Hardware Reference
In-Depth Information
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
Search WWH ::
Custom Search