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-- Improved PCA, including illustrative graphics
import Numeric.LinearAlgebra
import Graphics.Plot
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
-- Vector with the mean value of the columns of a Mat
mean x = sumColumns x / fromIntegral (rows x)
-- covariance matrix of a list of observations as rows of a matrix
cov x = (trans xc <> xc) / fromIntegral (rows x -1)
where xc = center x
center m = m - constant 1 (rows m) `outer` mean m
type Stat = (Vec, [Double], Mat)
-- 1st and 2nd order statistics of a dataset (mean, eigenvalues and eigenvectors of cov)
stat :: Mat -> Stat
stat x = (m, toList s, trans v) where
m = mean x
(s,v) = eigSH' (cov x)
-- creates the compression and decompression functions from the desired reconstruction
-- quality and the statistics of a data set
pca :: Double -> Stat -> (Vec -> Vec , Vec -> Vec)
pca prec (m,s,v) = (encode,decode)
where
encode x = vp <> (x - m)
decode x = x <> vp + m
vp = takeRows n v
n = 1 + (length $ fst $ span (< (prec'*sum s)) $ cumSum s)
cumSum = tail . scanl (+) 0.0
prec' = if prec <=0.0 || prec >= 1.0
then error "the precision in pca must be 0<prec<1"
else prec
shdigit :: Vec -> IO ()
shdigit v = imshow (reshape 28 (-v))
-- shows the effect of a given reconstruction quality on a test vector
test :: Stat -> Double -> Vec -> IO ()
test st prec x = do
let (pe,pd) = pca prec st
let y = pe x
print $ dim y
shdigit (pd y)
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
let x = toRows xs !! 4 -- an arbitrary test vector
shdigit x
let st = stat xs
test st 0.90 x
test st 0.50 x
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