📄 matlab central - file detail - partial least-squares and discriminant analysis.mht
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<BR> <BR>Y =3D X*B + E <BR> <BR>the =
total least=20
squares regression solves the problem to minimize the error =
in least=20
squares sense: <BR> <BR>J =3D E'*E=20
<BR> <BR>Instead of directly fitting a model =
between X=20
and Y, the PLS decomposes X and Y into low-dimensional space =
(so=20
called laten variable space) first: <BR> <BR>X =
=3D T*P' +=20
E0, and <BR>Y =3D U*Q' + F0 <BR> <BR>where =
P and Q=20
are orthogonal matrices, i.e. P'*P=3DI, Q'*Q=3DI, T and U =
has the same=20
number of columns, a, which is much less than the number of =
columns=20
of X. Then, a least squares regression is performed between =
T and U:=20
<BR> <BR>U =3D T*B + F1 <BR> <BR>At =
the end, the=20
overall regression model is <BR> <BR>Y =3D =
X*(P*B*Q') + F=20
<BR> <BR>i.e. the overall regression coefficient =
is=20
P*B*Q'. <BR> <BR>The reason to perform PLS =
instead of=20
total LS regression is that the data sets X and Y may =
contain random=20
noises, which should be excluded from regression. =
Decomposing X and=20
Y into laten space can ensure the regression is performed =
based on=20
most reliable variation.</P></TD></TR>
<TR>
<TD class=3Dlabel>MATLAB release</TD>
<TD>MATLAB 7.5 (R2007b) </TD></TR>
<TR>
<TD class=3Dlabel><SPAN class=3Dheading>Zip File =
Content</SPAN></TD>
<TD> </TD></TR>
<TR>
<TD class=3Dlabel><A name=3Dmfiles></A>Published M Files</TD>
<TD><A=20
onclick=3D"var =
w=3Dwindow.open('/matlabcentral/fx_files/18760/1/content/html/learningpca=
pls.html','small','toolbar=3Dno,location=3Dyes,resizable=3Dyes,status=3Dy=
es,menu=3Dno,scrollbars=3Dyes,width=3D700,height=3D600');w.focus();return=
false;"=20
=
href=3D"http://www.mathworks.com/matlabcentral/fx_files/18760/1/content/h=
tml/learningpcapls.html">Principal=20
Component Analysis and Partial Least Squares</A> </TD></TR>
<TR>
<TD class=3Dlabel>Other Files </TD>
<TD>
<DIV class=3Dtextframe>pls.m, =
<BR>html/learningpcapls_01.png,=20
<BR>html/learningpcapls_eq14726.png,=20
<BR>html/learningpcapls_eq1475.png,=20
<BR>html/learningpcapls_eq1937.png,=20
<BR>html/learningpcapls_eq2092.png, <BR>learningpcapls.m,=20
<BR>html/learningpcapls_eq38356.png,=20
<BR>html/learningpcapls_eq48172.png,=20
<BR>html/learningpcapls_eq7260.png,=20
<BR>html/learningpcapls_eq955.png,=20
<BR>html/learningpcapls_eq29314.png =
</DIV></TD></TR></TBODY></TABLE>
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<DIV id=3Dall_tags><SPAN><A=20
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A%22discriminant+analysis%22">discriminant=20
analysis</A></SPAN>, <SPAN><A=20
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<TH colSpan=3D4><SPAN class=3Dheading>Comments and =
Ratings</SPAN> <SPAN=20
class=3Dinfo>(8)</SPAN></TH></TR>
<TR>
<TD class=3Ddate><SPAN class=3Ddate>14 Mar 2008</SPAN></TD>
<TD><SPAN class=3Dauthor>fielen cathnic </SPAN></TD>
<TD><SPAN class=3Dcomment>good</SPAN></TD>
<TD width=3D80>
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<DIV style=3D"WIDTH: 100%"></DIV></DIV></TD></TR>
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<TD class=3Ddate><SPAN class=3Ddate>23 Jul 2008</SPAN></TD>
<TD><SPAN class=3Dauthor>kevin chen </SPAN></TD>
<TD><SPAN class=3Dcomment>it is excellent for a PLS algorithm =
beginner=20
like me, but, is this non-linear PLS algorithm? or only=20
PLS1?</SPAN></TD>
<TD width=3D80>
<DIV class=3Dstarrating title=3D5>
<DIV style=3D"WIDTH: 100%"></DIV></DIV></TD></TR>
<TR>
<TD class=3Ddate><SPAN class=3Ddate>23 Jul 2008</SPAN></TD>
<TD><SPAN class=3Dauthor>kevin chen </SPAN></TD>
<TD><SPAN class=3Dcomment>Are you also interested in the =
convolution=20
algorithms in Reading's Modulated Differential Scanning =
Calorimetry?=20
-- I read a lot of books and technical articles, but only =
got=20
confusion: how to deconvolute the modulated profile into =
reversible=20
and non-reversible parts?</SPAN></TD>
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<TD class=3Ddate><SPAN class=3Ddate>18 Dec 2008</SPAN></TD>
<TD><SPAN class=3Dauthor><A=20
=
href=3D"http://www.mathworks.com/matlabcentral/fileexchange/authors/37679=
">Su</A>=20
</SPAN></TD>
<TD><SPAN class=3Dcomment>I have a general question regarding =
PLS=20
regression that confused me; <BR> <BR>Suppose the =
response=20
variables Y is binary, can we run a PLS regression on it =
directly?=20
or we need to resort to logistic=20
version? <BR> <BR>Thanks</SPAN></TD>
<TD width=3D80>
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<TD class=3Ddate><SPAN class=3Ddate>11 Jan 2009</SPAN></TD>
<TD><SPAN class=3Dauthor><A=20
=
href=3D"http://www.mathworks.com/matlabcentral/fileexchange/authors/41925=
">Paul</A>=20
</SPAN></TD>
<TD><SPAN class=3Dcomment>Su, I believe you can use the PLS =
algorithm=20
directly. Look at the example discussed in the HTML file - =
the IRIS=20
data set - where the Y responses are all binary.</SPAN></TD>
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<TD class=3Ddate><SPAN class=3Ddate>05 Apr 2009</SPAN></TD>
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<TH colSpan=3D2><SPAN class=3Dheading>Updates</SPAN></TH></TR>
<TR>
<TD class=3Ddate>15 Feb 2008</TD>
<TD>update description</TD></TR>
<TR>
<TD class=3Ddate>15 Feb 2008</TD>
<TD>update the example file.</TD></TR>
<TR>
<TD class=3Ddate>18 Feb 2008</TD>
<TD>update description</TD></TR>
<TR>
<TD class=3Ddate>18 Feb 2008</TD>
<TD>update pls function</TD></TR>
<TR>
<TD class=3Ddate>19 Feb 2008</TD>
<TD>update description</TD></TR></TBODY></TABLE>
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<TD><A=20
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analysis</A></TD>
<TD><A=20
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