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Fig. 1.17.
(
a
) Representation of a sample of the class “integrated circuit” in the
reflectivity-area plane. (
b
) Estimate of the conditional probability density of the
area of the pattern if the latter is an integrated circuit
probability density of the reflectivity
R
, for the class integrated circuit, as a
function of
r
.
Thus, given a sample of the population of patterns to be classified, esti-
mates of the prior probabilities of the classes
{
Pr(
C
i
)
}
, and of the conditional
probability densities
p
X
(
x
C
i
) of their features, are available. Then, by
Bayes formula, the solution of the classification problem, i.e., the posterior
probability of a class given an unknown pattern, is given by
|
p
X
(
x
|
C
i
)Pr(
C
i
)
Pr(
C
i
|
x
)=
.
p
X
(
x
|
C
j
)Pr(
C
j
)
j
Clearly, that estimate is relevant only if the features of the unknown pattern
have the same conditional density probabilities as the patterns that were used
to estimate the likelihoods.
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