Databases Reference
In-Depth Information
4.2.1.1
At the base layer (0):
The size of the bias array for a base layer neuron in an HGN composition
strictly follows the estimation given for the GN algorithm. The maximum
size of the bias array for each neuron is derived from the number of possible
adjacency information combinations (from preceding and succeeding neurons).
We consider the number of rows (different pattern elements), n
row
, for each
pattern set used. The maximum bias array size for a non-edge neuron in an
HGN for one-dimensional patterns, σ
(max,ne,0)
, is given by the following:
σ
(max,ne,0)
= n
row
(4.4)
Each neuron at the edge of the layer receives adjacency information only
from its preceding or succeeding neuron. Therefore, its maximum bias array
size, σ
(max,e,0)
, is given by the following:
σ
(max,e,0)
= n
row
(4.5)
The maximum bias array size for edge neurons is equivalent to the number
of different pattern elements. Consequently, the total size of the bias array for
all neurons in the base layer, σ
(total,0)
for patterns of size S = a is derived
using an approach similar to that described in Section 3.3:
σ
(max,ne0)
×(a−2) + 2σ
(max,e,0)
σ
(total,0)
= n
row
n
row
×(a−2) + 2n
row
= n
row
(4.6)
= n
row
(n
row
×(a−2) + 2)
4.2.1.2
At layer
i
:
In an HGN implementation, neurons in the middle layer receive indices from
lower/base layer neurons and perform a recognition procedure using these
values. Therefore, the maximum bias array size of neurons at lower/base layer
affects the calculation of bias array estimates for the middle layer neurons.
The maximum size of the bias array for a non-edge neurons in middle layer i,
is derived as follows:
σ
(max,ne,i)
= n
row
×σ
(max,ne,i−1)
= n
row
×n
2i
(4.7)
row
= n
2i+2
row
Similarly, for edge neurons:
