EE 649 Pattern Recognition – Spring 2008
Homework 2
Due on: Feb 29
Homework Policy
: Please return homework in my mailbox by 5 p.m. on Feb 29.
1. Solve Problem 2.9 in DHS.
2. Solve Problem 2.27 in DHS.
3. Solve Problem 2.32 in DHS.
Hint:
Rotate and translate the coordinate system so that the axis joining the means
coincides with one of the axes.
You do not need to specify the translation or rotation
matrix explicitly.
4. Solve Problem 4.8 in DHS.
Hint: Here,
P
denotes the same as
e
NN
, the asymptotic classification error for the 1NN
classifier. For arbitrary number of classes (
c>
2), it is given by equation (45) in DHS. For
example, for
c
= 3,
P
=
E
[1
−
(
η
1
(
X
)
2
+
η
2
(
X
)
2
+
η
3
(
X
)
3
]
,
where
η
i
(
X
) =
P
(
Y
=
i

X
). For
c
= 2, this reduces to what we discussed in class (you
can check it). The bayes error for an arbitrary number of classes is given by:
ǫ
∗
=
E
[1
−
max
i
η
i
(
X
)]
.
For
c
= 2, this reduces to the familiar expression we have been discussing. The key to this
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 Spring '08
 BragaNeto
 Normal Distribution, Probability theory, probability density function, p0 f0

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