diff --git a/Data/DecisionTree.hs b/Data/DecisionTree.hs new file mode 100644 --- /dev/null +++ b/Data/DecisionTree.hs @@ -0,0 +1,134 @@ +-- | This module provides a very simple implementation of a decisiontree. It is \"optimized\" for readability, not so much for performance. I doubt it can be used for real (=huge) datasets, but it should be ok for a couple of hundred (thousand?) items. +-- +-- You are encouraged to have a look at the source +-- +-- It is build (for now) using the ID3 algorithm (or at least something closely resembling that). That means the attributes you choose must have a finite set of possible values. +module Data.DecisionTree ( + build, + decide, + Datum(D, dName, attributes), + PreLabeled, + Attribute(A, aName, possibleValues), + DecisionTree) where + +import Data.Maybe (fromJust) +import Data.List hiding (partition) +import Data.Map (Map) +import qualified Data.Map as Map +import Data.Function (on) + +type PreLabeled a b= (b, Datum a) + +-- | The type for our DecisionTree +data DecisionTree a b= Leaf b -- ^ Leafs have labels + | Node { + att ::Attribute a, -- ^ a node asks for this attribute + child :: a -> (DecisionTree a b) -- ^ and has children which can be found with a value of the attribute + } + +-- | A Datum has Attributes +data Attribute a = A { + aName :: String, -- ^ Attributes have a name + possibleValues :: [a] -- ^ and a set of possible values + } + +-- | Things we want to find labels for +data Datum a= D { + dName :: String, -- ^ They have names + attributes :: [(Attribute a,a)] -- ^ and attributes + } deriving Show + +instance (Show a, Show b) => Show (DecisionTree a b) where + show x = showTree x "" + +showTree :: (Show a, Show b) => DecisionTree a b -> ShowS +showTree (Leaf x) = shows x +showTree (Node att child) = ('<':).shows att.("|\n"++).showList [child a | a <- possibleValues att].('>':) + +instance Eq (Attribute a) where + (==) = (==) `on` aName + +instance Show (Attribute a) where + show = aName + +-- | Build a DecisionTree from the given Trainingset +build :: (Ord a, Ord b) => [Attribute a] -> [PreLabeled a b] -> DecisionTree a b +build atts dataset = case inf of + 0 -> Leaf dominantLabel -- even the best Attribute doesn't gain any information. We're done + _ -> Node { + att = bAtt, + child = safeLookup + } + where + (inf,bAtt) = bestAttribute dataset atts -- get the best attribute + p = partition dataset bAtt -- use it to partition the set + children = Map.map (build atts) p -- recursivly build the children + dominantLabel = fst $ Map.findMax $ groupLabels (map label dataset) -- in case we are done, get the label + safeLookup a= fromJust $ Map.lookup a children + + +-- | Which value does this Datum have for the given Attribute? +getValue :: Datum a-> Attribute a -> a +getValue d att = fromJust $ lookup att (attributes d) + +-- | Extract a label +label :: PreLabeled a b -> b +label = fst + +-- | Decide which label belongs to this Datum +decide :: Eq a => DecisionTree a b -> Datum a -> b +decide (Leaf b) _ = b -- we reached a Leaf, done +decide (Node att child) d = decide (child v) d where -- we're in a node, walk down + v = getValue d att + +-- | Partitions the Dataset according to the possible values of the attribute +partition :: (Ord a) =>[PreLabeled a b] -> Attribute a -> Map a [PreLabeled a b] +partition set att= foldl (\m k -> Map.insertWith (++) k [] m) grouped (possibleValues att) where + grouped = groupWith (flip getValue att.snd) (:[]) (++) set + +-- | Computes the entropy of a Dataset +-- +-- the Entropy is defined as: sum (p_i * log_2 p_i) +-- where p_i = |{ x | x has Label i}|/|Dataset| +entropy :: (Ord b) => [b] -> Double +entropy set= (-1)*( Map.fold help 0 $ groupLabels set ) + where + n = fromIntegral $ length set + help s acc | s/=0 = let p = fromIntegral s / n in acc+p*log p/log 2 + help _ _ = error "entropy: we are not supposed to get p=0" + +-- we want to count how many Data we have for each label. Thus we group it with 1 as +-- singleton value and add 1 whenever we find another Datum with the same label +groupLabels :: Ord b => [b] -> Map b Int +groupLabels = groupWith id (const (1::Int)) (const succ) + +-- | How much information does this Attribute give us for the given Dataset +-- it is defined as +-- +-- entropy(set) - sum p_i * entropy {dat_i | dat has value i for attribute a} +information :: (Ord b, Ord a) => [PreLabeled a b] -- ^ the