📄 pca.htm
字号:
<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns="http://www.w3.org/TR/REC-html40"><head><title>Rotations of PCA models</title>
<meta http-equiv="Content-Type" content="text/html; charset=windows-1252">
<link rel="File-List" href="http://www.models.kvl.dk/source/rotation/index_files/filelist.xml">
<link rel="stylesheet" type="text/css" href="pca_files/style.css"></head><body><div align="center">
<center>
<table style="border-color: rgb(17, 17, 17); border-collapse: collapse;" border="0" cellpadding="0" cellspacing="0" width="95%">
<tbody><tr>
<td height="35" width="95%">
<table style="border-color: rgb(17, 17, 17); border-collapse: collapse;" border="0" cellpadding="2" cellspacing="0" width="100%">
<tbody><tr>
<td width="21%">
<p align="left">
<a href="http://www.life.ku.dk/" class="topmenu"><b>Faculty of Life Sciences<br>
University of Copenhagen</b></a></p></td>
<td width="79%">
<p style="margin-top: 3pt; margin-bottom: 6pt;" align="right"><b>
<a href="http://www.models.kvl.dk/" class="topmenu"><b>Quality & Technology</b></a><br>
<a class="topmenu" href="http://en.ifv.life.ku.dk/"><b>Department of Food Science</b></a></b></p></td>
</tr>
<tr>
<td class="red" colspan="2" bgcolor="#800000" height="20" width="100%">
<table style="border-color: rgb(17, 17, 17); border-collapse: collapse;" border="0" cellpadding="0" cellspacing="0" width="100%">
<tbody><tr>
<td class="red">Latest news: <a href="http://www.models.life.ku.dk/research/posters" class="topmenu"><b>Check out our research posters</b></a>
</td>
<td class="red" align="right"> </td>
</tr>
</tbody></table>
</td>
</tr>
</tbody></table>
</td>
</tr>
</tbody></table>
</center>
</div>
<center>
<table style="border: 1px solid rgb(17, 17, 17); border-collapse: collapse;" border="0" cellpadding="5" cellspacing="0" width="95%">
<tbody><tr>
<td valign="top" width="12%">
<p style="line-height: 200%; margin-top: 0pt;">
<a class="menu" href="http://www.models.life.ku.dk/">Home </a><br>
<a href="http://www.models.kvl.dk/staff/" class="menu">Staff </a><br>
<a href="http://www.models.kvl.dk/research/" class="menu">Research </a><br>
<a href="http://www.models.kvl.dk/teaching/" class="menu">Teaching </a><br>
<a href="http://www.models.kvl.dk/about/" class="menu">About </a></p><div class="searchlogin">Download</div>
<p style="margin-top: 0pt;">
<a href="http://www.models.kvl.dk/source/" class="menusmall"> <b>Algorithms</b> </a><br>
<a href="http://www.models.kvl.dk/teaching/" class="menusmall"> <b>Courses</b> </a><br>
<a href="http://www.models.kvl.dk/research/data/" class="menusmall"> <b>Data Sets</b> </a><br>
<a href="http://www.models.kvl.dk/ris/risweb.isa" class="menusmall"> <b>References</b> </a><br>
<a href="http://www.models.kvl.dk/research/theses/" class="menusmall"> <b>Theses</b> </a>
</p><div class="searchlogin">Data Bases</div>
<a class="menusmall" href="http://www.models.kvl.dk/research/foodfluor/"> <b>FoodFlour</b> </a><br>
<a class="menusmall" href="http://www.models.life.ku.dk/research/domfluor/"> <b>DOMFlour</b></a><br>
<a class="menusmall" href="http://www.models.life.ku.dk/users/engelsen/specarb/specarb.html"> <b>SpeCarb</b> </a><p style="margin-top: 0pt;"> <!-- <div class="searchlogin">Search Site:</div> -->
<!-- <form method="POST" action="http://webtools.kvl.dk/cgi-bin/htsearch" style="margin:0pt;"> -->
<!-- <input type=hidden name=config value="models"> -->
<!-- <input type="text" name="words" size="20" style="width:100px; background-color: #E2E2E2; border: 1px solid #FFFFFF; font-size: 80%; font-family: Verdana;"> -->
<!-- <input type=hidden name="format" value="short"> <!-- short | long-->
<!-- <input type=hidden name="sort" value="score"> <!-- Score | Time | Title | Reverse score | Reverse Time | Reverse Title -->
