Stat841f09 - Wiki Course Notes

# Comwindexphptitle stat841pr intable yes we can define

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Unformatted text preview: variance of projected points will be and If we sum this two quantities we have The quantity is called within clas s covariance or The goal is to minimize Obje ctive Function Instead of maximizing and minimizing wikicour senote.com/w/index.php?title= Stat841&pr intable= yes we can define the following objective function: 19/74 10/09/2013 Stat841 - Wiki Cour se Notes This maximization problem is equivalent to subject to constraint , where is no upper bound and is no lower bound. We can use the Lagrange multiplier method to solve it: where With we get: Note that Here is the weight is sum of two positive matrices and so it has an inverse. is the eigenvector of corresponding to the largest eigenvalue . In facts, this expression can be simplified even more. with The quantity and λ are scalars. So we can say the quantity is proportional to FDA vs . PCA Example in M atlab We can compare PCA and FDA through the figure produced by matlab. The following are the code to produce the figure step by step and the explanation for steps. >X=vrd[,][ 15153,0) >1mnn(11,1 .;.30; >X=vrd[,][ 15153,0) >2mnn(53,1 .;.30; >X[1X] >=X;2; Create two multivariate normal random variables with . >po((:0,)X1302,.) >ltX1301,(:0,)''; >hl o >od n >p=ltX31601,(0:0,)'.) >1po((0:0,)X31602,r'; Plot the the data of the two classes respectively. >[ Y=rnopX; >U ]picm() >po(0U11*0,0U21*0) >lt[ (,)1][ (,)1]; Using PCA to find the principal component and plot it. >s=*115153; >w2[ .;. >s=[;1-5;]*[;1-5 3); >b(1[ 3)(1[; ]' >g=n(w*b > ivs)s; >[ w=isg; >v ]eg() >po(v11* 0,v21* 0,r) >lt[(,)5 ][(,)5 ]'' Using FDA to find the principal component and plot it. Now we can compare them through the figure. wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 20/74 10/09/2013 Stat841 - Wiki Cour se Notes P CA and FDA primary dimension for normal multivariate data, using matlab From the graph: when we see using PCA, we have a huge overlap for two classes, so PCA is not good. Ho...
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## This document was uploaded on 03/07/2014.

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