Bio-medical Ontologies Maintenance and Change Management

Classifying Patterns in Bioinformatics Databases 199
For every μ ∈{1, 2, ...p}, from the couple (x μ , y μ ) the vector partition
operator is applied to each x μ , then the new fundamental set is expressed by:
� (x μ1 , y μ ), (x μ2 , y μ ), ..., (x μq , y μ ) | μ =1, 2, ..., p, l =1, 2, ...q �
Now, from the couple (xμl , yμ � ) the q matrices are built as follows:
μ μl t y ⊠ (x ) �
mx( n
q ). Then apply the binary � operator to the corresponding
matrices obtained to get Λl as follows: Λl = p � �
μ μl t y ⊠ (x )
μ=1
�
mx( n
q ).The
ij−th component of each l matrices is given by:
λ l ij =
p�
μ=1
α(y μ
i ,xμl
j )
RECALLING PHASE
STEP 1:
A pattern xω , that could be or not from the fundamental set, is presented
to Λl . First, we have to apply the vector partition operator to xω :
ρ(x ω ,q)= � x ω1 , x ω2 , ..., x ωq�
For every Λ l matrix and x ωl partition with l = {1, 2, ..., q}, the∇β operation
is done and the resulting vector is assigned to a vector called z ωl : z ωl =
Λ l ∇βx ωl the i−th component of the resulting vector is given as:
z ωl
i =
n�
j=1
β(λ l ij ,xωl
j )
STEP 2:
It is necessary to build the min sum vector r according to the definition
3, therefore the corresponding zint ωl is given as:
zint ωl
i =
� 1ifri = �
k∈θ
0 otherwise
rk AND zint ωl
i =0
where θ = � i|zint ωl
i =0� .
Once we have obtained each zint ωl vector from step 2, in order to obtain
one resultant vector the step 3 is applied.
STEP 3:
An intermediate vector I is created. This vector will contain the sum of
the i − th components of the zint ωl vectors:
I ω i =
q�
l=1
zint ωl
i
then the corresponding y ω vector is obtained by: