Biomedical Engineering Reference
In-Depth Information
unknown what combinations of features make it possible to obtain better recogni-
tion results. The task of the evolutionary algorithm, which simulates biological
evolution, is the search for such combinations.
Let us term “individual” the 41-bit binary vector
E
=(
e
1
,
e
2
,
,
e
41
) in which
each bit corresponds to one feature. If
e
i
= 1, the feature
i
is included in the subset
for recognition, but if
e
i
= 0, the feature is not included in the subset. Let us define
the mutation
m
i
as a change in the value of the component
i
of vector
E
(0 to 1 or 1
to 0). The “unisexual” evolutionary algorithm in which all “offsprings” are born to
one “parent” but not to a pair of “parents” was used. Random mutations occurred.
The probability of the mutation of each feature
p
(
m
i
) depends only on the function
of quality of the parent:
...
pmðÞ¼
pQ
ðÞ
;
(6.14)
where the quality function
Q
was defined as the fourth power of the error number of
recognition,
cN
4
Q
¼
(6.15)
;
where
N
is the number of errors and
c
is a constant. The number of errors was
calculated during recognition of different variants of ten handwritten words. In
order to calculate quality function for a certain “individual,” the neural network was
trained to recognize words with the use of the feature subset of this “individual.”
As the test, we selected the task of recognizing handwritten words written by
different authors. The special shapes for writing English words (
one
,
two
,
,
ten
)
were prepared. Each author prepared 12 versions of ten handwritten words. From
this word set were formed two subsets,
Q
1
and
Q
2
:
Q
1
was for training (80 samples)
and
Q
2
was the control subset (40 samples). No training was done on the control
samples. These samples were used for recognizing words and determining the
percentage of correctly identified words. The words were input to the computer
using a scanner with a resolution of 300-400 dots per inch.
For the simulation of natural selection, we used the algorithm in which the
probability of the creation of “offspring” was proportional to the value of 1 /
Q
,
allowing for an “individual” with the minimum quality function to generate more
“offsprings” than an “individual” with a large quality function. The initial indivi-
duals were generated with the aid of a random-number generator.
The associative-projective ensemble neural network selected for the test of the
evolutionary algorithm consisted of 4,096 neurons (experiments were also con-
ducted with the network that consisted of 8,192 neurons, but only the first version
will be described here). The coded input vector was supplied to the entrance of the
network while the mask of the word was decoded in the output of the network.
Connections between the neurons belonging to the input vector and the neurons
forming the mask of the word were established in the matrix of the neuron connec-
tions. During recognition, the network's response was formed by the greatest
intersection of the output vector with the masks of words. The neural network
...
