Bio-medical Ontologies Maintenance and Change Management

Classifying Patterns in Bioinformatics Databases 203
Once we have the fundamental sets we must apply the vector partition operator
to each one, in this case let q = 3 be the number of partitions. In order
to apply the vector partition operator we need to verify if it is possible to
partition the vector in this manner:
n
q
6
= =2∈ Z+
3
as 2 ∈ Z + it is possible to divide the vector, therefore the new fundamental
sets are given as:
�� x 11 ,y 1 � , � x 21 ,y 2� , � x 31 ,y 3� , � x 41 ,y 4� , � x 51 ,y 5� , � x 61 ,y 6� ,
� x 12 ,y 1 � , � x 22 ,y 2� , � x 32 ,y 3� , � x 42 ,y 4� , � x 52 ,y 5� , � x 62 ,y 6� ,
� x 13 ,y 1 � , � x 23 ,y 2� , � x 33 ,y 3� , � x 43 ,y 4� , � x 53 ,y 5� , � x 63 ,y 6��
�� x 11 ,yz 1 � , � x 21 ,yz 2� , � x 31 ,yz 3� , � x 41 ,yz 4� , � x 51 ,yz 5� , � x 61 ,yz 6� ,
� x 12 ,yz 1 � , � x 22 ,yz 2� , � x 32 ,yz 3� , � x 42 ,yz 4� , � x 52 ,yz 5� , � x 62 ,yz 6� ,
� x 13 ,yz 1 � , � x 23 ,yz 2� , � x 33 ,yz 3� , � x 43 ,yz 4� , � x 53 ,yz 5� , � x 63 ,yz 6��
now the heteroassociative multimemories type Max and Min are created.
V 1 ⎛ ⎞
12
⎜ 21 ⎟
⎜
= ⎜ 12 ⎟
⎜ 11⎟,
V
⎟
⎝ 12⎠
11
2 ⎛ ⎞
11
⎜ 22 ⎟
⎜
= ⎜ 21 ⎟
⎜ 21⎟,
V
⎟
⎝ 21⎠
12
3 ⎛ ⎞
22
⎜ 21 ⎟
⎜
= ⎜ 21 ⎟
⎜ 11 ⎟
⎝ 11⎠
22
Λ 1 ⎛ ⎞
01
⎜ 10 ⎟
⎜
= ⎜ 01 ⎟
⎜ 00⎟,
Λ
⎟
⎝ 01⎠
00
2 ⎛ ⎞
00
⎜ 11 ⎟
⎜
= ⎜ 10 ⎟
⎜ 10⎟,
Λ
⎟
⎝ 10⎠
01
3 ⎛ ⎞
11
⎜ 10 ⎟
⎜
= ⎜ 10 ⎟
⎜ 00 ⎟
⎝ 00⎠
11
Once we have trained the ABMMC, in order to classify a pattern, be it
known or unknown, it is necessary to do the following procedure. Let x4 be the input pattern to be classified, then the pattern is presented to both
alpha-beta heteroassociative multimemories type Max and Min, obtaining
the following vectors:
ymax = � V l Δβx 4l� ⎛ ⎞
0
⎜ 0 ⎟
⎜
= ⎜ 0 ⎟
⎜ 1 ⎟
⎝ 0 ⎠
0