Bio-medical Ontologies Maintenance and Change Management

Classifying Patterns in Bioinformatics Databases 193
the autoassociative kind and not for the heteroassociative one. Therefore, in
this subsection we propose a new heteroassociative algorithm, based on the
original model, to ensure this correct recall.
In order to guarantee the complete recall of the fundamental set it is
necessary to redefine the learning and recalling phase of the original model,
building new ones. The lemmas and theorems that prove the complete recall
in this new alpha-beta heteroassociative memories are discussed in [29],[30].
Definition 1. Let V be an alpha-beta heteroassociative memory type Max
and {(x μ , y μ ) | μ =1, 2, ..., p} its fundamental set with x μ ∈ A n and y μ ∈
A p ,A = {0, 1} ,B = {0, 1, 2} ,n ∈ Z + . The sum of the components of the
i−th row of V with value equal to one is given as:
n�
si =
Tj
j=1
where T ∈ Bn �
1 ←→ νij =1
and its components are defined as: Ti =
0 ←→ νij �= 1
∀j ∈{1, 2, ..., n} and the si components conform the max sum vector with
s ∈ Zp .
Definition 2. Let xω ∈ An with ω, n ∈ Z + ,A = {0, 1} ; each component of
the negated vector of xω , denoted by ˜xω , is given as:
˜x ω i =
�
ω 1 xi =0
0 xω i =1
Definition 3. Let Λ be an alpha-beta heteroassociative memory type Min
and {(x μ , y μ ) | μ =1, 2, ..., p} its fundamental set with x μ ∈ A n and y μ ∈
A p ,A= {0, 1} ,B = {0, 1, 2} ,n∈ Z + . The sum of the components with value
equaltozeroofthei−th row of Λ is given as:
n�
ri =
Tj
j=1
where T ∈ Bn �
1 ←→ λij =0
and its components are defined as: Ti =
0 ←→ λij �= 0
∀j ∈{1, 2, ..., n} and the ri components conform the min sum vector with
r ∈ Zp .
Definition 4. Let y ω ∈ A n be a binary vector with ω, n ∈ Z + ,A = {0, 1}.
Its k-th component is assigned as follows: y μ
k = 1,andyμ j = 0 for j =
1, 2,...,k− 1,k+1,...,m where k ∈{1, 2,...,m} and k = μ. This is known
as one-hot vector.
Definition 5. Let y ω ∈ A n be a binary vector with ω, n ∈ Z + ,A= {0, 1}. Its
k-th component is assigned as follow: y μ
k =0,andyμ j =1for j =1, 2,...,k−
1,k+1,...,m where k ∈{1, 2,...,m} and k = μ. This is known as zero-hot
vector.