Digital Signal Processing Reference
In-Depth Information
of a network in the first layer has the following steps:
1. Initialize the sample mean vector
m
j
, the sample dispersion matrix
S
j
, and the number of patterns
z
j
associated with each class.
2. Determine the class
c
represented by the weight vector
v
c
with
which the training pattern
x
C
is most closely associated.
3. Increment the number of patterns belonging to
(
n
)
C
c
by one and update
the sample mean vector and the sample dispersion matrix of this
class. For the remaining classes,
j
c
, the
number of patterns, the sample mean, and the sample dispersion
matrix are not altered.
=
1
,
2
,
...
,p
with
j
=
The SOM network of the second layer is used to find the weight vectors
provided by the first-layer SOMs that are candidates for merging. As has
already been discussed, the criterion of minimum Euclidean distance metric
used in the SOM is not sufficient for the above-described task, because it
does not take into account the presence of outliers. Consequently, additional
tests must be implemented to test the similarity between the weight vector
provided by the first-layer SOMs and the winner vector determined by the
second-layer SOM. The following
learning algorithm
for the second-layer SOM
is proposed:
ALGORITHM 3
T
,
1. Initialize randomly all the weight vectors
w
l
=
(w
1
l
,
w
2
l
,
...
,
w
pl
)
1.
2. For each weight vector provided by the first-layer SOMs
v
l
=
1
,
2
,
...
,q
, where
N
≤
q
<
LN
. Set
k
=
(
n
)
=
T
:
a. Find the closest weight vector of the second-layer SOM, i.e., the
final winner vector
w
c
(v
(
n
)
,
v
(
n
)
,
...
,
v
(
n
))
1
2
p
(
n
)
by using
q
min
j
v
(
n
)
−
w
c
(
n
)
=
1
{
v
(
n
)
−
w
j
(
n
)
}
.
(11.103)
=
b. If there is an output node of the second-layer SOM that has not
been activated yet, i.e., if there is a free class:
(i)
Test the similarity between
w
c
(
n
)
and
v
(
n
)
(to be described
subsequently).
(
)
(
)
(ii)
are proved similar, then merge them. The
final winner is updated as SOM suggests:
If
w
c
n
and
v
n
w
c
(
n
+
1
)
=
w
c
(
n
)
+
α(
k
)
[
v
(
n
)
−
w
c
(
n
)
]
.
(11.104)
To achieve a faster rate of convergence, the sequence of step-
size parameters is chosen to be
α(
k
)
=
1
/(
k
+
1
)
. Let
z
c
(
n
)
,
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