Associative-Projective Neural Networks (APNNs) - Neural Networks and Micromechanics - page 82

5.2.1.1 Coding the numbers and sets of the numerical parameters

To code the numbers, it is necessary to represent them in the form of discrete sets. In
our work, we bring the numbers to the specific range and consider that they have
only integer values (for example, in the range of 0 to 100). To code the numbers in
this range, it is necessary for each number to generate the mask in such a manner
that the masks with large overlap correspond to close numbers and the masks with
small overlap correspond to distant numbers. Let us describe one of the procedures
of mask creation that possesses this property and was used in different applied
systems based on neural networks.
Let us generate the random binary vector with the probability of the appearance
of 1s equal to m / n , where m is the size of the neural ensemble and n is a quantity of
neurons in the neural field. With this selection of probability, a quantity of 1s in the
vector will approximately equal m . We will consider the selected vector as the
mask, which codes the number “0” ( M 0 ). To obtain the mask that codes the number
“1,” let us build a new random vector X with the probability of the units of p ( X ). Let
us make a bitwise disjunction of vector X with the mask of the number “0”:

Y ¼ M 0 U X ; (5.9)

thereafter, we normalize the vector Y in such a way that it would also contain
approximately m “1”s. The normalized vector Y is the mask that codes the number
“1.” Let us denote it as M 1 .
It is not difficult to see that the mask that codes “1” will have a certain quantity of
common unit elements with the mask that codes “0.” This quantity decreases with
an increase of the probability of p ( X ). The mask that codes “2” is obtained from the
mask that codes “1” with the aid of the same procedure. The random vector X is
created anew, independently of the preceding one. The plot of the mask intersection
versus the number values is shown in Fig. 5.8 . Along the X -axis on the plot is given
the difference of two number values, and along the Y -axis is given the quantity of
common elements in their masks. The form of the curve represented in Fig. 5.8
plays a large role in the use of the associative-projective structures for the solution
of pattern recognition problems.
Many objects in the environment are described not only by the presence or the
absence of any features but also by the sets of numerical parameters. In order to
code the set of numerical parameters, it is necessary to bring each of these para-
meters within the range selected for the masks. After this, it is necessary to create

Fig. 5.8 The mask
intersection