feat(pca): implement PCA and visualize data using it

README.md

@@ -87,11 +87,27 @@ the thief robs the man
 the thief robs the woman
 ```
 
-The computed vectors are transformed to two dimensions using SVD:
+The computed vectors are transformed to two dimensions using PCA:
 
 `king` and `queen` have a relation with `man` and `woman`, `love` and `hate` are close to each other,
 and `dwarf` and `thief` have a relation with `poisons` and `robs`, also, `dwarf` is close to `queen` and `king` while
 `thief` is closer to `man` and `woman`. `the` doesn't relate to anything.
 ![word2vec results](https://raw.githubusercontent.com/mdibaiee/sibe/master/w2v.png)
 
-This is a very small dataset and I have to test it on larger datasets.
+_You can reproduce this result using these parameters:_
+```haskell
+let session = def { learningRate = 0.1
+                  , batchSize = 1
+                  , epochs = 10000
+                  , debug = True
+                  } :: Session
+    w2v = def { docs = ds
+              , dimensions = 30
+              , method = SkipGram
+              , window = 2
+              , w2vDrawChart = True
+              , w2vChartName = "w2v.png"
+              } :: Word2Vec
+```
+
+This is a very small development dataset and I have to test it on larger datasets.

examples/word2vec.hs

@@ -32,32 +32,32 @@ module Main where
     sws <- lines <$> readFile "examples/stopwords"
 
     -- real data, takes a lot of time to train
-    ds <- do
-        files <- filter ((/= "xml") . take 1 . reverse) <$> listDirectory "examples/blogs-corpus/"
-        contents <- mapM (rf . ("examples/blogs-corpus/" ++)) files
+    {-ds <- do-}
+        {-files <- filter ((/= "xml") . take 1 . reverse) <$> listDirectory "examples/blogs-corpus/"-}
+        {-contents <- mapM (rf . ("examples/blogs-corpus/" ++)) files-}
 
-        let texts = map (unwords . splitOn "&nbsp;") contents
-        let tags = ["<Blog>", "</Blog>", "<date>", "</date>", "<post>", "</post>", "&nbsp;"]
-        return $ map cleanText $ removeWords (sws ++ tags) texts
+        {-let texts = map (unwords . splitOn "&nbsp;") contents-}
+        {-let tags = ["<Blog>", "</Blog>", "<date>", "</date>", "<post>", "</post>", "&nbsp;"]-}
+        {-return $ map cleanText $ removeWords (sws ++ tags) texts-}
 
-    {-let ds = ["the king loves the queen", "the queen loves the king",-}
-              {-"the dwarf hates the king", "the queen hates the dwarf",-}
-              {-"the dwarf poisons the king", "the dwarf poisons the queen",-}
-              {-"the man loves the woman", "the woman loves the man",-}
-              {-"the thief hates the man", "the woman hates the thief",-}
-              {-"the thief robs the man", "the thief robs the woman"]-}
+    let ds = ["the king loves the queen", "the queen loves the king",
+              "the dwarf hates the king", "the queen hates the dwarf",
+              "the dwarf poisons the king", "the dwarf poisons the queen",
+              "the man loves the woman", "the woman loves the man",
+              "the thief hates the man", "the woman hates the thief",
+              "the thief robs the man", "the thief robs the woman"]
 
-    let session = def { learningRate = 5e-1
+    let session = def { learningRate = 0.1
                       , batchSize = 1
-                      , epochs = 200
+                      , epochs = 10000
                       , debug = True
                       } :: Session
         w2v = def { docs = ds
-                  , dimensions = 300
+                  , dimensions = 30
                   , method = SkipGram
                   , window = 2
                   , w2vDrawChart = True
-                  , w2vChartName = "w2v-big-data.png"
+                  , w2vChartName = "w2v.png"
                   } :: Word2Vec
 
     (computed, vocvec) <- word2vec w2v session

sibe.cabal

@@ -16,7 +16,6 @@ cabal-version:       >=1.10
 library
   hs-source-dirs:      src
   exposed-modules:     Sibe, Sibe.NaiveBayes, Sibe.NLP, Sibe.Word2Vec, Sibe.Utils
-  ghc-options:         -threaded -rtsopts -with-rtsopts=-N
   build-depends:       base >= 4.7 && < 5
                      , hmatrix
                      , random

src/Sibe/Utils.hs

@@ -3,6 +3,7 @@ module Sibe.Utils
   , ordNub
   , onehot
   , average
+  , pca
   ) where
     import qualified Data.Vector.Storable as V
     import qualified Data.Set as Set
@@ -26,3 +27,15 @@ module Sibe.Utils
 
     average :: Vector Double -> Vector Double
     average v = cmap (/ (V.sum v)) v
+
+    pca :: Matrix Double -> Int -> Matrix Double
+    pca m d =
+      let rs = toRows m
+          means = map (\v -> V.sum v / fromIntegral (V.length v)) rs
+          meanReduced = map (\(a, b) -> V.map (+ (negate b)) a) $ zip rs means
+          mat = fromRows meanReduced
+          
+          (u, s, v) = svd mat
+          diagS = diagRect 0 s (rows mat) (cols mat)
+
+      in u ?? (All, Take d) <> diagS ?? (Take d, Take d)

src/Sibe/Word2Vec.hs

@@ -1,3 +1,5 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+
 module Sibe.Word2Vec
   ( word2vec
   , Word2Vec (..)
@@ -9,7 +11,7 @@ module Sibe.Word2Vec
     import Data.Char
     import Data.Maybe
     import Data.List
-    import Numeric.LinearAlgebra hiding (find)
+    import Numeric.LinearAlgebra as H hiding (find)
     import qualified Data.Vector.Storable as V
     import Data.Default.Class
     import Data.Function (on)
@@ -59,13 +61,9 @@ module Sibe.Word2Vec
       let computedVocVec = map (\(w, v) -> (w, runLayer' v hidden)) vocvec
 
       when (w2vDrawChart w2v) $ do
-        let mat = fromColumns . map snd $ computedVocVec
-            (u, s, v) = svd mat
-            cut = subMatrix (0, 0) (2, cols mat)
-            diagS = diagRect 0 (V.take 2 s) (rows mat) (cols mat)
-
-            twoDimensions = cut $ u <> diagS <> tr v
-            textData = zipWith (\s l -> (V.head l, V.last l, s)) (map fst computedVocVec) (toColumns twoDimensions)
+        let m = fromRows . map snd $ computedVocVec
+            twoDimensions = pca m 2
+            textData = zipWith (\s l -> (V.head l, V.last l, s)) (map fst computedVocVec) (toRows twoDimensions)
 
             chart = toRenderable layout
               where