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Table 1.
Computation of Minimum value of
r
max
Training Percentage of Convergence
Noise For
n
= 20,
k
=5For
n
= 30,
k
=7For
n
= 45,
k
=10
(
r
max
)
r
=1
r
=2
r
=3
r
=1
r
=2
r
=3
r
=1
r
=2
r
=3
1
84.57 64.65 44.87 84.88 67.57 50.90 79.30 63.92 51.06
2
83.62 63.98 44.65 81.57 61.99 44.59 75.65 59.41 46.31
3
82.67 61.70 41.55 81.57 61.79 44.56 74.89 59.34 46.01
The reason for such a phenomenon can be explained as follows.
If we consider
noise in more than one bit, then the total number of entry in state transition
table is higher. As a result the Simulated Annealing program fails to arrive at
the desired GMACA.
3.5 Selection of Attractor Cycle Length
In the context of the observation noted in
Section 3.4
, we have analyzed the
attractor cycle length of the evolved
GMACA
. We have observed that the length
of the attractor cycle of the evolved
GMACA
is equal to one in majority of cases.
The reason for which attractor cycle length of
GMACA
is equal to one is
as follows.
If the cycle length of attractor is equal to one, same neighborhood
configurations of i
th
cell of attractor map to same next state more times; in
effect collision of state '0' and '1' gets reduced. As a result, the convergence rate
of the Simulated Annealing program gets accelerated.
4 Experimental Results and Performance Analysis
In this section, we report experimental results based on randomly generated
data set for different values of
n
(number of bits in a pattern) and
k
(number of
patterns to be learnt) to analyze the performance of
CAM
. The memorizing ca-
pacity, evolution time and identification/recognition complexity of the proposed
model confirm that
GMACA
based
CAM
can be employed as an excellent pat-
tern recognition machine.
4.1 Memorizing Capacity
For an associative memory to be useful, the stored patterns should be stable in
the configuration space in the sense that if the network state is a stored pattern,
the state should not change. Moreover, if the stored patterns are correlated their
stability becomes less likely. The maximum capacity of a conventional Hopfield
Network is roughly 0
ยท
14
n
random patterns [12].
The experiments to evolve pattern recognizable
n
-cell
GMACA
for different
values of
n
are carried out. For each
n
, 15 different sets of unbiased patterns to
be trained are selected randomly. The number of patterns to be learned by the
CAM
is progressively increased.