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
  22 import qualified Data.Map as M
  23
  24 import Data.Vector (Vector)
  25 import qualified Data.Vector as V
  26
  27 import Gargantext.Prelude
  28 import Gargantext.Viz.Graph.Utils
  29
  30
  31 distributional :: (Floating a, Ord a) => Matrix a -> [((Int, Int), a)]
  32 distributional m = filter (\((x,y), d) -> foldl' (&&) True (conditions x y d) ) distriList
  33   where
  34     conditions x y d  =  [ (x /= y)
  35                          , (d > miniMax')
  36                          , ((M.lookup (x,y) distriMap) > (M.lookup (y,x) distriMap))
  37                          ]
  38     distriList   = toListsWithIndex distriMatrix
  39     distriMatrix = ri (mi m)
  40
  41     distriMap    = M.fromList $ distriList
  42     miniMax'     = miniMax distriMatrix
  43
  44 ri :: (Ord a, Fractional a) => Matrix a -> Matrix a
  45 ri m = matrix c r doRi
  46   where
  47     doRi (x,y)     = doRi' x y m
  48     doRi' x y mi'' = sumMin x y mi'' / (V.sum $ ax Col x y mi'')
  49
  50     sumMin x y mi' = V.sum $ V.map (\(a,b) -> min a b )
  51                            $ V.zip (ax Col x y mi') (ax Row x y mi')
  52     (c,r) = (nOf Col m, nOf Row m)
  53
  54
  55 mi :: (Ord a, Floating a) => Matrix a -> Matrix a
  56 mi m = matrix c r createMat
  57   where
  58     (c,r) = (nOf Col m, nOf Row m)
  59     createMat (x,y) = doMi x y m
  60     doMi x y m' = if x == y then 0 else (max (log (doMi' x y m')) 0 )
  61
  62     doMi' x y m' = (getElem x y m) / ( cross x y m / total m' )
  63
  64     cross x y m' = (V.sum $ ax Col x y m) * (V.sum $ ax Row x y m')
  65
  66
  67
  68 ax :: Axis -> Int -> Int -> Matrix a -> Vector a
  69 ax a  i j m  = dropAt j' $ axis a i' m
  70                   where
  71                     i' = div i c + 1
  72                     j' = mod r j + 1
  73                     (c,r) = (nOf Col m, nOf Row m)
  74
  75 miniMax :: (Ord a) => Matrix a -> a
  76 miniMax m = V.minimum $ V.map (\c -> V.maximum $ getCol c m) (V.enumFromTo 1 (nOf Col m))
  77
  78