src/Gargantext/Viz/Graph/Distances/Distributional.hs

   1 {-|
   2 Module      : Gargantext.Graph.Distances.Distributional
   3 Description :
   4 Copyright   : (c) CNRS, 2017-Present
   5 License     : AGPL + CECILL v3
   6 Maintainer  : team@gargantext.org
   7 Stability   : experimental
   8 Portability : POSIX
   9
  10 Motivation and definition of the @Distributional@ distance.
  11 -}
  12
  13 {-# LANGUAGE BangPatterns      #-}
  14 {-# LANGUAGE Strict            #-}
  15
  16
  17 module Gargantext.Viz.Graph.Distances.Distributional
  18   where
  19
  20 import Data.Matrix hiding (identity)
  21 import qualified Data.Map as M
  22 import Data.Vector (Vector)
  23 import qualified Data.Vector as V
  24 import Gargantext.Prelude
  25 import Gargantext.Viz.Graph.Utils
  26
  27
  28 distributional' :: (Floating a, Ord a) => Matrix a -> [((Int, Int), a)]
  29 distributional' m = filter (\((x,y), d) -> foldl' (&&) True (conditions x y d) ) distriList
  30   where
  31     conditions x y d  =  [ (x /= y)
  32                          , (d > miniMax')
  33                          , ((M.lookup (x,y) distriMap) > (M.lookup (y,x) distriMap))
  34                          ]
  35     distriList   = toListsWithIndex distriMatrix
  36     distriMatrix = ri (mi m)
  37
  38     distriMap    = M.fromList $ distriList
  39     miniMax'     = miniMax distriMatrix
  40
  41 ri :: (Ord a, Fractional a) => Matrix a -> Matrix a
  42 ri m = matrix c r doRi
  43   where
  44     doRi (x,y)     = doRi' x y m
  45     doRi' x y mi'' = sumMin x y mi'' / (V.sum $ ax Col x y mi'')
  46
  47     sumMin x y mi' = V.sum $ V.map (\(a,b) -> min a b )
  48                            $ V.zip (ax Col x y mi') (ax Row x y mi')
  49     (c,r) = (nOf Col m, nOf Row m)
  50
  51 mi :: (Ord a, Floating a) => Matrix a -> Matrix a
  52 mi m = matrix c r createMat
  53   where
  54     (c,r) = (nOf Col m, nOf Row m)
  55     createMat (x,y) = doMi x y m
  56     doMi x y m' = if x == y then 0 else (max (log (doMi' x y m')) 0 )
  57
  58     doMi' x y m' = (getElem x y m) / ( cross x y m / total m' )
  59
  60     cross x y m' = (V.sum $ ax Col x y m) * (V.sum $ ax Row x y m')
  61
  62
  63
  64 ax :: Axis -> Int -> Int -> Matrix a -> Vector a
  65 ax a  i j m  = dropAt j' $ axis a i' m
  66                   where
  67                     i' = div i c + 1
  68                     j' = mod r j + 1
  69                     (c,r) = (nOf Col m, nOf Row m)
  70
  71 miniMax :: (Ord a) => Matrix a -> a
  72 miniMax m = V.minimum $ V.map (\c -> V.maximum $ getCol c m) (V.enumFromTo 1 (nOf Col m))
  73
  74