60
Chapter 11.
Solutions: Case Study: Classified Information
1.5
1
0.5
0
0.5
1
1.5
0
0.5
1
1.5
c
R(c)
D(c)
Figure 11.1.
The functions
R
and
D
for a particular dataset.
(c) We want to minimize the function
D
(
c
) =
n
i
=1
x
i
−
c
2
over all choices of
c
.
Since there is only one center
c
, this function is convex
and differentiable everywhere, and the solution must be a zero of the gradient.
Differentiating with respect to
c
we obtain
n
i
=1
2(
x
i
−
c
) =
0
,
so
c
=
1
n
n
i
=1
x
i
.
It is easy to verify that this is a minimizer, not a maximizer or a stationary point,
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 Fall '11
 Dr.Robin
 Statistics, Optimization, Means, Fermat's theorem, general purpose optimization

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