Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

The restriction of hypotheses can be implemented by adding a conjunct
to the previous hypothesis. The preferential ordering among the hypotheses
can be made by a heuristic evaluation function that excludes some objects
from the target concept. The hypothesis that is not supported by the excluded
class is preferred to the hypothesis that is supported by it .
The Candidate Elimination Algorithm
The candidate elimination algorithm is employed to reduce the concept
(version) space from both general to specific and from specific to general
form. It, thus, is a bi-directional search. Positive instances are used for
generalization and negative instances are utilized to prevent the algorithm
from over-generalization. The learned concept will, therefore, be general
enough to include all positive instances and exclude all negative instances.
We now present the procedure candidate-elimination [5], [9].
Procedure Candidate-Elimination
Begin
Initialize G to be the most general concept in the space;
Initialize S to be the first positive training instance;
For each new positive instance p do
Begin
Eliminate the members of G that do not match with p;
for all s ∈ S, if s does not match with p, replace s with its most
specific generalization that match with p;
Eliminate from S any hypothesis that is more general than some
other in S;
Eliminate from S any hypothesis, which is no more specific than
some hypothesis in G;
End For ;
For each negative instance n do
Begin
Eliminate all members of S that match with n;
for each g ∈ G that matches with n, replace g by its most general
specialization that does not match with n;
Eliminate from G any hypothesis, which is more specific in some
other hypothesis in G;
Eliminate from G any hypothesis, which is more specific than
some other hypothesis in S;
End For
If G=∅ and S=∅ Then report “no concept supports all positive and
refutes all negative instances”;