Hardware Reference
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as follows:
N
( x , w )
=
w k γ (
x
x k
)
(4.11)
k =
1
where γ is a scalar distance function, w k are the weights of the RBF and N is
the number of samples in the training set. In this paper, we consider the following
definitions for γ
z
linear
z 2 log z
thin plate spline
z 2 ) 1 / 2
γ ( z )
=
(4.12)
(1
+
multiquadric
z 2 ) 1 / 2
(1
+
inverse multiquadric
e z 2
gaussian
The weights w k are the solution of a matrix equation which is determined by the
training set of configurations x k and the associated observations y k :
A 11
A 12
...
A 1 N
w 1
w 2
.
w N
y 1
y 2
.
y N
=
A 21
A 22
... A 2 N
(4.13)
.
.
. . . .
A N 1
A N 2
...
A NN
where:
A jk =
x j
x k
=
γ (
),
j , k
1, 2, ... , N ,
(4.14)
4.4.3
Splines
Spline-based regression has been recently proposed by Lee and Brooks [ 7 ]asa
powerful method for the prediction of power consumption and performance metrics.
A spline RSM is composed of a number of piecewise polynomials σ L associated with
each of the parameters x j of the architecture:
N
( x , w
=
[ a , b , k ])
= a 0 +
a j σ L ( x j , b , k )
(4.15)
j = 1
The piece-wise polynomial σ L is divided into L intervals defining multiple different
continuous polynomials with endpoints called knots . The number of knots L can
vary depending on the amount of available data for fitting the function and the
number of levels associated with parameter x j , but more knots generally lead to better
fits. In fact, relatively simple linear splines may be inadequate for complex, highly
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