<!-- <input type=hidden name="method" value="and"> <!-- and | or -->
<!-- </form> -->
</p><form method="get" action="http://www.google.com/custom">
<div class="searchlogin">Search Site:</div>
<input name="q" size="20" maxlength="255" value="" style="border: 1px solid rgb(255, 255, 255); width: 100px; background-color: rgb(226, 226, 226); font-size: 80%; font-family: Verdana;" type="text">
<input name="cof" value="LW:300;L:http://www.models.life.ku.dk/images/search_image.jpg" type="hidden">
<input name="domains" value="www.models.life.ku.dk" type="hidden">
<input name="sitesearch" value="www.models.life.ku.dk" type="hidden">
</form>
<!-- NEW SEARCH -->
<p><a href="http://www.odin.life.ku.dk/">
<img src="pca_files/odin_thumb.jpg" border="0"></a></p>
<p><a href="http://www.models.life.ku.dk/Build_Your_Food/index.asp">
<img src="pca_files/BYF_thumb.jpg" border="0"></a></p>
<hr>
<p style="line-height: 200%; margin-top: 0pt;">
<a href="http://www.campusnet.kvl.dk/" class="menusmall">CampusNet</a><br>
<a class="menusmall" href="http://uk.ifv.kvl.dk/intra/index.htm">IFV IntraNet</a><br>
<a class="menusmall" href="http://www.life.ku.dk/Service/Telefonbog.aspx">
LIFE phone.b.</a><br>
</p><hr>
<a href="http://www.models.kvl.dk/intranet/index.asp" class="menusmall">Q&T IntraNet</a><br>
<table style="border-color: rgb(17, 17, 17); border-collapse: collapse;" border="0" cellpadding="0" cellspacing="0" width="100">
<tbody><tr>
<td class="searchlogin" width="148">
<form method="post" action="/intranet/userlogin_motor.asp?" style="margin: 0pt;">
<input name="EMail" size="25" style="border: 1px solid rgb(255, 255, 255); width: 100px; background-color: rgb(226, 226, 226); font-size: 80%; font-family: Verdana;" value="" type="text"><br>
<input name="password" size="25" style="border: 1px solid rgb(255, 255, 255); width: 100px; background-color: rgb(226, 226, 226); font-size: 80%; font-family: Verdana;" type="password">
<center>
<input value=" Login " style="border: 1px solid Black; margin: 1pt; font-size: 80%; font-family: Verdana;" type="submit">
</center>
</form>
</td>
</tr>
</tbody></table>
<hr>
<a target="_top" href="http://t.extreme-dm.com/?login=fvdberg">
<img src="pca_files/i.gif" alt="" border="0" height="38" width="41"></a><script language="javascript1.2"><!--
EXs=screen;EXw=EXs.width;navigator.appName!="Netscape"?
EXb=EXs.colorDepth:EXb=EXs.pixelDepth;//-->
</script><script language="javascript"><!--
EXd=document;EXw?"":EXw="na";EXb?"":EXb="na";
EXd.write("<img src=\"http://t0.extreme-dm.com",
"/c.g?tag=fvdberg&j=y&srw="+EXw+"&srb="+EXb+"&",
"l="+escape(parent.document.referrer)+"\" height=1 width=1>");//-->
</script><img src="pca_files/c.gif" height="1" width="1"><noscript><img height=1 width=1 alt=""
src="http://t0.extreme-dm.com/c.g?tag=fvdberg&j=n"></noscript>
<hr>
</td>
<td bgcolor="#e2e2e2" valign="top" width="84%">
<!--[if !mso]>
<style>
v\:* { behavior: url(#default#VML) }
o\:* { behavior: url(#default#VML) }
.shape { behavior: url(#default#VML) }
</style>
<![endif]--><!--[if gte mso 9]>
<xml><o:shapedefaults v:ext="edit" spidmax="1027"/>
</xml><![endif]-->
<h1 align="center">
Orthomax Rotation of a PCA model </h1>
<p style="text-align: justify;">
<font size="2">In factor analysis rotations of the loadings are very often
applied, whereas in chemometrics these methods are very seldom used. This is in
spite of the fact that it is possible to obtain better conditions for
interpretation of PCA models on complex data.<br>
<br>
</font><font size="2">We here provide an algorithm by which it is possible to
apply rotations from the Orthomax family (quartimax and varimax) to a PCA-model.
