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linear
Figure 5.26
Line fitting for a noise variance of 0.5: plot of the index parameter (expressed
in decibels) for MCA EXIN
with hyperbolic
scheduling (blue). The values are averaged using a temporal mask with width equal to the
number of iterations up to a maximum of 500. (
See insert for color representation of the
figure
.)
+
with linear scheduling (red) and MCA EXIN
+
line with respect to the tangent to the hyperbolic scheduling curve at the first
iteration. Figure 5.26 shows this comparison.
5.6.1 MCA EXIN
+
Flowchart
•
Goal:
to find the minimum eigenvector
x
(
t
)
of the matrix
A
.
•
Inputs:
1.
η (
t
)
: learning rate, decreasing to zero
2.
x
(
0
)
: initial conditions (better as small as possible, but not null)
3.
ζ (
t
)
: GeTLS parameter, increasing from 0 to 1
4.
a
(
t
)
:therowof
A
that is input at instant
t
5.
ε
: stop threshold
6.
t
max
: maximum number of iterations
•
Algorithm:
1. For each
t
(a) Compute:
x
(
t
+
1
)
=
x
(
t
)
−
η (
t
) γ (
t
)
a
(
t
)
+
ζ (
t
) η (
t
) γ
(
t
)
a
(
t
)
2
where
a
T
(
t
)
x
(
t
)
1
−
ζ(
t
)
+
ζ(
t
)
x
T
γ (
t
)
=
(
t
)
x
(
t
)
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