B Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 144

h is algorithm also proposes a hierarchical organization of the IN. Hence,
the goal is to keep a small network organized in subnetworks. An interaction
occurring between an external agent and any D-W-B cell in the IN is called an
external interaction. However, those interactions occurring among D-W-B cells is
called internal interactions . h e main idea is then to cluster D-W-B cells to form
subnetworks. Hence, if high-level (coarse) interactions are considered, then, inter-
subnetwork interactions should be considered. Accordingly, in the case of external
interactions, contacts between antigens and subnetworks are taken into account,
instead of considering interactions of the antigen with all the D-W-B cells in the
IN. h is is intended to reduce the number of computations, because when external
stimuli appear, only some subnetworks are stimulated. Figure 5.13 illustrates the
hierarchical organization of the D-W-B cell network model and external and inter-
nal interactions. In contrast, if low-level relations are considered, then interactions
among all the D-W-B cells in the network should be evaluated.
Clustering of D-W-B cells in subnetworks is done by associating a centroid
to each cluster defi ned as the centroid of all the D-W-B cells in the cluster. h us,
the network is characterized by such centroid, which is used to compute the
contributions of the D-W-B cells in internal and external interactions.
It is important to note that by clustering the D-W-B cells, a signifi cant reduction
on the computation may be achieved as follows. Assume that the network consists
of N D-W-B cells. h en, the number of internal interactions is O ( N 2 ). For the sake
of a general analysis, assume that the IN consists of K subnetworks of equal size.
h ereby, the number of interactions of a D-W-B cell reduced to those interactions
in the corresponding subnetwork (intra-network interactions) is O ( N 2 / K ); also, the
number of inter-subnetwork interactions is K

−

1.

5.3 A General Model of Artifi cial Immune Network
González et al. (2005) proposed an algorithm, which presents common features of
various AIN models. h is general AIN (GAIN) algorithm is shown in Figure 5.14.
h e fi rst step of this algorithm creates an initial set of B cells denoted by B . h e
second step calculates the stimulation for each of the antigen and B cell. h is can
be represented as follows:

f stimulation

A

:A B →ℜ

In some models, the stimulation is the function of a nity, which is given as
follows:

f

A

(,): a b g f ( (,)) a b

stimulation affinity