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 NoImplicitPrelude #-}
  15 {-# LANGUAGE FlexibleContexts  #-}
  16 {-# LANGUAGE Strict            #-}
  17
  18
  19 module Gargantext.Viz.Graph.Distances.Distributional
  20   where
  21
  22 import Data.Matrix hiding (identity)
  23
  24 import qualified Data.Map as M
  25
  26 import Data.Vector (Vector)
  27 import qualified Data.Vector as V
  28
  29 import Gargantext.Prelude
  30 import Gargantext.Viz.Graph.Utils
  31
  32
  33 distributional :: (Floating a, Ord a) => Matrix a -> [((Int, Int), a)]
  34 distributional m = filter (\((x,y), d) -> foldl' (&&) True (conditions x y d) ) distriList
  35   where
  36     conditions x y d  =  [ (x /= y)
  37                          , (d > miniMax')
  38                          , ((M.lookup (x,y) distriMap) > (M.lookup (y,x) distriMap))
  39                          ]
  40     distriList   = toListsWithIndex distriMatrix
  41     distriMatrix = ri (mi m)
  42
  43     distriMap    = M.fromList $ distriList
  44     miniMax'     = miniMax distriMatrix
  45
  46 ri :: (Ord a, Fractional a) => Matrix a -> Matrix a
  47 ri m = matrix c r doRi
  48   where
  49     doRi (x,y)     = doRi' x y m
  50     doRi' x y mi'' = sumMin x y mi'' / (V.sum $ ax Col x y mi'')
  51
  52     sumMin x y mi' = V.sum $ V.map (\(a,b) -> min a b )
  53                            $ V.zip (ax Col x y mi') (ax Row x y mi')
  54     (c,r) = (nOf Col m, nOf Row m)
  55
  56
  57 mi :: (Ord a, Floating a) => Matrix a -> Matrix a
  58 mi m = matrix c r createMat
  59   where
  60     (c,r) = (nOf Col m, nOf Row m)
  61     createMat (x,y) = doMi x y m
  62     doMi x y m' = if x == y then 0 else (max (log (doMi' x y m')) 0 )
  63
  64     doMi' x y m' = (getElem x y m) / ( cross x y m / total m' )
  65
  66     cross x y m' = (V.sum $ ax Col x y m) * (V.sum $ ax Row x y m')
  67
  68
  69
  70 ax :: Axis -> Int -> Int -> Matrix a -> Vector a
  71 ax a  i j m  = dropAt j' $ axis a i' m
  72                   where
  73                     i' = div i c + 1
  74                     j' = mod r j + 1
  75                     (c,r) = (nOf Col m, nOf Row m)
  76
  77 miniMax :: (Ord a) => Matrix a -> a
  78 miniMax m = V.minimum $ V.map (\c -> V.maximum $ getCol c m) (V.enumFromTo 1 (nOf Col m))
  79
  80