What Decision Trees Are

A decision tree is a tree data structure that allows selecting from a list of options and then from more options until reaching a terminal node, preventing the need to painstakingly check each whole set of possibilities.

The following algorithm takes a set of options and converts them into a decision tree.

Some Prolog Code


/*
decision_tree([[a,a],[a,b],[b,b]],A).
A = [[a, 2, [[a, 1, []], [b, 1, []]]], [b, 1, [[b, 1, []]]]].
*/

decision_tree([],[]) :- !.
decision_tree(A,B) :-
    findall(C,(member([C|_D],A)),E),
    frequency_list2(E,L),
    findall([G,K1,P],(member([G,K1],L),
    findall(D,member([G|D],A),D2),
    decision_tree(D2,P)),B).

frequency_list2(E,L) :-
    msort(E, Sorted),
    clumped(Sorted, Freq1),
    findall([B,A],member(B-A,Freq1),L),!.

The following variant is faster:

decision_tree([],[]) :- !.
decision_tree(A,B) :-
    findall(C,(member([C|_D],A)),E),
    frequency_list2(E,L),
    decision_tree1(A,L,[],B).
    decision_tree1(_,[],B,B) :- !.

decision_tree1(A,L,B1,B2) :-
    L=[[G,K1]|Ls],
    decision_tree2(A,G,[],B3),
    decision_tree(B3,P),
    append(B1,[[G,K1,P]],B4),
    decision_tree1(A,Ls,B4,B2),!.

decision_tree2([],_,B,B) :- !.
decision_tree2(A,G,B1,B2) :-
    A=[[G1|D]|As],
    (G1=G->append(B1,[D],B3);
    B1=B3),
    decision_tree2(As,G,B3,B2).

decision_tree2(A,G,B1,B2) :-
    A=[[]|As],
    decision_tree2(As,G,B1,B2).

frequency_list2(E,L) :-
    msort(E, Sorted),
    clumped(Sorted, Freq1),
    findall([B,A],member(B-A,Freq1),L),!.

The decision tree uses the frequency list algorithm, a variant that sorts by frequency in descending order.

/*
frequency_list([a,a,b],A).
A = [[2, a], [1, b]].
*/


frequency_list(A,B) :-

frequency_list1(A,C),sort(C,D),reverse(D,B),!.

frequency_list1(E,L) :-

msort(E, Sorted),
clumped(Sorted, Freq1), findall([A,B],member(B-A,Freq1),L),!.

You can read more about how this algorithm is used on GitHub by my Mind Reader repository, my Essay Helper repository, my Text to Breasonings repository, Strings to Grammar and Spec to Algorithm and my Music Composer repository.

Cover image by Svilen Milev (svilen001-32617, FreeImages).

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Creating a Decision Tree in Prolog

Lucian Green

What Decision Trees Are

Some Prolog Code

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