</font> </p>
<p>
<span style="font-size: 12pt; font-family: 'Times New Roman',serif;" lang="EN-GB"><!--[if gte vml 1]><v:shapetype id="_x0000_t75"
coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_s1027" type="#_x0000_t75" style='width:425.25pt;
height:197.25pt'>
<v:imagedata src="index_files/image001.png" o:title="interpretation quercetin"/>
</v:shape><![endif]--><!--[if !vml]--><img src="pca_files/image002.jpg" v:shapes="_x0000_s1027" border="0" height="263" width="567"><!--[endif]--></span></p>
<p class="MsoNormal" style="text-align: center;" align="center">
</p>
<p class="MsoNormal" style="text-align: center;" align="center">
<i><span lang="en-us"><font size="2">Back-transformed loadings corresponding to
the first twelve components derived from a PCA model based on 1H NMR spectra of
24 preparations of St. John抯 wort. (A) and the corresponding rotated PCA model
(loadings rotated) (B). The score plot of the sixth and seventh component of the
rotated PCA model shows a tight clustering of preparations (C). </font></span>
</i>
<span style="font-size: 10pt;" lang="EN-US"> </span></p>
<p class="MsoNormal" align="left"> <br>
<font size="2">The above figure shows how rotations can make complex loadings
much simpler, and thus easier to interpret. The example clearly illustrates how
interpretation of the influence of a specific compound on the observed
clustering is facilitated using the rotated loadings (B) as compared to the
non-rotated loadings (A). Interpretation is aided since the influence of this
compound on the observed clustering is partitioned over many components in the
non-rotated PCA model, whereas in the rotated PCA model the influence is
described mainly by the sixth and seventh components. A score plot of the sixth
and seventh component of the rotated PCA model is shown in C. The plot shows,
that the clustering of preparation 3 in the positive direction of the seventh
component is due only to higher levels of the specific compound as compared with
other preparations. <br>
<br>
The example shows an example of rotation of loadings, but it is also possible to
rotate the scores. This can be particularly useful when you want simpler
conditions for understanding the influence of variables on the clustering of
individual samples.<br>
<br>
<br>
<br>
Download:</font></p>
<blockquote>
<ul>
<li>
<span lang="en-us">
<a href="http://www.models.kvl.dk/intranet/dl-monitor/go.asp?get=mf.m" style="text-decoration: none;">
<font size="2">Rotation function</font></a><font size="2"> (uses PLS_Toolbox)</font></span></li>
</ul>
</blockquote>
<p><font size="2">Please refer to the below paper when using the function:</font></p>
<p><font size="2">A Juul Lawaetz, B Schmidt, D St鎟k, JW Jaroszewski, R Bro,
Application of rotated PCA models to metabolite profiles to facilitate
interpretation: Commercial preparations of St. John's wort, Journal of
Chemometrics, Submitted</font></p>
<p> </p>
</td>
</tr>
</tbody></table>
</center>
<div align="center">
<center>
<table style="border: 1px solid rgb(17, 17, 17); border-collapse: collapse;" border="0" cellpadding="0" cellspacing="0" width="95%">
<tbody><tr>
<td class="webmaster" align="right" bgcolor="#000000" height="20" width="100%">
Last edited:
Monday, January 14, 2008 8:20:29 PM
⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -