Bio-medical Ontologies Maintenance and Change Management

196 I.R. Godínez et al.
VΔβx 4 ⎛ ⎞
12112
⎜
= ⎜ 21222 ⎟
⎝ 12212
11211
⎠ Δβ
⎛ ⎞
1
⎜ 1 ⎟
⎜ 0 ⎟
⎝ 1 ⎠
1
=
⎛ ⎞
0
⎜ 1 ⎟
⎝ 1 ⎠
1
the resulting vector is not an output pattern from the fundamental set, in
other words, it is an ambiguous pattern. According to step 2 of the recall
phase of the new heteroassociative memory type Max, the resulting vector is
known as z4 , then the max sum vector s must be built:
z 4 ⎛ ⎞ ⎛ ⎞
0 3
⎜
= ⎜ 1 ⎟ ⎜
⎟
⎝ 1 ⎠ , s = ⎜ 1 ⎟
⎝ 2 ⎠
1 4
after that, according to the expression 1 of the recall phase the corresponding
output pattern is:
y 4 ⎛ ⎞
0
⎜
= ⎜ 0 ⎟
⎝ 0 ⎠
1
since the minimum value of sj where z 4 j
=1∀j ∈{1, 2, 3, 4} is 4.
Remark 2. Note that alpha-beta heteroassociative memories of kind ∧ are
built by duality from alpha-beta heteroassociative memories of kind ∨. In
order to 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 ω ) i =
n�
j=1
β(λij,x ω j )
• Use zero-hot vectors instead of one-hot vectors when building the fundamental
set.
• Use min sum vectors instead of max sum vectors to obtain the output
vector according to:
�
0ifri = �
where θ = {i|z ω i
y ω i =
=0} .
1 otherwise
rk AND z
k∈θ
ω i =0