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October 23, 2019 17:17
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Iterative Dichotemizer example in Prolog
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id3 :- ['id3.pl']. | |
:- ['id3.data']. | |
:- ['oklog.pl']. | |
test1(Tree) :- | |
data1(D), attrlist(L), id3(L, D, Tree). | |
test2(Tree) :- | |
data2(D), attrlist(L), id3(L, D, Tree). | |
id3( _, Data, Tree ) :- | |
all_same_category( Data, Categ ), !, | |
Tree = leaf( Categ). | |
id3( AttrList, Data, Tree ) :- | |
select_and_split( AttrList, Data, BestAttr, BestDataPartition ), | |
% nl,write('splitting attribute: '), write(BestAttr),nl, | |
generate_children_trees( AttrList, BestDataPartition, ChildrenTrees ), | |
Tree = tree( internal( BestAttr ), ChildrenTrees ). | |
all_same_category( [ ], _ ). | |
all_same_category( [ (Categ,_) | MoreData ], Categ ) :- | |
all_same_category( MoreData, Categ ). | |
select_and_split( AttrList, Data, BestAttr, BestPartition ) :- | |
findall( ( Attr, Partition, Entropy), | |
( member( ( Attr, PosAttrValues ), AttrList ), | |
partition( Data, Attr, PosAttrValues, Partition, Entropy ) ), | |
AllPartitions ), | |
select_minimal_entropy( AllPartitions, BestAttr, BestPartition ). | |
partition( _, _, [ ] , [ ], 0 ). | |
partition( Data, Attr, | |
[ OnePosAttrValue | RestValues ] , Partition, Entropy ) :- | |
select_by_attr_value( Data, Attr, OnePosAttrValue, SubData ), | |
( SubData = [ ] | |
-> partition( Data, Attr, RestValues , Partition, Entropy ) | |
; | |
compute_set_entropy( SubData, SubEntropy ), | |
partition( Data, Attr, RestValues , RestPartition, RestEntropy ), | |
Partition = [ OnePosAttrValue-SubData | RestPartition ], | |
Entropy is SubEntropy + RestEntropy ). | |
select_by_attr_value( [ ], _, _, [ ] ). | |
select_by_attr_value( [ (V,Datum) | MoreData ], Attr, AttrValue, SubData ) :- | |
member( (Attr,AttrValue), Datum ) | |
-> select_by_attr_value( MoreData, Attr, AttrValue, MoreSubData ), | |
SubData = [ (V,Datum) | MoreSubData ] | |
; select_by_attr_value( MoreData, Attr, AttrValue, SubData ). | |
/* Older implementation of the second clause for 'partition': | |
partition( Data, Attr, | |
[ OnePosAttrValue | RestValues ] , Partition, Entropy ) :- | |
bagof( (Categ,Datum), | |
( member( (Categ,Datum), Data ), | |
member( (Attr, OnePosAttrValue), Datum ) ), | |
SubData ) | |
-> | |
compute_set_entropy( SubData, SubEntropy ), | |
partition( Data, Attr, RestValues , RestPartition, RestEntropy ), | |
Partition = [ OnePosAttrValue-SubData | RestPartition ], | |
Entropy is SubEntropy + RestEntropy | |
; | |
partition( Data, Attr, RestValues , Partition, Entropy ). | |
*/ | |
compute_set_entropy( Data, Entropy ) :- | |
count_positive( Data, Pnum ), | |
length( Data, Dnum ), | |
Pp is Pnum / Dnum, | |
Pn is 1 - Pp, | |
xlogx( Pp, PpLogPp ), | |
xlogx( Pn, PnLogPn ), | |
Entropy is - ( PpLogPp + PnLogPn ). | |
count_positive( [ ], 0 ). | |
count_positive( [ (p,_) | More ], Pnum ) :- !, | |
count_positive( More, Pnum1 ), Pnum is Pnum1 + 1. | |
count_positive( [ (n,_) | More ], Pnum ) :- count_positive( More, Pnum ). | |
xlogx( X, N) :- X is 0.0E+00, !, N = 0. | |
xlogx( X, N) :- mylog(X, LogX), N is X * LogX. | |
select_minimal_entropy( | |
[ (Attr, Partition, Entropy ) | MorePartitions ], | |
BestAttr, BestPartition ):- | |
select_minimal_entropy_aux( MorePartitions, | |
(Attr, Partition, Entropy), | |
BestAttr, BestPartition ). | |
select_minimal_entropy_aux( [ ], (Attr, Partition, _), Attr, Partition ). | |
select_minimal_entropy_aux( | |
[ (Attr1, Partition1, Entropy1) | MorePartitions ], | |
( _, _, Entropy), BestAttr, BestPartition ) :- | |
Entropy1 < Entropy , !, | |
select_minimal_entropy_aux( | |
MorePartitions, (Attr1, Partition1, Entropy1), BestAttr, BestPartition ). | |
select_minimal_entropy_aux( | |
[ _ | MorePartitions ], | |
(Attr, Partition, Entropy), BestAttr, BestPartition ) :- | |
select_minimal_entropy_aux( | |
MorePartitions, (Attr, Partition, Entropy), BestAttr, BestPartition ). | |
generate_children_trees( _, [ ], [ ] ). | |
generate_children_trees( | |
AttrList, [ Value-SubData | MoreData ], ChildrenTrees ) :- | |
id3( AttrList, SubData, ChildTree ), | |
generate_children_trees( AttrList, MoreData, MoreTrees ), | |
ChildrenTrees = [ Value-ChildTree | MoreTrees ]. | |
mylog(X,N) :- X is 1.0, !, N is 0. | |
mylog(X,N) :- X is 0.5, !, N is -0.30103. | |
mylog(X,N) :- X is 0.25, !, N is -0.60206. | |
mylog(X,N) :- X is 0.75, !, N is -0.12494. | |
mylog(X,N) :- X is 0.6, !, N is -0.22185. | |
mylog(X,N) :- X is 0.4, !, N is -0.39794. | |
mylog(X,N) :- X is 0.8, !, N is -0.09691. | |
mylog(X,N) :- X is 0.2, !, N is -0.69897. | |
mylog(X,N) :- X is 2/3, !, N is -0.17609. | |
mylog(X,N) :- X is 1-(1/3), !, N is -0.17609. | |
mylog(X,N) :- X is 1- (2/3), !, N is -0.47712. | |
mylog(X,N) :- X is 1/3, !, N is -0.47712. | |
mylog(X,N) :- X is 5/6, !, N is -0.07918. | |
mylog(X,N) :- X is 1-(1/6), !, N is -0.07918. | |
mylog(X,N) :- X is 1-(5/6), !, N is -0.77815. | |
mylog(X,N) :- X is 1/6, !, N is -0.77815. | |
mylog(X,N) :- X is 0.375, !, N is -0.42596873. | |
mylog(X,N) :- X is 0.625, !, N is -0.20412. | |
mylog(X,N) :- X is 0.285714, !, N is -0.54409. | |
mylog(X,N) :- X is 0.714286, !, N is -0.14613. | |
mylog(X,LogX) :- | |
nl, write('Enter the log of '),write(X), write(' : '), | |
read(LogX). |
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