Bio-medical Ontologies Maintenance and Change Management

200 I.R. Godínez et al.
y ω i =
⎧
⎨
1 I
⎩
ω i = p �
k=0
0 otherwise
Due to a matter of space we only show an example of the alpha-beta
heteroassociative multimemory type max, the type min could be induced
from this.
Example 2. Let x 1 ,x 2 ,x 3 ,x 4 be the input patterns
x 1 ⎛ ⎞
1
⎜ 0 ⎟
⎜
= ⎜ 1 ⎟
⎜ 1 ⎟ ,x
⎟
⎝ 0 ⎠
0
2 ⎛ ⎞
0
⎜ 1 ⎟
⎜
= ⎜ 0 ⎟
⎜ 0 ⎟ ,x
⎟
⎝ 0 ⎠
1
3 ⎛ ⎞
1
⎜ 0 ⎟
⎜
= ⎜ 0 ⎟
⎜ 1 ⎟ ,x
⎟
⎝ 0 ⎠
1
4 ⎛ ⎞
1
⎜ 1 ⎟
⎜
= ⎜ 0 ⎟
⎜ 1 ⎟
⎝ 1 ⎠
1
The output vectors are built with the One-Hot codification, and for each
output pattern corresponds one and just one input pattern, therefore the
fundamental set is expressed as follows:
�� x 1 ,y 1 � , � x 2 ,y 2� , � x 3 ,y 3� , � x 4 ,y 4��
Each input pattern from the fundamental set must be divided into as many
partitions as we choose, in this case in 3. Therefore, it is necessary to verify
whether it is possible to divide the input pattern through the definition 6.
n
q
6
= =2∈ Z+
3
Since 2 ∈ Z + , it is possible to divide each input pattern in 3 partitions
of equals dimension. After that, the vector partition operator is applied, obtaining
the new input patterns similar to this:
ρ � x 1 , 3 � = �� 10 � , � 11 � , � 00 ��
ρ � x 2 , 3 � = �� 01 � , � 00 � , � 01 ��
ρ � x 3 , 3 � = �� 10 � , � 01 � , � 01 ��
ρ � x 4 , 3 � = �� 11 � , � 01 � , � 11 ��
then the new fundamental set is:
�� x 11 ,y 1 � , � x 21 ,y 2� , � x 31 ,y 3� , � x 41 ,y 4� , � x 12 ,y 1� , � x 22 ,y 2� , � x 32 ,y 3� ,
� x 42 ,y 4 � , � x 13 ,y 1� , � x 23 ,y 2� , � x 33 ,y 3� , � x 43 ,y 4��
finally, from the new fundamental set, the q matrices V l are built:
I ω k