The rule to minimize the error rate by maximizing
the posterior probability is the same for the discrete and continuous
case. The only difference is that probabilities are used instead of
probability densities. The following discriminant functions are
equivalent decision rules:

## The 2-Category Case

This is a classifier that places a pattern in one
of two possible categories and is called a dichotomizer. Since we have
2 categories, we will have 2 discriminant function *g*_{1}(*x*)
and *g*_{2}(*x*).
As before, we would assign *x* to *w*_{1}
if *g*_{1}(*x*)_{
> }g_{2}(*x*).
Instead, we can define:

and decide *w*_{1}
if *g*(*x*)>0. Two forms of
the dIscriminant function are therefore: