fc1 sc0">i</span><span class="fc1 sc0">f</span><span class="fc1 sc0"> </span><span class="fc1 sc0">|</span><span class="fc1 sc0">|</span><span class="_ _1"> </span><span class="fc1 sc0">&#8722;</span><span class="_ _18"> </span><span class="fc1 sc0">|</span><span class="fc1 sc0">|</span><span class="_ _17"> </span><span class="fc1 sc0">&lt;</span></div><div class="t m0 xf h7 y3b ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#1013;</span></div></div><div class="c x1 y38 w2 hc"><div class="t m0 x10 h7 y39 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">W</span></div></div><div class="c x1 y3a w2 hd"><div class="t m0 x11 h9 y3c ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span><span class="fc1 sc0">j</span></div></div><div class="c x1 y3d w2 he"><div class="t m0 x12 h7 y3e ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">x</span></div></div><div class="c x1 y3a w2 hd"><div class="t m0 x13 h9 y3c ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span></div></div><div class="c x1 y3d w2 he"><div class="t m0 x14 h7 y3e ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">x</span></div></div><div class="c x1 y3a w2 hd"><div class="t m0 x15 h9 y3c ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">j</span></div></div><div class="c x1 y3f w2 hf"><div class="t m0 x16 h7 y40 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">,</span></div></div><div class="c x1 y3d w2 he"><div class="t m0 x17 h7 y3e ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">x</span></div></div><div class="c x1 y3f w2 hf"><div class="t m0 x18 h9 y41 ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span></div></div><div class="c x1 y3d w2 he"><div class="t m0 x19 h7 y3e ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">x</span></div></div><div class="c x1 y3f w2 hf"><div class="t m0 x1a h9 y41 ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">j</span></div></div><div class="c x1 y42 w2 h10"><div class="t m0 x1b h7 y43 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span><span class="_ _17"> </span><span class="fc1 sc0">e</span><span class="fc1 sc0">x</span><span class="fc1 sc0">p</span><span class="fc1 sc0">(</span><span class="fc1 sc0">&#8722;</span><span class="_ _19"> </span><span class="fc1 sc0">)</span></div></div><div class="c x1 y44 w2 ha"><div class="t m0 x1c h7 y45 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">W</span></div></div><div class="c x1 y42 w2 h10"><div class="t m0 x1d h9 y46 ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span><span class="fc1 sc0">j</span></div></div><div class="c x1 y47 w2 hb"><div class="t m0 x1e h9 y48 ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">|</span><span class="fc1 sc0">|</span><span class="_ _1a"> </span><span class="fc1 sc0">&#8722;</span><span class="_ _1a"> </span><span class="fc1 sc0">|</span></div></div><div class="c x1 y49 w2 h11"><div class="t m0 x1f h9 y4a ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">x</span></div></div><div class="c x1 y47 w2 hb"><div class="t m0 x20 h9 y4b ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span></div></div><div class="c x1 y49 w2 h11"><div class="t m0 xa h9 y4a ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">x</span></div></div><div class="c x1 y47 w2 hb"><div class="t m0 x21 h9 y4b ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">j</span></div></div><div class="c x1 y4c w2 h8"><div class="t m0 x22 h9 y4d ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">|</span></div></div><div class="c x1 y47 w2 hb"><div class="t m0 x23 h9 y4e ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">2</span></div></div><div class="c x1 y4f w2 h12"><div class="t m0 x24 h9 y50 ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">2</span></div></div><div class="c x1 y51 w2 h11"><div class="t m0 x25 h9 y4a ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#1013;</span></div></div><div class="c x1 y4f w2 h12"><div class="t m0 xa h9 y52 ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">2</span></div></div><div class="c x1 y44 w2 ha"><div class="t m0 x26 h7 y45 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">D</span></div></div><div class="c x1 y53 w2 h13"><div class="t m0 x27 h7 y54 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">W</span></div></div><div class="c x1 y55 w2 h8"><div class="t m0 x28 h7 y56 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">L</span></div><div class="t m0 x29 h7 y56 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span></div><div class="t m0 x2a h7 y56 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">D</span></div><div class="t m0 x2b h7 y56 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#8722;</span></div><div class="t m0 x2c h7 y56 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">W</span></div></div><div class="c x1 y57 w2 h14"><div class="t m0 x2d h7 y58 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span></div><div class="t m0 x2e h7 y58 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">I</span></div><div class="t m0 x2f h7 y58 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#8722;</span></div><div class="t m0 x30 h7 y58 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">W</span></div></div><div class="c x1 y59 w2 h13"><div class="t m0 x31 h7 y5a ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">L</span></div></div><div class="c x1 y57 w2 h14"><div class="t m0 x32 h9 y5b ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">s</span><span class="fc1 sc0">y</span><span class="fc1 sc0">m</span></div></div><div class="c x1 y59 w2 h13"><div class="t m0 x13 h7 y5a ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">D</span></div></div><div class="c x1 y57 w2 h14"><div class="t m0 x33 h9 y5c ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#8722;</span><span class="fc1 sc0">0.