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Apriori.hs

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+module Apriori where
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.List as List
+import Debug.Trace (traceShow)
+
+data Item = Item String deriving (Eq, Ord)
+instance Show Item where
+	show (Item s) = s --"Item " ++ s
+
+data ItemSet = ItemSet (Set Item) deriving (Eq, Ord)
+instance Show ItemSet where
+	show (ItemSet x) = foldr ((\y old -> y ++ " " ++ old).show) "" (Set.toList x)
+
+data Rule = Rule ItemSet ItemSet deriving (Eq)
+instance Show Rule where
+	show (Rule a b) = show a ++ "-> " ++ show b
+
+type Frequency = Double
+
+type Count = Int
+
+frequency :: [ItemSet] -> ItemSet -> Frequency
+frequency table (ItemSet set) = setCount / fromIntegral (length table) where
+	setCount = fromIntegral $ count table (ItemSet set)
+
+
+semiUnion :: ItemSet -> ItemSet -> ItemSet
+semiUnion (ItemSet set1) (ItemSet set2) = ItemSet (if max1 <= max2 && Set.delete max1 set1 == Set.delete max2 set2 then set1 `Set.union` set2 else Set.empty) where
+	max1 = Set.findMax set1
+	max2 = Set.findMax set2
+
+-- generate all possible combinations from a set of singletons
+generateLevels :: [Item] -> [[ItemSet]]
+generateLevels singles = until (\x -> head x == lastLevel) (\x -> generateNextLevel (head x) : x) [firstLevel] where
+	firstLevel = map (\x -> ItemSet $ Set.fromList [x]) singles
+	lastLevel = [ItemSet $ Set.fromList singles]
+
+-- generate the next level in a bottom-up route
+generateNextLevel :: [ItemSet] -> [ItemSet]
+generateNextLevel level = traceShow ("Computing level " ++ show (isSize (head level))) $ foldr (\value old -> generate value ++ old) [] level where
+	generate value = takeWhile (/= empty) (foldr (\x old -> semiUnion value x : old) [] (tail $ List.dropWhile (/= value) level))
+	empty = ItemSet $ Set.fromList []
+	isSize (ItemSet set) = Set.size set
+
+count :: [ItemSet] -> ItemSet -> Count
+count table (ItemSet set) = length (filter (\(ItemSet row) -> set `Set.isSubsetOf` row) table)
+
+singletons :: [ItemSet] -> [Item]
+singletons table = Set.toList $ foldr (\(ItemSet row) old -> old `Set.union` row) (Set.fromList []) table where
+
+frequentPatterns :: Frequency -> [ItemSet] -> [[ItemSet]]
+frequentPatterns thresh table = until (\x -> [] == head x) (\x -> filterByFrequency (generateNextLevel (head x)) : x) [firstLevel] where
+	firstLevel = map (\x -> ItemSet $ Set.fromList [x]) (singletons table)
+	filterByFrequency = filter (\x -> frequency table x >= thresh)