Biomedical Engineering Reference
In-Depth Information
predetermined value. The neurocomputer realization is based on the fact that the
generation of such vectors is connected by the logical bit operations with the binary
vectors.
The procedure is realized as follows. Let the number
p
, which indicates the
probability of the appearance of a 1 in any position, be represented in the binary
form, where
p
1
,
p
2
,
,p
k
are the bits of this number and
p
1
is the most significant
bit. Furthermore, there is the uniformly distributed random binary number
X
, i.e.,
the probability of the appearance of a 1 is equal to 1/2. This vector is easily formed
with a random-number generator. The required binary vector
Y
, i.e., the vector with
the predetermined probability of the appearance of a 1, can be obtained as follows:
if
p
1
= 0, then
...
Y
¼ð
P
2
& ð
X
21
&
X
22
ÞÞ
U
...
U
ð
P
k
& ð
X
kl
& ... &
X
kk
ÞÞ;
(5.8)
where
P
2
is the vector that consists of all 1s if
p
2
= 1, or of all 0s if
p
2
=0;
P
k
is
the analogous vector determined by component
p
k
; all vectors
X
(
X
21
,
X
22
,
)
with indices are independent pseudorandom vectors with the probability of 1s equal
to 1/2: if
p
1
= 1, then the inversion of the number
p
is taken, on which the vector
Y
is formed, and it is inverted. With this approach, the maximum error does not
exceed 12.5%.
Other procedures for the formation of vectors with the given probability are
proposed, which have greater accuracy [
1
]. These procedures are used in the initial
stage of the work of neural networks. The formed vectors (masks) are stored in the
neurocomputer's memory. If it is necessary to feed the object that contains several
features to the network input, then the object mask is formed as the bitwise
disjunction of the feature masks. In this case, a quantity of unit elements in the
mask exceeds
m
, and in order to preserve the approximately constant size of all
ensembles, the normalization of the obtained object mask is produced. The normali-
zation consists of the removal of excessive unit elements with the aid of the special
procedure, which guarantees the approximately equal representation of all features
in the resulting object mask. (The normalization will be described in detail later.)
One of the basic special features of associative-projective neural networks is the
fact that any information can be represented as a neuron subset. Therefore, it is
necessary to have a method for transforming different types of data into the subsets
of neurons. Moreover, it is necessary to find such methods of mapping that the
properties of the data are presented in some manner in the properties of neuron
subsets. A certain metric could be one such property. If each set of the parameters
corresponds to a point in the metric space, then it is possible to determine the
distance between two sets. In order to preserve this property, it is necessary to
determine the metric in the coding subsets and to ensure the similarity of the
metrics. It is possible to consider a quantity of common unit elements in both
subsets (overlap) as a natural measure of the proximity of two subsets. We will use
this measure in this chapter for evaluating the codes obtained in this and another
method of coding.
...
