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