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(c)
The only option left is to choose a CA cell such that:
1
i.e. to let
the pattern evolve beyond the 3×3 rectangle in the middle but never ex-
U
U
crit
panding out of the boundaries of the CA array. The traces left in the CA
will carry an information about the overall sequence much like a free pen-
dulum leaves a trace of its movement in a sheet of fine sand (Fig. 8.9). The
crit
value has to be established experimentally. In what follows we
.
U
crit
U
is considered as it was experimentally determined as the most
convenient.
1
Using the sieving methods exposed in Chap. 6 we found 42 different IDs
(among all 1,024 from the
2s5
family) satisfying this condition. Though, for many
of them no interesting dynamics evolves and the patterns are usually confined to
the initial 3×3 rectangle. This is probably the effect of the correlation present in
the speech signal samples, while purely random samples were used to determine
the value of
U
as explained in Chap. 5. It turns out that only
ID = 49
and
ID = 463
lead to expected behaviors, i.e. that of a
excitable membrane with temporal mem-
ory (EMTM).
The diversity of EMTMs may be increased sieving among larger
populations of cells (e.g. within the 2s9 family) since as observed in the end of
Chap. 7, the 2s5 family does not provide too many “slow growing” behaviors.
Another possibility would be to consider a one-dimensional version of the method
with cells selected among the
1s5
family, knowing that it has a richer repertoire of
“slow growing” behaviors that its two-dimensional counterpart
2s5
.
8.3.3 Experimental Results in Sound Classification
In our experiments a speaker produced ten utterances for both “one” and “zero”.
The result is a set of 20 signal sequences
^ `
10
0
,
1
k
SS
, where
k
is an index of the
utterance. Each sequence is applied to the EMTM built as described previously
and a set of binary terminal patterns
^
k
k
1
,..
`
0
,
1
k
X
results when the algorithm discussed
in Sect. 8.3.1 is applied. These patterns are represented in Fig. 8.10. Although the
sequence of terminal states
^
k
`
0
,
1
k
X
can be applied to any neural classifier de-
scribed in the literature, for the sake of implementation simplicity, herein we may
consider an ad-hoc classifier constructed around some prototypes of the signals
to be recognized. In our example we use the first three instances as training
samples to compute the prototype matrices A0 and A1 as follows:
k
3
3
0
1
,
A
0
¦
X
A
1
¦
X
k
k
k
1
k
1
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