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where w
x
represents the voting element of pattern p
x
in the voting vector
W
P
. Note that the recognition process for each pattern occurs in a single-
cycle containing a fixed number of steps. Additionally, the DHGN can adopt
an unsupervised learning approach, which requires no prior training on pattern
data.
5.2 Dimensionality Reduction in Pattern Pre-Processing
Pre-processing is an important task carried out before any recognition pro-
cedure. To ensure that pattern data are in the specific form required by the al-
gorithm or implementation, pre-processing is a pre-requisite for some pattern
recognition systems. Moreover, to ensure that the data are well-distributed
and do not contain any outlier values, raw pattern data might need to be
normalized before recognition.
Complex data, such as images, environmental sensory readings, and biomed-
ical and biochemical structural data, are usually of high dimensions (more
than one). There are two approaches that can be used to reduce the dimen-
sional complexity of data:
1. Structural reduction: In this approach, the structure of the data is re-
duced to a lower dimension.
2. Content reduction: In this approach, high dimension data are reduced to
an equivalent low-dimension form using a data dimensionality reduction
technique.
In this section, these two approaches are discussed in relation to a DHGN
implementation.
5.2.1 Structural Reduction
Structural reduction in DHGN pre-processing reduces the structural com-
position of patterns from high-dimensional structure to its corresponding low-
dimensional representation. In this approach, pattern data undergoes struc-
tural deformation, but the contents or elements within the pattern remain
intact. Structural reduction works on the premise that the structure of data
is unlikely to be play a significant role in determining the characteristics of
the pattern.
Consider two-dimensional binary images of size 7-by-5 bits, i.e., 35-bit im-
ages, as shown in Figure 5.5. In the structural reduction approach, images
are rearranged into a one-dimensional bit-string. This rearrangement enables
the algorithm to work on patterns in a low structural dimension. From the
perspective of a DHGN implementation, this approach enables each subnet to
