Bio-medical Ontologies Maintenance and Change Management

194 I.R. Godínez et al.
3.1.1 New Alpha-Beta Heteroassociative Memory Type Max
LEARNING PHASE
Let A = {0, 1} ,n,p ∈ Z + ,μ ∈{1, 2, ...p} ,i ∈{1, 2, ..., p} and j ∈{1, 2, ...n}
and let x ∈ An and y ∈ Ap be an input and output vectors, respectively. The
corresponding fundamental set is denoted by {(xμ , yμ ) | μ =1, 2, ..., p}.
The fundamental set must be built according to the following rules. First,
all the y vectors are built with the one-hot codification. Second, to each yμ vector corresponds one and only one xμ vector, this is, there is only one
couple (xμ , yμ ) in the fundamental set.
STEP 1:
For each μ ∈ {1, 2, ...p}, from the couple (xμ , yμ ) build the matrix:
[yμ ⊠ (xμ ) t ] mxn
STEP 2:
Apply the binary ∨ operator to the matrices obtained in step 1 to get
the new alpha-beta heteroassociative memory type max V as follow: V =
p�
[yμ ⊠ (xμ ) t ]withtheij−th component given by:
μ=1
vij =
p�
μ=1
α(y μ
i ,xμ
j )
RECALLING PHASE
STEP 1:
A pattern x ω is presented to V, the Δβ operation is done and the resulting
vector is assigned to a vector called z ω : z ω = VΔβx ω
The i−th component of the resulting column vector is:
z ω i =
n�
j=1
β(vij,x ω j )
STEP 2:
It is necessary to build the max sum vector s according to the definition
1, therefore the corresponding yω is given as:
�
1ifsi = �
y ω i =
=1} .
0 otherwise
sk AND z
k∈θ
ω i =1
where θ = {i|zω i
Example 1. Let x1 ,x2 ,x3 ,x4 be the input patterns
x 1 ⎛ ⎞
1
⎜ 0 ⎟
= ⎜ 1 ⎟
⎝ 1 ⎠
0
,x2 ⎛ ⎞
0
⎜ 1 ⎟
= ⎜ 0 ⎟
⎝ 0 ⎠
0
,x3 ⎛ ⎞
1
⎜ 0 ⎟
= ⎜ 0 ⎟
⎝ 1 ⎠
0
,x4 ⎛ ⎞
1
⎜ 1 ⎟
= ⎜ 0 ⎟
⎝ 1 ⎠
1
(1)