Bio-medical Ontologies Maintenance and Change Management

192 I.R. Godínez et al.
The ij-thentryisgivenas:vij = p �
μ=1
B, ∀i ∈{1, 2,...,n} , ∀j ∈{1, 2,...,n}.
α � x μ
i ,xμ
�
j .Itisobviousthatvij ∈
RECALLING PHASE
A pattern x ω , that could be or not a fundamental pattern, with ω ∈
{1, 2, ..., p} is presented to the alpha-beta autoassociative memory of kind
∨ and the following operation is done: VΔβx ω . The result is a column vector
of dimension n, withthei-th component given as:
(VΔβx ϖ ) i =
n�
j=1
β � vij,x ϖ j
Remark 1. Note that alpha-beta autoassociative memories of kind ∧ are built
by duality from alpha-beta autoassociative memories of kind ∨. Inorderto
do so, the following changes are made:
• Use operator ∨ instead of operator ∧.
• Use operator ∧ instead of operator ∨.
• Use operator ∇β instead of operator Δβ; operator∇β is defined as:
(Λ∇βx ϖ ) i =
n�
j=1
�
β(λij,x ϖ j )
The greatest limitation of alpha-beta associative memories is perhaps that
they only work with binary data, being unable to manipulate integer or real
numbers. However, there have been numerous efforts to extend the original
model [25]-[28]. With these advances, alpha-beta memories can be applied to
binary and integer pattern recognition, as well as gray-level and color image
processing, and all the different fields these imply.
3 Proposed Solution
This section is dedicated to the main contribution presented in this chapter,
the Alpha-Beta MultiMemories Classifier, used to broach the subjects of promoter
identification and splice-junction zone localization. First, an extension
to the heteroassociative kind of the original alpha-beta associative memory
model is introduced, followed by a new model of associative memory based
in the former extension: the alpha-beta heteroassociative multimemories. Finally,
the concepts presented in the model of multimememories are applied
to build the proposed classifier.
3.1 New Alpha-Beta Heteroassociative Memory
The alpha-beta associative memories model guarantee, through theorems 4.28
and 4.32 from [22], the complete recall of the fundamental set, but only for