Immunity-Based Computational Models - Immunological Computation: Theory and Applications - page 49

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v

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c

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Figure 3.4 A detector represents a subset of the shape-space, in fact, a subset
of the nonself space. A detector corresponds to an N -dimensional hypersphere;
a hypersphere may be represented by its center (c) and radius ( ε ), where V ε
denotes the hypersphere's volume.

agent, among others; however, such type of implementations may be di cult to
analyze (Hofmeyr, 1999).
Usually, a detector describes a region of the shape-space; therefore, it may be
defi ned by a formal representation of a subspace of the shape-space. For instance,
when the shape-space is a Euclidean space, a detector could have the shape of a
hypersphere; thus, it may be defi ned by a hypersphere's equation, which is determined
by two parameters—its center and radius (Figure 3.4). Another example of a detector
is a hyperrectangle, which can be characterized by two of its (opposite) corners, simi-
lar to the way a rectangle is specifi ed in two dimensions by the left-hand side lower
corner and right-hand side upper corner. h ereby, in the case of binary representa-
tions, a detector may be defi ned by a binary string (which may be thought of as
the “center” of the detector) and threshold value; the detector will represent all the
strings that are at a distance from the center below such threshold.
In specifi c applications, a set of variables will defi ne the shape-space. h erefore,
a detector is defi ned on a data space; and although a detector could be defi ned
as one of the points in the dataset, in general, this is not the case. A detector is
rather defi ned as a set of data points. Intuitively, the “size” of the set associated to
a detector will indicate its specifi city; thus, the larger the set, the more general the
detector will be. Accordingly, the smaller the set of points covered by a detector, the
more specifi c the detector.
A matching rule is a key concept in immune algorithms, because it is used to
determine when a detector matches a data item. A particular immune algorithm
is distinguished by the way entities are modeled, as well as the matching rule and
the mechanisms to generate the detectors. It is important to note that the matching
rule is used in both detector generation and detection.