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by the number of neurons required for the recognition processes. The recogni-
tion accuracy is comparable to the HGN implementation. In the DHGN, the
recognition process can be deployed as a composition of sub-processes that
are being executed in parallel across a distributed network. Each sub-process
is conducted independently, making it less cohesive than other pattern recog-
nition approaches.
5.1.1 Associative Memory (AM) Concept in Pattern Recog-
nition
From a pattern recognition perspective, AM refers to a set of functions
(or a learning network) that has the ability to make an association between
input and output. Associative memory, M, as defined in [65], is a system
that provides an input-output relationship as follows: a → M → b where a
and b are the input and output, respectively. From this perspective, each input
vector is associated with an output vector. The association can be represented
as a fundamental set of associations: {(a
µ
, b
µ
) | µ = 1, 2, . . . , p}. This set is a
priori knowledge that must be known by the AM system.
There are two types of AM for pattern recognition, namely auto-associative
memory (auto-AM) and hetero-associative memory (hetero-AM). In auto-AM,
the system recognizes an input pattern and produces its associated output pat-
tern. Therefore, for a given set of associations, (a
µ
, b
µ
), the auto-AM rule is
true under the following condition: a
µ
= b
µ
, ∀µ ∈ {1, 2, . . . , p}. Auto-AM
enables the system (either neural network or learning system) to pass input
patterns through as output patterns without any changes, due to input pat-
terns and output patterns having similar characteristics. The Hopfield network
is an example of an auto-AM algorithm.
Alternatively, hetero-AM pattern recognition follows the rule of association;
incomplete input patterns can lead to complete output patterns. Therefore, in
terms of the association set, (a
µ
, b
µ
), when a
µ
= b
µ
, the following rule applies:
for ∃µ ∈ {1, 2, . . . , p}. In this case, given distorted pattern a
x
of original
pattern a
x
, the hetero-AM system will be able to gain full recall of pattern a
x
.
Bidirectional associative memory (BAM) is a neural network approach that
adopts the hetero-AM concept. Hetero-AM also offers the ability to conduct
a recognition based on patterns of different sizes, such as demonstrated in the
work of Kosko [66].
Associative Memory approaches, such as the Hopfield network and Fuzzy
Associative Memory (FAM) [67], tend to be computationally intensive and
iterative. In contrast, Morphological Associative Memory (MAM) [68] pro-
vides a solution within a single iteration, and thus implements single-cycle
learning. However, MAM is a tightly coupled scheme, which relies on global
maximum/minimum computations and is not readily distributed.
Graph Neuron (GN) based algorithms, including the HGN and DHGN,
implement an auto-associative memory approach in their recognition proce-
dure. GN has the ability to recall patterns that have been memorized by the
