Databases Reference
In-Depth Information
σ
(max,e,i)
= n
row
×σ
(max,e,i−1)
= n
row
×n
2i
(4.8)
row
= n
2i+1
row
The total size of the maximum bias array for all neurons in middle layer i,
is determined from the following equation:
σ
(total,i)
= n
row
σ
(max,ne,i)
(a−(2i + 2)) + 2σ
(max,e,i)
n
2i+2
row
(a−(2i + 2)) + 2n
2i+1
row
= n
row
(4.9)
= n
2i+3
row
n
row
(a−(2i + 2)) + 2n
2i+2
row
4.2.1.3
Neurons at the top layer:
At the top layer, the maximum size of the bias array is derived from the
maximum bias array size of the non-edge neuron in the previous level. There-
fore, the maximum size of the bias array at the top level is as follows:
σ
(max,top)
= n
row
×σ
(max,ne,top−1)
= n
row
×n
a−1
(4.10)
row
= n
row
The maximum bias array size for the HGN composition, σ
HGN
, is obtained
by summing of all the bias arrays given in the previous equations.
(
a+
2
)
−2
σ
HGN
=σ
(total,0)
+
σ
(total,i)
+ σ
(max,top)
i=1
σ
HGN
=n
row
(n
row
(a−2) + 2)
0
@
(
a+
2
)
−2
1
A
(4.11)
n
2i+3
row
(a−(2i + 2) + 2) + 2n
2i+2
row
+
i=1
+ n
row
To analyze the complexity of an HGN implementation, the maximum bias
array size was derived. The results indicate that the size of the bias array is
sensitive to the size of the network and the pattern size. However, this result
is based on totally unique patterns and does not account for patterns that
have similar subpattern features or a close resemblance. In this context, a
uniform distribution could be used to estimate the average bias array size for
