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Unformatted text preview: id previously, it actually beats QDA, which only correctly classified 371 data points for this data set. Continuing this
procedure by adding another two dimensions with x 4 (i.e. we set X s a ( , + ) = X s a ( , ) 4 we can correctly classify 376 points.
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_trij^) Introduction to Fisher's Discriminant Analysis  October 7, 2009
Fis he r's Dis criminant Analys is (FDA), also known as Fis he r's Line ar Dis criminant Analys is (LDA) in some sources, is a classical feature extraction technique. It
was originally described in 1936 by Sir Ronald Aylmer Fisher (http://en.wikipedia.org/wiki/Ronald_A._Fisher) , an English statistician and eugenicist who has been
described as one of the founders of modern statistical science. His original paper describing FDA can be found here
(http://digital.library.adelaide.edu.au/dspace/handle/2440/15227) ; a Wikipedia article summarizing the algorithm can be found here
(http://en.wikipedia.org/wiki/Linear_discriminant_analysis#Fisher.27s_linear_discriminant) .
LDA is for classification and FDA is used for feature extraction. Contras ting FDA with PCA
The goal of FDA is in contrast to our other main feature extraction technique, principal component analysis (PCA).
In PCA, we map data to lower dimensions to maximize the variation in those dimensions.
In FDA, we map data to lower dimensions to best separate data in different classes. wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 16/74 10/09/2013 Stat841  Wiki Cour se Notes 2 clouds of data, and the lines that might be produced by P CA and FDA. Because we are concerned with identifying which class data belongs to, FDA is often a better feature extraction algorithm for classification.
Another difference between PCA and FDA is that FDA is a supervised algorithm; that is, we know what class data belongs to, and we exploit that knowledge to find a
good projection to lower dimensions. Intuitive Des cription of FDA
An intuitive description of FDA can be given by visualizing two clouds of data, as shown above. Ideally, we would like to collapse all of the data points in eac...
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