data + -> Attribute a -- ^ the Attribute + -> Double -- ^ the Information +information dat att= entropy (map label dat) - sum (zipWith (*) pi (map entropy ps)) where + ps = map (map label) $ Map.elems $ partition dat att -- the partitions, we're only interested in the labels + pi = map ((/ n).fromIntegral.length) ps -- the size of the partition/size dataset + n = fromIntegral $ length dat + +-- | Return the attribute which gives us greatest gain in information +bestAttribute :: (Ord b, Ord a) => [PreLabeled a b] -> [Attribute a] -> (Double,Attribute a) +bestAttribute dat = head.sortBy (compare `on` negatedInf).computeInformation where + negatedInf (inf,_) = -inf + computeInformation = map (\x -> (information dat x,x)) + +-- | groups a Dataset using a Map. According to #haskell \"efficient\" grouping needs Ord. I agree with that +groupWith :: Ord k => (a -> k) -- ^ how to extract a key from a Datum + -> (a -> v) -- ^ how to make a Datum into a value for the map + -> (v -> v -> v) -- ^ how to fuse two values (should we have > 1 Data for this key) + -> [a] -- ^ the list we want to group + -> Map k v +groupWith getKey singleton fuse = + foldl (\m x -> Map.insertWith fuse (getKey x) (singleton x) m) Map.empty + + + + diff --git a/DecisionTree.cabal b/DecisionTree.cabal new file mode 100644 --- /dev/null +++ b/DecisionTree.cabal @@ -0,0 +1,21 @@ +Name: DecisionTree +Version: 0.0 +Cabal-Version: >= 1.2 +Synopsis: A very simple implementation of decision trees for discrete attributes. +Description: A very simple implementation of decision trees, built with ID3. You can use it to classify data with a set of discrete attributes. +License: LGPL +License-file: LICENSE +Author: Adrian Neumann +Homepage: http://page.mi.fu-berlin.de/~aneumann/decisiontree.html +Category: Algorithms, Pattern Classification +Maintainer: aneumann@inf.fu-berlin.de +stability: alpha +build-type: Simple +extra-source-files: README, test.hs, lgpl-3.0.txt + +Library + exposed-modules: Data.DecisionTree + build-depends: + base, + containers >=0.2.0.0 + GHC-Options: -O2 diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,3 @@ +Copyright 2009 Adrian Neumann + +You may use this library under the terms of the LGPL, which is included in the file lgpl-3.0.txt diff --git a/README b/README new file mode 100644 --- /dev/null +++ b/README @@ -0,0 +1,4 @@ +This is the DecisionTree library. +Build it as you would build any cabal package. Have a look at the Haskellwiki (haskell.org) if you don't know how. + +Feel free to send me patches, comments, suggestions. diff --git a/Setup.lhs b/Setup.lhs new file mode 100644 --- /dev/null +++ b/Setup.lhs @@ -0,0 +1,4 @@ +#! /usr/bin/env runhaskell + +> import Distribution.Simple +> main = defaultMain diff --git a/dist/doc/html/DecisionTree/Data-DecisionTree.html b/dist/doc/html/DecisionTree/Data-DecisionTree.html new file mode 100644 Binary files /dev/null and b/dist/doc/html/DecisionTree/Data-DecisionTree.html differ diff --git a/dist/doc/html/DecisionTree/DecisionTree.haddock b/dist/doc/html/DecisionTree/DecisionTree.haddock new file mode 100644 Binary files /dev/null and b/dist/doc/html/DecisionTree/DecisionTree.haddock differ diff --git a/dist/doc/html/DecisionTree/doc-index.html b/dist/doc/html/DecisionTree/doc-index.html new file mode 100644 --- /dev/null +++ b/dist/doc/html/DecisionTree/doc-index.html @@ -0,0 +1,150 @@ + + +DecisionTree-0.0: A very simple implementation of decision trees for discrete attributes. (internal documentation) (Index)
DecisionTree-0.0: A very simple implementation of decision trees for discrete attributes. (internal documentation)ContentsIndex
Search:
AData.DecisionTree
aNameData.DecisionTree
AttributeData.DecisionTree
attributesData.DecisionTree
buildData.DecisionTree
DData.DecisionTree
DatumData.DecisionTree
decideData.DecisionTree
DecisionTreeData.DecisionTree
dNameData.DecisionTree
possibleValuesData.DecisionTree
PreLabeledData.DecisionTree
