Discovery of Positive and Negative Rules from Medical Databases Based on Rough Sets - Advanced Techniques in Knowledge Discovery and Data Mining - page 232

234 Shusaku Tsumoto

also plays an important role in cutting the search space of a differential di-
agnosis process [9.10]. Thus, medical reasoning includes both positive and
negative reasoning, though conventional rule-induction methods do not re-
flect this aspect. This is one of the reasons medical experts have di culty
in interpreting induced rules, and interpreting rules for a discovery proce-
dure does not proceed easily. Therefore, negative rules should be induced
from databases in order not only to induce rules reflecting experts' decision
processes, but also to induce rules that will be easier for domain experts to
interpret, both of which are important to enhance the discovery process done
by the cooperation of medical experts and computers.
In this chapter, first the characteristics of medical reasoning are discussed
and then two kinds of rules, positive rules and negative rules, are introduced
as a model of medical reasoning. Interestingly, from the set-theoretic point
of view, sets of examples supporting both rules correspond to the lower and
upper approximations in rough sets [9.5]. On the other hand, from the view-
point of propositional logic, both positive and negative rules are defined as
classical propositions or deterministic rules with two probabilistic measures,
classification accuracy, and coverage. Second, two algorithms for induction of
positive and negative rules are introduced, defined as search procedures using
accuracy and coverage as evaluation indices. Finally, the proposed method is
evaluated on several medical databases. The experimental results show that
the induced rules correctly represent experts' knowledge. In addition, several
interesting patterns are discovered.

9.2 Focusing Mechanism

One of the characteristics in medical reasoning is a focusing mechanism,
which is used to select the final diagnosis from many candidates [9.10], [9.11].
For example, in differential diagnosis of headache, more than 60 diseases
will be checked by present history, physical examinations, and laboratory
examinations. In diagnostic procedures, a candidate is excluded if a symptom
necessary to diagnose is not observed.
This style of reasoning consists of the following two processes: exclusive
reasoning and inclusive reasoning. Relations of this diagnostic model with
another diagnostic model are discussed in [9.12]. The diagnostic procedure
proceeds as follows (Fig. 9.2): First, exclusive reasoning excludes a disease
from candidates when a patient does not have a symptom that is necessary
to diagnose that disease. Second, inclusive reasoning suspects a disease in
the output of the exclusive process when a patient has symptoms specific to
a disease. These two steps are modeled as two kinds of rules, negative rules
(or exclusive rules) and positive rules; the former corresponds to exclusive
reasoning, the latter to inclusive reasoning. In the next two sections, these
two rules are represented as special kinds of probabilistic rules.