Associative-Projective Neural Networks (APNNs) - Neural Networks and Micromechanics - page 89

a

j

b

j ( j +1)

c

j

00000
10000
00000
00000
00000

00000
10000
01000
00000
00000

00000
10000
01000
00100
00010

i i

i +1

i

Fig. 5.14 Matrix of synaptic weights

a b - - - - - - - - - - - + - - - - - + - -

- + - - - - - + - - - - - - - - - - - -

Y Y +2

i +2 k j +2 k

Fig. 5.15 Codes of object shifting

Let us consider the shift of the object along coordinate Y . In this case, the neural
code is to be shifted by the given number of small segments. The code of the object
located at the point with coordinates X , Y is presented in Fig. 5.15a . The code of the
image at the point with coordinates X , Y + 2 will be as shown in Fig. 5.15b , where k
is the number of points in the small segment.
For the initial position of the object, the synaptic weights are formed as
represented in Fig. 5.16a . With the shift to the points with coordinates ( X , Y +1)
and ( X , Y + 2), the matrix of synaptic weights takes the form represented in
Fig. 5.16b . The situation in which the shifts are carried out along the coordinates
X and Y is shown in Fig. 5.16c .
In the case of cyclical permutation without absorption, the matrix of synaptic
weights after the shifts both on X and on Y will take the form represented in
Fig. 5.17 . During this coding, the object or fragment corresponding to the formed
ensemble will be recognized in any place of the image. It is obvious that the
network's memory capacity in this mode of training will be less than that for
local connected coding, since each new ensemble introduces considerably more
unit elements into the matrix of synaptic weights (compared to each unit during
local connected coding, k * r /4 unit elements appear here, where k is a quantity of
points in the small segment, and r is a quantity of small segments in the large
segment). Therefore, shift coding needs a neural network that considerably exceeds
previous neural networks in size, i.e., the speed advantage of recognition obtained
during shift coding requires high memory consumption. Since at present the cost of
memory is small and is decreasing continuously, this approach makes sense.

5.2.2.1 Centering the shift code

For shift coding, it is necessary to know how to restore the value of the code and to
determine the coordinates of the coded object. For this purpose, the concept of the