Stat841f09 - Wiki Course Notes

# X is a matrix of size 64400 and each column

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Unformatted text preview: wever, there is no overlap for the two classes and they are seperated pretty. Thus, FDA is better than PCA here. Practical e xample of 2_3 In this matlab example we explore FDA using our familiar data set 2_3 which consists of 200 handwritten "2" and 200 handwritten "3". X is a matrix of size 64*400 and each column represents an 8*8 image of "2" or "3". Here X1 gets all "2" and X2 gets all "3". >la 23 >od _ >X =X: 120; >1 (, :0) >X =X: 2140; >2 (, 0:0) Next we calculate within class covariance and between class covariance as before. >m1=ma(1 2; >u enX, ) >m2=ma(2 2; >u enX, ) >s =(u -m2 *(u -m2' >b m1 u) m1 u); >s =cvX' +cvX'; >w o(1) o(2) We use the first two eigenvectors to project the dato in a two- dimensional space. >[ d =eg(ivs)*s ) >v ] is n(w b; >w=v: 12; > (, :) >Xht=w*; >_a 'X Finally we plot the data and visualize the effect of FDA. > satroe(,0)Xht120) > cte(ns120,_a(:0) > hl o > od n > satroe(,0)Xht2140,r) > cte(ns120,_a(0:0)'' wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 21/74 10/09/2013 Stat841 - Wiki Cour se Notes FDA projection of data 2_ 3, using Matlab (http://www.mathwork.com) . Map the data into a linear line, and the two classes are seperated perfectly here. An e xte ns ion of Fis he r's dis criminant analys is for s tochas tic proce s s e s A general notion of Fisher's linear discriminant analysis can extend the classical multivariate concept to situations that allow for function- valued random elements. The development uses a bijective mapping that connects a second order process to the reproducing kernel Hilbert space generated by its within class covariance kernel. This approach provides a seamless transition between Fisher's original development and infinite dimensional settings that lends itself well to computation via smoothing and regularization. Link for Algorithm introduction:[[11] (http://statgen.ncsu.edu/icsa2007/talks/HyejinShin.pdf) ] FD...
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## This document was uploaded on 03/07/2014.

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