T Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 102

Nonself set

Self-detectors

Figure 4.19 PS approaches. The goal of PS is to cover the self-set with an
appropriate set of detectors.

on the self-sample points. h erefore, a sample point can be classifi ed as belonging
to a cluster by measuring its distance to it. A measure of the distance from a sample
to a cluster may be defi ned in terms of the Euclidean distance to the “cluster cen-
troid.” Another way to defi ne such distance is a “normalized Euclidean distance”
defi ned as

s K

dist ()

where K is the cluster centroid and σ K the standard deviation that represents the
sparseness of the cluster.
A basic positive characterization approach can be defi ned using a nearest
neighbor criterion. A “crisp characterization,” will classify a feature vector as
normal or abnormal. However, a “noncrisp characterization” can be considered by
introducing degrees of “abnormality,” represented by a values in the interval [0, 1],
with 1 indicating “normal” and 0 “abnormal.” h us, a function µ nonself , defi ned on
[0, 1] n associate to each feature vector, measures the distance to the nearest self-
sample point. In this case, no additional model of the self-space was considered;
the self-sample points were considered as the defi nition of the self-sub-space. h us,
µ nonself is defi ned as

K

nonself

() x Dxself (, ) min{(,): dxs s ∈ self }

where d ( x , s ) denotes the distance between x and a self-sample point s . h us,
D ( x , self ) is the distance from x to the closest point in the self-sample set. Other
distance measures such as a “Minkowski metric” can also be used.