Can you use clpfd to implement a coverage algorithm?

Question

Say that I want to find a set of signs / attributes that distinguish two classes in a simple mapping. Can clpfd be used in the prolog for this?

c_s_mining(Features,Value):-
 Features = [F1,F2,F3,F4],
 Features ins 0..1,
 ExampleA = [A1,A2,A3,A4],
 ExampleB =[B1,B2,B3,B4],
 ExampleC =[C1,C2,C3,C4],
 A1 #=0, A2#=1,A3#=0,A4#=1,
 B1 #=0, B2#=1,B3#=0,B4#=1,
 C1 #=1, C2#=0,C3#=0,C4#=1,

 ExampleD =[D1,D2,D3,D4],
 ExampleE =[E1,E2,E3,E4],
 ExampleQ =[Q1,Q2,Q3,Q4],
 D1#=1,D2#=0,D3#=1,D4#=0,
 E1#=1,E2#=0,E3#=1,E4#=0,
 Q1#=0,Q2#=1,Q3#=1,Q4#=0,

 Positives =[ExampleA,ExampleB,ExampleC],
 Negatives = [ExampleD,ExampleE,ExampleQ],
 TP in 0..sup,
 FP in 0..sup,
 covers(Features,Positives,TP),
 covers(Features,Negatives,FP),
 Value  in inf..sup,
 Value #= TP-FP.


covers(Features,Examples,Number_covered):-
   findall(*,(member(E,Examples),E=Features),Covers), length(Covers,Number_covered).

Each example is described by four binary functions, and there are three positive examples (A, B, C) and three negative examples (D, E, Q).

An example is covered by a set of selected functions, if they match. So, for example, if Featurescombined with [0,1,0,1], then it will correspond to two positive and negative.

I set Valueequal TP(true positives) - TN(true negatives). I want to maximize the value and find the appropriate feature set.

?-c_s_mining(Features,Value),labelling([max(Value)],[Value]). , , : Features =[0,1,0,1], Value =2, Features =[_G1,_G2,_G3,G4],Value =0, G1 in 0..1, G2 in 0..1, G3 in 0..1, G4 in 0..1.

Answer 1

CLP (FD)

, , , : CLP (FD), .

, ..

, :

:- use_module(library(clpfd)).

c_s_mining(Features, Value) :-
    ExampleA = [0,1,0,1],
    ExampleB = [0,1,0,1],
    ExampleC = [1,0,0,1],

    ExampleD = [1,0,1,0],
    ExampleE = [1,0,1,0],
    ExampleQ = [0,1,1,0],

    same_length(Features, ExampleA),
    Features ins 0..1,
    Positives = [ExampleA,ExampleB,ExampleC],
    Negatives = [ExampleD,ExampleE,ExampleQ],
    covers_number(Features, Positives, TP),
    covers_number(Features, Negatives, FP),
    Value #= TP-FP.


covers_number(Features, Examples, Number):-
    maplist(covers_(Features), Examples, Numbers),
    sum(Numbers, #=, Number).

covers_([F1,F2,F3,F4], [E1,E2,E3,E4], Covered) :-
    Covered #<==> (F1#=E1 #/\ F2#=E2 #/\ F3#=E3 #/\ F4#=E4).

labeling/2, :

?- c_s_mining(Fs, Value), labeling([max(Value)], Fs).
Fs = [0, 1, 0, 1],
Value = 2 ;
Fs = [1, 0, 0, 1],
Value = 1 ;
Fs = [0, 0, 0, 0],
Value = 0 ;
etc.

, , Value in inf..sup, .

---

CLP (B):

CLP (B): Constraint , , , SICStus Prolog SWI. CLP (B) , -, CLP (FD). , CLP (FD), CLP (B) , .

CLP (FD), , CLP (B) . labeling/1 ( , library(clpb), CLP (FD) labeling/2) CLP (B). , : , , CLP (B).

:- use_module(library(clpb)).
:- use_module(library(clpfd)).

c_s_mining(Features, Value):-
    ExampleA = [0,1,0,1],
    ExampleB = [0,1,0,1],
    ExampleC = [1,0,0,1],

    ExampleD = [1,0,1,0],
    ExampleE = [1,0,1,0],
    ExampleQ = [0,1,1,0],

    same_length(Features, ExampleA),
    Positives = [ExampleA,ExampleB,ExampleC],
    Negatives = [ExampleD,ExampleE,ExampleQ],
    [TP,FP] ins 0..3, % (in this case)
    Value #= TP-FP,
    labeling([max(Value)], [TP,FP]),
    covers_number(Features, Positives, TP),
    covers_number(Features, Negatives, FP),
    labeling(Features).

covers_number(Features, Examples, Number):-
    maplist(covers_(Features), Examples, Numbers),
    sat(card([Number], Numbers)).

covers_([F1,F2,F3,F4], [E1,E2,E3,E4], Covered) :-
    sat(Covered =:= ((F1=:=E1)*(F2=:=E2)*(F3=:=E3)*(F4=:=E4))).