Bio-medical Ontologies Maintenance and Change Management

198 I.R. Godínez et al.
RECALLING PHASE
STEP 1:
A pattern xω , that could be or not from the fundamental set, is presented
to each Vl , l =1, 2,...,q. First, we have to apply the vector partition operator
to xω :
ρ(x ω ,q)= � x ω1 , x ω2 , ..., x ωq�
then for each Vl matrix and xωl partition with l = {1, 2, ..., q}, theΔβ
operation is done and the resulting vector is assigned to a vector called zωl :
zωl = VlΔβxωl .Thei−th component of the resulting vector is given as:
z ωl
i =
n�
j=1
β(V l ij,x ωl
j )
STEP 2:
It is necessary to build the max sum vector s according to the definition
1, in order to obtain the corresponding zint ϖl given as:
zint ωl
i =
� 1ifsi = �
k∈θ
0 otherwise
sk ∧ zint ωl
i =1
where θ = � i|zint ωl
i =1� .
STEP 3:
An intermediate vector I is created. This vector will contain the sum of
the i−th components of the zint ϖl vectors:
I ϖ i =
q�
l=0
zint ϖl
i
then the corresponding yϖ vector is obtained by:
y ϖ i =
⎧
⎨
1 I
⎩
ϖ i = p �
I
k=1
ω k
0 otherwise
3.2.2 Alpha-Beta Heteroassociative Multimemories of Type Min
LEARNING PHASE
Let A = {0, 1} ,n,p ∈ Z + ,μ ∈{1, 2, ...p} ,i ∈{1, 2, ..., p} and j ∈{1, 2, ...n}
and let be x ∈ A n and y ∈ A p 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 zero-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.
(2)