Bio-medical Ontologies Maintenance and Change Management

Classifying Patterns in Bioinformatics Databases 197
3.2 Alpha-Beta Heteroassociative Multimemories
Former associative memory models, particularly the alpha-beta model, used
to keep a one-to-one correspondence between the fundamental set and the
associative memory. That is, for each fundamental set there is one associative
memory. To build many associative memories, which behave as one, from one
fundamental set, could be helpful in both the treatment of mixed alterations
and the development of new applications.
As presented in [29], it is possible to divide xω in q equal partitions if
n
q ∈ Z+ .
Definition 6. Let xμ ∈ An be a column vector, with μ, n ∈ Z + ,A = {0, 1},
and q be the number of partitions in which xμ will be divided. The vector
partition operator, denoted by ρ, defined as the set of n
q −dimensional column
vectors and it is denoted by:
ρ(x μ ,q)= � x μ1 , x μ2 , ..., x μq�
such that x μl ∈ A n
q for ∀l ∈ {1, 2, ..., q} , ∀i ∈
{1, 2, ..., n} is expressed as:
x μ1
i
= xμ
j
such as j =
�
�
(l − 1) ∗ n
�
+ i
q
1, 2, ..., n
q
�
and ∀j ∈
3.2.1 Alpha-Beta Heteroassociative Multimemories of Type Max
LEARNING PHASE
Let A = {0, 1} ,n,p ∈ Z + ,μ ∈{1, 2, ...p} ,i ∈{1, 2, ..., p}, j ∈{1, 2, ...n}
and let x ∈ A n and y ∈ A p be input and output vectors, respectively. The
corresponding fundamental set is denoted by {(x μ , y μ ) | μ =1, 2, ..., p}. The
fundamental set must be built according to the following rules: First, the y
vectors are built with the one-hot codification. Second, to each y μ vector
correspond one and only one x μ vector, this is, there is only one couple
(x μ , y μ ) in the fundamental set.
For every μ ∈{1, 2, ...p}, from the couple (x μ , y μ ) the vector partition
operator is applied to each x μ , then the new fundamental set is expressed by:
� (x μ1 , y μ ), (x μ2 , y μ ), ..., (x μq , y μ ) | μ =1, 2, ..., p, l =1, 2, ...q �
Now, from the couple (xμl , yμ ) the q matrices are built as follow:
m×( n
q ).Then apply the binary � operator to the correspond-
� y μ ⊠ (x μl ) t �
ing matrices obtained to get V l as follow: V l = p�
ij−th component of the l matrix is given by:
v l ij =
p�
μ=1
α(y μ
i ,xμl
j )
μ=1
� y μ ⊠ (x μl ) t �
m×( n
q ).The