</span><span class="fc1 sc0">5</span></div></div><div class="c x1 y59 w2 h13"><div class="t m0 x34 h7 y5a ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">D</span></div></div><div class="c x1 y57 w2 h14"><div class="t m0 x35 h9 y5c ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#8722;</span><span class="fc1 sc0">0.</span><span class="fc1 sc0">5</span></div></div><div class="c x1 y5d w2 h15"><div class="t m0 x36 h7 y5e ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span></div><div class="t m0 x37 h7 y5e ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">I</span></div><div class="t m0 x1c h7 y5e ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#8722;</span></div><div class="t m0 x38 h7 y5e ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">W</span></div></div><div class="c x1 y5f w2 h13"><div class="t m0 xe h7 y60 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">L</span></div></div><div class="c x1 y5d w2 h15"><div class="t m0 x39 h9 y3e ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">r</span><span class="fc1 sc0">w</span></div></div><div class="c x1 y5f w2 h13"><div class="t m0 x33 h7 y60 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">D</span></div></div><div class="c x1 y5d w2 h15"><div class="t m0 x1b h9 y61 ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#8722;</span><span class="fc1 sc0">1</span></div></div><div class="c x1 y62 w2 h8"><div class="t m0 x3a h7 y63 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#955;</span></div><div class="t m0 x3b h7 y63 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span><span class="_ _17"> </span><span class="fc1 sc0">0</span></div></div><div class="c x1 y64 w2 ha"><div class="t m0 x3c h7 y65 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">D</span></div></div><div class="c x1 y66 w2 h16"><div class="t m0 x3d h9 y67 ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">0.</span><span class="fc1 sc0">5</span></div></div><div class="c x1 y64 w2 ha"><div class="t m0 x3e h7 y65 ff6 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">1</span></div></div><div class="c x1 y68 w2 h17"><div class="t m0 x3f h9 y69 ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">S</span></div></div><div class="c x1 y66 w2 h16"><div class="t m0 x40 h9 y6a ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span></div></div><div class="c x1 y64 w2 ha"><div class="t m0 x41 h7 y65 ff6 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">1</span></div></div><div class="c x1 y68 w2 h17"><div class="t m0 x42 h9 y69 ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">S</span></div></div><div class="c x1 y6b w2 h18"><div class="t m0 x43 h9 y6c ff3 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">i</span></div></div><div class="c x1 y6d w2 h13"><div class="t m0 x44 h7 y54 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">E</span><span class="_ _1b"> </span><span class="fc1 sc0">N</span></div><div class="t m0 x23 h7 y54 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#215;</span></div><div class="t m0 x45 h7 y54 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">c</span><span class="_ _1c"> </span><span class="fc1 sc0">N</span></div></div><div class="c x1 y6e w2 h19"><div class="t m0 x12 h7 y5a ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">c</span></div></div><div class="c x1 y6f w2 h1a"><div class="t m0 x46 h7 y2f ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">P</span><span class="_ _1d"></span><span class="fc1 sc0">A</span></div><div class="t m0 x47 h7 y2f ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">=</span></div><div class="t m0 x48 h7 y2f ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">L</span><span class="fc1 sc0">U</span></div></div><div class="c x1 y70 w2 h13"><div class="t m0 x2 h7 y71 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">E</span><span class="_ _14"> </span><span class="fc1 sc0">M</span><span class="_ _1e"> </span><span class="fc1 sc0">N</span></div><div class="t m0 x49 h7 y71 ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#215;</span></div><div class="t m0 x37 h7 y71 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">c</span></div></div><div class="c x1 y72 w2 h19"><div class="t m0 x4a h7 y73 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">c</span></div></div><div class="c x1 y70 w2 h13"><div class="t m0 x4b h7 y71 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">P</span><span class="_ _1d"></span><span class="fc1 sc0">E</span></div></div><div class="c x1 y74 w2 hb"><div class="t m0 x4c h7 y75 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">E</span></div></div><div class="c x1 y70 w2 h13"><div class="t m0 x4d h7 y71 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">M</span></div></div><div class="c x1 y74 w2 hb"><div class="t m0 x4e h9 y76 ff5 fs5 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#8722;</span><span class="fc1 sc0">1</span></div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><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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