diff --git a/dist/doc/html/DecisionTree/haddock-util.js b/dist/doc/html/DecisionTree/haddock-util.js new file mode 100644 --- /dev/null +++ b/dist/doc/html/DecisionTree/haddock-util.js @@ -0,0 +1,133 @@ +// Haddock JavaScript utilities +function toggle(button,id) +{ + var n = document.getElementById(id).style; + if (n.display == "none") + { + button.src = "minus.gif"; + n.display = "block"; + } + else + { + button.src = "plus.gif"; + n.display = "none"; + } +} + + +var max_results = 75; // 50 is not enough to search for map in the base libraries +var shown_range = null; +var last_search = null; + +function quick_search() +{ + perform_search(false); +} + +function full_search() +{ + perform_search(true); +} + + +function perform_search(full) +{ + var text = document.getElementById("searchbox").value.toLowerCase(); + if (text == last_search && !full) return; + last_search = text; + + var table = document.getElementById("indexlist"); + var status = document.getElementById("searchmsg"); + var children = table.firstChild.childNodes; + + // first figure out the first node with the prefix + var first = bisect(-1); + var last = (first == -1 ? -1 : bisect(1)); + + if (first == -1) + { + table.className = ""; + status.innerHTML = "No results found, displaying all"; + } + else if (first == 0 && last == children.length - 1) + { + table.className = ""; + status.innerHTML = ""; + } + else if (last - first >= max_results && !full) + { + table.className = ""; + status.innerHTML = "More than " + max_results + ", press Search to display"; + } + else + { + // decide what you need to clear/show + if (shown_range) + setclass(shown_range[0], shown_range[1], "indexrow"); + setclass(first, last, "indexshow"); + shown_range = [first, last]; + table.className = "indexsearch"; + status.innerHTML = ""; + } + + + function setclass(first, last, status) + { + for (var i = first; i <= last; i++) + { + children[i].className = status; + } + } + + + // do a binary search, treating 0 as ... + // return either -1 (no 0's found) or location of most far match + function bisect(dir) + { + var first = 0, finish = children.length - 1; + var mid, success = false; + + while (finish - first > 3) + { + mid = Math.floor((finish + first) / 2); + + var i = checkitem(mid); + if (i == 0) i = dir; + if (i == -1) + finish = mid; + else + first = mid; + } + var a = (dir == 1 ? first : finish); + var b = (dir == 1 ? finish : first); + for (var i = b; i != a - dir; i -= dir) + { + if (checkitem(i) == 0) return i; + } + return -1; + } + + + // from an index, decide what the result is + // 0 = match, -1 is lower, 1 is higher + function checkitem(i) + { + var s = getitem(i).toLowerCase().substr(0, text.length); + if (s == text) return 0; + else return (s > text ? -1 : 1); + } + + + // from an index, get its string + // this abstracts over alternates + function getitem(i) + { + for ( ; i >= 0; i--) + { + var s = children[i].firstChild.firstChild.data; + if (s.indexOf(' ') == -1) + return s; + } + return ""; // should never be reached + } +} diff --git a/dist/doc/html/DecisionTree/haddock.css b/dist/doc/html/DecisionTree/haddock.css new file mode 100644 --- /dev/null +++ b/dist/doc/html/DecisionTree/haddock.css @@ -0,0 +1,267 @@ +/* -------- Global things --------- */ + +BODY { + background-color: #ffffff; + color: #000000; + font-family: sans-serif; + } + +A:link { color: #0000e0; text-decoration: none } +A:visited { color: #0000a0; text-decoration: none } +A:hover { background-color: #e0e0ff; text-decoration: none } + +TABLE.vanilla { + width: 100%; + border-width: 0px; + /* I can't seem to specify cellspacing or cellpadding properly using CSS... */ +} + +TABLE.vanilla2 { + border-width: 0px; +} + +/* font is a little too small in MSIE */ +TT { font-size: 100%; } +PRE { font-size: 100%; } + +LI P { margin: 0pt } + +TD { + border-width: 0px; +} + +TABLE.narrow { + border-width: 0px; +} + +TD.s8 { height: 8px; } +TD.s15 { height: 15px; } + +SPAN.keyword { text-decoration: underline; } + +/* Resize the buttom image to match the text size */ +IMG.coll { width : 0.75em; height: 0.75em; margin-bottom: 0; margin-right: 0.5em } + +/* --------- Contents page ---------- */ + +DIV.node { + padding-left: 3em; +} + +DIV.cnode { + padding-left: 1.75em; +} + +SPAN.pkg { + position: absolute; + left: 50em; +} + +/* --------- Documentation elements ---------- */ + +TD.children { + padding-left: 25px; + } + +TD.synopsis { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace + } + +TD.decl { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace; + vertical-align: top; + } + +TD.topdecl { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace; + vertical-align: top; +} + +TABLE.declbar { + border-spacing: 0px; + } + +TD.declname { + width: 100%; + } + +TD.declbut { + padding-left: 5px; + padding-right: 5px; + border-left-width: 