Biomedical Engineering Reference
In-Depth Information
Using Bayes' Theorem to determine whether given a data point should be classified as a member of,
for example, the open-circle group, the following equation applies:
p
(
OpenCircles
|
X
i
Y
i
) =
p
(
OpenCircles
|
X
i
) x
p
(
OpenCircles
|
Y
i
)
For the data point A (
x
= 7,
y
= 3), B (
x
= 10,
y
= 5), and C (
x
= 14,
y
= 3) the equations take the
form:
p
(
OpenCircles
|
X
a
Y
a
) =
p
(
OpenCircles
| 7) x
p
(
OpenCircles
| 3)
p
(
OpenCircles
|
X
b
Y
b
) =
p
(
OpenCircles
| 10) x
p
(
OpenCircles
| 5)
p
(
OpenCircles
|
X
c
Y
c
) =
p
(
OpenCircles
| 14) x
p
(
OpenCircles
| 3)
Visually, the data point C in
Figure 6-24
can reasonably be classified as a member of the open-circle
group. Conversely, the probability that data point A is a member of the open-circle group is high. The
main issue surrounds the cutoff probability for evaluating the equations. If the probability must be
high in order to accept the hypothesis that a given data point is a member of the open-circle group,
then data point B may not be able to be classified in the open-circle group, and may best be assigned
to another group.
