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-- Principal component analysis
import Numeric.LinearAlgebra
import System.Directory(doesFileExist)
import System(system)
import Control.Monad(when)
type Vec = Vector Double
type Mat = Matrix Double
sumColumns m = constant 1 (rows m) <> m
-- Vec with the mean value of the columns of a Mat
mean x = sumColumns x / fromIntegral (rows x)
-- covariance Mat of a list of observations as rows of a Mat
cov x = (trans xc <> xc) / fromIntegral (rows x -1)
where xc = center x
center m = m - constant 1 (rows m) `outer` mean m
-- creates the compression and decompression functions from the desired number of components
pca :: Int -> Mat -> (Vec -> Vec , Vec -> Vec)
pca n dataSet = (encode,decode)
where
encode x = vp <> (x - m)
decode x = x <> vp + m
m = mean dataSet
c = cov dataSet
(_,v) = eigSH c
vp = takeRows n (trans v)
norm = pnorm PNorm2
main = do
ok <- doesFileExist ("mnist.txt")
when (not ok) $ do
putStrLn "\nTrying to download test datafile..."
system("wget -nv http://dis.um.es/~alberto/material/sp/mnist.txt.gz")
system("gunzip mnist.txt.gz")
return ()
m <- fromFile "mnist.txt" (5000,785)
let xs = takeColumns (cols m -1) m -- the last column is the digit type (class label)
let x = toRows xs !! 4 -- an arbitrary test Vec
let (pe,pd) = pca 10 xs
let y = pe x
print y -- compressed version
print $ norm (x - pd y) / norm x --reconstruction quality
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