src/Gargantext/Core/Methods/Similarities/Accelerate/SpeGen.hs

   1 {-|
   2 Module      : Gargantext.Core.Methods.Similarities.Accelerate.SpeGen
   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 This module aims at implementig distances of terms context by context is
  11 the same referential of corpus.
  12
  13 Implementation use Accelerate library which enables GPU and CPU computation
  14 See Gargantext.Core.Methods.Graph.Accelerate)
  15
  16 -}
  17
  18 {-# LANGUAGE TypeFamilies        #-}
  19 {-# LANGUAGE TypeOperators       #-}
  20 {-# LANGUAGE ScopedTypeVariables #-}
  21 {-# LANGUAGE ViewPatterns        #-}
  22
  23 module Gargantext.Core.Methods.Similarities.Accelerate.SpeGen
  24   where
  25
  26 -- import qualified Data.Foldable as P (foldl1)
  27 -- import Debug.Trace (trace)
  28 import Data.Array.Accelerate
  29 import Data.Array.Accelerate.Interpreter (run)
  30 import Gargantext.Core.Methods.Matrix.Accelerate.Utils
  31 import qualified Gargantext.Prelude as P
  32
  33
  34 -----------------------------------------------------------------------
  35 -----------------------------------------------------------------------
  36 -- * Specificity and Genericity
  37
  38 {- | Metric Specificity and genericity: select terms
  39
  40 - let N termes and occurrences of i \[N{i}\]
  41
  42 - Cooccurrences of i and j \[N{ij}\]
  43 - Probability to get i given j : \[P(i|j)=N{ij}/N{j}\]
  44
  45 - Genericity of i  \[Gen(i)  = \frac{\sum_{j \neq i,j} P(i|j)}{N-1}\]
  46 - Specificity of j \[Spec(i) = \frac{\sum_{j \neq i,j} P(j|i)}{N-1}\]
  47
  48 - \[Inclusion (i) = Gen(i) + Spec(i)\)
  49 - \[GenericityScore = Gen(i)- Spec(i)\]
  50
  51 - References: Science mapping with asymmetrical paradigmatic proximity
  52 Jean-Philippe Cointet (CREA, TSV), David Chavalarias (CREA) (Submitted
  53 on 15 Mar 2008), Networks and Heterogeneous Media 3, 2 (2008) 267 - 276,
  54 arXiv:0803.2315 [cs.OH]
  55 -}
  56 type GenericityInclusion  = Double
  57 type SpecificityExclusion = Double
  58
  59 data SquareMatrix      = SymetricMatrix | NonSymetricMatrix
  60 type SymetricMatrix    = Matrix
  61 type NonSymetricMatrix = Matrix
  62
  63
  64 incExcSpeGen :: Matrix Int
  65              -> ( Vector GenericityInclusion
  66                 , Vector SpecificityExclusion
  67                 )
  68 incExcSpeGen m = (run' inclusionExclusion m, run' specificityGenericity m)
  69   where
  70     run' fun mat = run $ fun $ map fromIntegral $ use mat
  71
  72     -- | Inclusion (i) = Gen(i)+Spec(i)
  73     inclusionExclusion :: Acc (Matrix Double) -> Acc (Vector Double)
  74     inclusionExclusion mat = zipWith (+) (pV mat) (pV mat)
  75
  76     -- | Genericity score = Gen(i)- Spec(i)
  77     specificityGenericity :: Acc (Matrix Double) -> Acc (Vector Double)
  78     specificityGenericity mat = zipWith (+) (pH mat) (pH mat)
  79
  80     -- | Gen(i)  : 1/(N-1)*Sum(j!=i, P(i|j)) : Genericity  of i
  81     pV :: Acc (Matrix Double) -> Acc (Vector Double)
  82     pV mat = map (\x -> (x-1)/(cardN-1)) $ sum $ p_ij mat
  83
  84     -- | Spec(i) : 1/(N-1)*Sum(j!=i, P(j|i)) : Specificity of j
  85     pH :: Acc (Matrix Double) -> Acc (Vector Double)
  86     pH mat = map (\x -> (x-1)/(cardN-1)) $ sum $ p_ji mat
  87
  88     cardN :: Exp Double
  89     cardN = constant (P.fromIntegral (dim m) :: Double)
  90
  91
  92 -- | P(i|j) = Nij /N(jj) Probability to get i given j
  93 --p_ij :: (Elt e, P.Fractional (Exp e)) => Acc (SymetricMatrix e) -> Acc (Matrix e)
  94 p_ij :: (Elt e, P.Fractional (Exp e)) => Acc (Matrix e) -> Acc (Matrix e)
  95 p_ij m = zipWith (/) m (n_jj m)
  96   where
  97     n_jj :: Elt e => Acc (SymetricMatrix e) -> Acc (Matrix e)
  98     n_jj myMat' = backpermute (shape m)
  99                          (lift1 ( \(Z :. (_ :: Exp Int) :. (j:: Exp Int))
 100                                    -> (Z :. j :. j)
 101                                 )
 102                          ) myMat'
 103
 104 -- | P(j|i) = Nij /N(ii) Probability to get i given j
 105 -- to test
 106 p_ji :: (Elt e, P.Fractional (Exp e))
 107      => Acc (Array DIM2 e)
 108      -> Acc (Array DIM2 e)
 109 p_ji = transpose . p_ij
 110
 111
 112 -- | Step to ckeck the result in visual/qualitative tests
 113 incExcSpeGen_proba :: Matrix Int -> Matrix Double
 114 incExcSpeGen_proba m = run' pro m
 115   where
 116     run' fun mat = run $ fun $ map fromIntegral $ use mat
 117
 118     pro mat = p_ji mat
 119
 120 {-
 121 -- | Hypothesis to test maybe later (or not)
 122 -- TODO ask accelerate for instances to ease such writtings:
 123 p_ :: (Elt e, P.Fractional (Exp e)) => Acc (Array DIM2 e) -> Acc (Array DIM2 e)
 124 p_ m = zipWith (/) m (n_ m)
 125   where
 126     n_ :: Elt e => Acc (SymetricMatrix e) -> Acc (Matrix e)
 127     n_ m = backpermute (shape m)
 128                          (lift1 ( \(Z :. (i :: Exp Int) :. (j:: Exp Int))
 129                                    -> (ifThenElse (i < j) (lift (Z :. j :. j)) (lift (Z :. i :. i)) :: Exp DIM2)
 130                                 )
 131                          ) m
 132 -}
 133