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paradigm: supervised or unsupervised. As SRABNET is founded on supervised
learning, new ideas have been proposed for the stages that follow.
2.1
Weight Updating
The weight updating procedure for SRABNET is similar to the one used in
Learning Vector Quantization (LVQ) [18], [19]. Equation (2) shows the weight
updating rule used here, where α is the learning rate and Ab K is the antibody
that wins the competition for representing antigen Ag . In other words, the most
similar antibody is the one that presents the highest anity (minimum Euclidean
distance) to the given antigen as in equation 1.
K = arg min k
Ag
Ab k
,
k
(1)
Ab K ( t +1)= Ab K ( t )+ α ∗ ( Ag − Ab K ( t )) , If Class ( Ab k )= Class ( Ag )
Ab K ( t )
(2)
α
( Ag
Ab K ( t )) , Otherwise.
According to equation 2, if the antibody has the same label, or class, of the anti-
gen which it is recognizing, its weights are updated towards the weight pattern
of the antigen. Otherwise, the antibody is moved away from the antigen in the
shape space.
2.2
Network Growing
The network growing is performed at each epoch. The antibody chosen to be
duplicated is the one that represents an antigen with the lowest anity (highest
Euclidean distance). The location of the new antibody in the shape space, asso-
ciated with a weight vector, is defined as the midpoint of the straight line con-
necting the antibody to be duplicated and that antigen with the lowest anity.
In Fig. 1(a-b) the duplication process is depicted; the sample with a circle is
the antigen with the lowest anity and the cloned antibody is marked with a
square. The new antibody will belong to the class with the maximum number
of elements (antigens) among the elements that will now be represented by this
new antibody. A tie will lead to a random choice of the class. Depending on
the distribution of antigens in the shape space, the class to be attributed to the
newly-generated antibody may differ from the class of its immediate ancestor as
illustrated in Fig. 1(b-c). The dynamic of the whole process to obtain the final
network structure can be seen in Fig. 1(a-h).
2.3
Network Pruning
The pruning on the network occurs when an antibody does not win or when it
does not represent at least one antigen. In supervised learning, each class should
have at least one antibody representing its samples. Based on this requisite, the
pruning process is not performed if the antibody to be pruned is the unique
representative of that class. In a more immunological view, the antibodies that
were not stimulated by any antigen suffer apoptosis.
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