T Cell–Inspired Algorithms - Immunological Computation: Theory and Applications - page 81

h e parameter r “specifi es” the radius of detection of each detector of fi xed size.
Accordingly, for a new sample, s is detected by a detector d , if the distance between
d and s is at most r . Because we do not want the detectors to match self-points, the
shortest allowable distance for a good detector to the self-set is r . h erefore, the
parameter r also specifi es the allowed variability in the self-space.
To determine if a detector d matches a self-point, the algorithm calculates
the k -nearest neighbors of d in the self-set. It then calculates the median distance
of these k neighbors. If this distance is less than r , the detector d is considered to
match self. h is strategy makes the algorithm more robust to noise and outliers.
h e function µ d ( x) is the matching function used for single the detector d . It
indicates the degree of matching between x , an element of the self/nonself space,
and d . It is defi ned as

2

dx
r

−

() xe

2

2

d

Each detector has an assigned age that is increased at each iteration, if it is inside the
self-set. If the detector becomes old, that is, it reaches the maturity age t and has not
been able to move out of the self-space, it will be replaced by a new randomly gener-
ated detector. h e age is reset to zero when the detector is outside of the self-space.
h e parameter η represents the size of the step used to move the detectors. To
guarantee that the algorithm converges to a stable state, it is necessary to decrease
this parameter at each iteration in such a way that lim i → ∞ η i = 0. h e following

updating rule is used:

NS Algorithm 4 describes an RNS algorithm .

i

i

e

o

NS Algorithm 4: Real-valued-negative-selection, rns( r , η , t , k )
r radius of detection
η adaptation rate, i.e., the rate at which the detectors will adapt on
each step
t once a detector reaches this age it will be considered to be mature
k number of neighbors to take into account
1 while stopping criteria is not satisfi ed
2 for each detector d do

3 NearCells ← k -nearest neighbors of d in the Self set

4 NearCells is ordered with respect to the distance to d

5 NearestSelf ← median of NearCells

<

6 If dist (d, NearestSelf) r h en

∑
∑

c NearCells d ( −

−

c )

7 dir ←

c NearCells d ( c )