Dealing with Missing Values in a Probabilistic Decision Tree during Classification - Mining Complex Data - page 65

is to be compared with the classification result obtained by the PAT approach
for the same test instance. For this purpose, we propose an algorithm which is
presented below 10 .

4.5.3 Instance Analysis Algorithm

Input: Inst test instance ,
n training instances I;
Output: for Inst:
frequency of nearest instances from the same class and frequency of
nearest instances from the different class;

Function Instance-Analysis(Inst:test instance,
I:array[1..n] of instances): Pc:array[1..2] of real;

Const near=5;

Var nbSCL, nbDCL, k, near: integer;

dis: real;

begin
nbSCL=0, nbDCL=0;
For k:=1 to n do
begin
dis= Distance(Inst,I[k])
If dis < near {the two instances are nearest neighbor}

then
If(both Inst and I[k] are from same Class)
then nbSCL++
else nbDCL++;
end; (*for k*)
Pc1= P(nearest instances from same class) = nbSCL/(nbDCL+nbSCL)
Pc2= P(nearest instances from different class)= nbDCL/(nbDCL+nbSCL)
end;
return(Pc);

In the above algorithm, we present only the treatment of two-class problems.
However, in our experiment, we also deal with the mutli-class problem. The con-
stant near is fixed by the user. We consider that two instances are nearest if
the distance between them is lower than near . For a test instance, this algorithm
tells us statistically about the proportion of its nearest instances from each class.
We then compare this frequency with the classification result obtained by the
PAT approach for the same test instance.

Results: To illustrate our experience using the Instance Analysis Algorithm
proposed above, we present only the result of testing this algorithm on three
examples as presented in Table 4.13 from the vote database. The vote database

10

This algorithm is a K-Nearest Neighbour method from instance-based learning. We
use the distance function in equation 4.5 because it is the most appropriate to our
problem.