Databases Reference
In-Depth Information
FIGURE 4.1: The layout of a Hierarchical Graph Neuron (HGN) for a binary
pattern of size 5 bits.
of the HGN was to expand the capability of “perceiving neighbors” within the
network. This was achieved by adding higher layers of GNs that see all of
the pattern information and provide a bird's eye view of the overall pattern.
Figure 4.1 shows the hierarchical layout of the HGN for a binary pattern of
size 5 bits.
Figure 4.1 demonstrates that the HGN comprises of layers of GN networks
arranged in a pyramid-like formation. This arrangement holds all of the in-
formation related to the structure of the patterns stored in the network. The
HGN network, as shown in Figure 4.1, is only used in pattern recognition
applications involving one-dimensional patterns. However, the HGN does not
limit the dimensionality of patterns. For applications that involve complex
patterns, the HGN can be expanded to two, three, or even multi-dimensional
hierarchies. Figure 4.2 shows examples of an HGN composition for a two-
dimensional pattern of size 49 (7 × 7) and a three-dimensional pattern of size
147 (7 × 7 × 3). For simplicity, several pattern elements have been omitted
from this figure.
There is an interesting side effect to increasing the dimensions of an HGN
network. According to Nasution [52], an increase in the dimension of the
hierarchical composition leads to a significant reduction in the number of
GNs in the hierarchy. This behavior improves the e
ciency of the network
for large-scale patterns. For example, given a one-dimensional pattern of size
147, the total number of GNs required is: 147 + 145 + 143 + . . . + 3 + 1
= 5476. A two-dimensional (21 × 7 = 147) GN composition requires: 21 × 7
+ 21 × 5 + 21 × 3 + 21 + 19 + . . . + 3 + 1 = 436 GNs. In this example,
increasing the dimensionality by 1 led to a 92% reduction in the number of