1px; + border-left-color: #000099; + border-left-style: solid; + white-space: nowrap; + font-size: small; + } + +/* + arg is just like decl, except that wrapping is not allowed. It is + used for function and constructor arguments which have a text box + to the right, where if wrapping is allowed the text box squashes up + the declaration by wrapping it. +*/ +TD.arg { + padding: 2px; + background-color: #f0f0f0; + font-family: monospace; + vertical-align: top; + white-space: nowrap; + } + +TD.recfield { padding-left: 20px } + +TD.doc { + padding-top: 2px; + padding-left: 10px; + } + +TD.ndoc { + padding: 2px; + } + +TD.rdoc { + padding: 2px; + padding-left: 10px; + width: 100%; + } + +TD.body { + padding-left: 10px + } + +TD.pkg { + width: 100%; + padding-left: 10px +} + +TABLE.indexsearch TR.indexrow { + display: none; +} +TABLE.indexsearch TR.indexshow { + display: table-row; +} + +TD.indexentry { + vertical-align: top; + padding-right: 10px + } + +TD.indexannot { + vertical-align: top; + padding-left: 20px; + white-space: nowrap + } + +TD.indexlinks { + width: 100% + } + +/* ------- Section Headings ------- */ + +TD.section1 { + padding-top: 15px; + font-weight: bold; + font-size: 150% + } + +TD.section2 { + padding-top: 10px; + font-weight: bold; + font-size: 130% + } + +TD.section3 { + padding-top: 5px; + font-weight: bold; + font-size: 110% + } + +TD.section4 { + font-weight: bold; + font-size: 100% + } + +/* -------------- The title bar at the top of the page */ + +TD.infohead { + color: #ffffff; + font-weight: bold; + padding-right: 10px; + text-align: left; +} + +TD.infoval { + color: #ffffff; + padding-right: 10px; + text-align: left; +} + +TD.topbar { + background-color: #000099; + padding: 5px; +} + +TD.title { + color: #ffffff; + padding-left: 10px; + width: 100% + } + +TD.topbut { + padding-left: 5px; + padding-right: 5px; + border-left-width: 1px; + border-left-color: #ffffff; + border-left-style: solid; + white-space: nowrap; + } + +TD.topbut A:link { + color: #ffffff + } + +TD.topbut A:visited { + color: #ffff00 + } + +TD.topbut A:hover { + background-color: #6060ff; + } + +TD.topbut:hover { + background-color: #6060ff + } + +TD.modulebar { + background-color: #0077dd; + padding: 5px; + border-top-width: 1px; + border-top-color: #ffffff; + border-top-style: solid; + } + +/* --------- The page footer --------- */ + +TD.botbar { + background-color: #000099; + color: #ffffff; + padding: 5px + } +TD.botbar A:link { + color: #ffffff; + text-decoration: underline + } +TD.botbar A:visited { + color: #ffff00 + } +TD.botbar A:hover { + background-color: #6060ff + } + diff --git a/dist/doc/html/DecisionTree/haskell_icon.gif b/dist/doc/html/DecisionTree/haskell_icon.gif new file mode 100644 Binary files /dev/null and b/dist/doc/html/DecisionTree/haskell_icon.gif differ diff --git a/dist/doc/html/DecisionTree/index.html b/dist/doc/html/DecisionTree/index.html new file mode 100644 --- /dev/null +++ b/dist/doc/html/DecisionTree/index.html @@ -0,0 +1,92 @@ + + +DecisionTree-0.0: A very simple implementation of decision trees for discrete attributes. (internal documentation)
DecisionTree-0.0: A very simple implementation of decision trees for discrete attributes. (internal documentation)ContentsIndex
DecisionTree-0.0: A very simple implementation of decision trees for discrete attributes. (internal documentation)
A very simple implementation of decision trees, built with ID3. You can use it to classify data with a set of discrete attributes. +
Modules
show/hideData
Data.DecisionTree
Produced by Haddock version 2.3.0
diff --git a/dist/doc/html/DecisionTree/minus.gif b/dist/doc/html/DecisionTree/minus.gif new file mode 100644 Binary files /dev/null and b/dist/doc/html/DecisionTree/minus.gif differ diff --git a/dist/doc/html/DecisionTree/plus.gif b/dist/doc/html/DecisionTree/plus.gif new file mode 100644 Binary files /dev/null and b/dist/doc/html/DecisionTree/plus.gif differ diff --git a/lgpl-3.0.txt b/lgpl-3.0.txt new file mode 100644 --- /dev/null +++ b/lgpl-3.0.txt @@ -0,0 +1,165 @@ + GNU LESSER GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + + This version of the GNU Lesser General Public License incorporates +the terms and conditions of version 3 of the GNU General Public +License, supplemented by the additional permissions listed below. + + 0. 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