CSE454
2003
:
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http://www.csse.monash.edu.au/~lloyd/tilde/CSC4/CSE454/
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estMixture ests dataSet = let -- [estimator]->[dataSpace] -> model of dataSpace -- i.e. [estimator] -> estimator
Takes a list of estimators, one per component of the mixture.
memberships (Mix mixer components) = let -- memberships|Mixture doAll (d:ds) = prepend (doOne d) (doAll ds) -- all data doAll [] = map (\x -> []) components doOne datum = normalise( -- one datum map (\(c, m) -> (pr mixer c)*(pr m datum)) (zip [0..] components)) -- pr(c) * pr(datum|c) for class #c = m in doAll dataSet
Given components, find (fit) the fractional memberships of things (data) to the components.
randomMemberships = let doAll seed [] = map (\_ -> []) ests doAll seed (_:ds) = -- all data let doOne seed [] ans = (seed, normalise ans) doOne seed (_:ests) ans = -- one datum doOne (prng seed) ests ((fromIntegral(1+ seed `mod` 10)) : ans) in let (seed2, forDatum) = doOne seed ests [] in prepend forDatum (doAll seed2 ds) in doAll 4321 dataSet
Allocate initial pseudo-random (prng) fractional memberships to things (data), not very interesting.
fit [] [] = [] -- Models|memberships fit (est:ests) (mem:mems) = (est dataSet mem) : (fit ests mems) fitMixture mems = Mix (freqs2model (map (foldl (+) 0) mems)) -- weights (fit ests mems) -- components
Calculate mixture-weights of the components, and fit components (use the given estimators) to their weighted members.
cycle mx = fitMixture (memberships mx) -- EM step cycles 0 mx = mx cycles n mx = cycles (n-1) (cycle mx) -- n x cycle in mixture( cycles ?? (fitMixture randomMemberships) ) -- --------------9/2002--L.Allison--CSSE--Monash--.au--
Fit memberships to components; fit components to the memberships. Iterate some number of times, or until convergence, or... etc..