Information Technology Reference
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similar (in fact: redundant) cells are removed from the memory. This step repre-
sents network suppression of the immune cells. Lastly
r
% (one more parameter)
worst individuals in
M
are replaced by freshly generated cells. This ends one
epoch, and next epoch begins until a termination condition is met.
Among all the parameters mentioned above the crucial one seems to be the
σ
s
as it critically influences the size of the global memory. Each memory cell can
be viewed as an exemplar which summarizes important features of ”bundles” of
stimulating it antigens.
3.2
Robust Construction of Mutated Antibodies
In case of high-dimensional data, such as text data represented in vector space,
calculation of stimulation level is quite costly (proportional to the number of
different terms in dictionary). Thus, the complexity of an immune algorithm
can be significantly reduced if we could restrict the number of required expensive
recalculations of stimulation level. The direct, high-dimensional calculations can
be replaced by operations on scalar values on the basis of the simple geometrical
observation that a stimulation of a mutated antibody clone can be expressed in
terms of original antibody stimulation.
Such optimization is based on the generalized Pythagoras theorem: if
v
1
,
v
2
,
v
3
are the sides of a triangle (
v
1
+
v
2
+
v
3
=0)then
2
2
+
2
|
v
3
|
=
|
v
1
|
|
v
2
|
−
2
k
)
c
,
where
c
is cloned antibody,
d
is antigen (document) and
k
is the mutation level
(random).
Taking advantage of equation (4) and Pythagoras theorem (where
v
1
:=
d
=
|
v
1
||
v
2
|
cos
(
v
1
,v
2
).
We can define mutated clone
m
as:
m
=
kd
+(1
−
k
m
) and having calculated original antibody
stimulation
aff
(
c, d
), we can calculate mutated clone stimulation level
aff
(
m, d
).
Dually, we can find mutation threshold
k
so that mutated antibody clone stim-
ulation
aff
(
m, d
)
<σ
d
. Precisely, we are looking for
k
0
such that
aff
(
m, d
)=
σ
d
,
which in turn can be used to create mutated antibody for random mutation
level
k
·
d
,
v
2
:=
c
=(1
−
k
)
·
c
,
v
3
:=
−
(0
,k
0
). The advantage of such an approach is the reduction of the
number of inecient (too specific) antibodies, which would be created and im-
mediately removed from the clonal memory. Analogically to the previous in-
ference, if we define
p
:=
aff
(
c, d
),
x
:=
∈
+
p
2
+
σ
d
(
p
−
p
|
d
|
|
c
|
|
d
|−
c
),
y
:=
|
(
p
2
2
+
p
2
2
σ
d
(
2
2
+2
p
|
d
|
−
2
p
|
c
||
d
|
|
c
|
−
|
d
|
−|
c
|
|
c
||
d
|
)and
z
:=
σ
d
·|
d
−
1)
·
(
σ
d
−
1),
then
k
0
=
|c|·
(
x
+
z
)
.
y
3.3
Stabilization Via Time-Dependent Parameters
Typical problem with immune based algorithms is the stabilization of the size
of the memory cells set. This explains why we decided to use time dependent
parameters. For each parameter
p
, we defined its initial value
p
0
and the final
value
p
1
as well as the time-dependent function
f
(
t
), such that
p
(
t
)=
f
(
t
)and
p
(0) =
p
0
,
p
(
T
)=
p
1
where
T
is the number of learning iterations.
In particular, both
σ
s
(
t
)and
σ
d
(
t
) are reciprocally increased, while
m
b
(
t
)
- the number of clones produced by a cell - is linearly decreased with time:
