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sigma (t)
sigma=0.1
sigma=0.2
sigma=0.3
sigma=0.4
sigma (t)
sigma=0.1
sigma=0.2
sigma=0.3
sigma=0.4
sigma (t)
sigma=0.1
sigma=0.2
sigma=0.3
sigma=0.4
sigma (t)
sigma=0.1
sigma=0.2
sigma=0.3
sigma=0.4
20
40
60
80
100
20
40
60
80
100
20
40
60
80
100
20
40
60
80
100
Iterations
Iterations
Iterations
Iterations
Fig. 1.
Time-dependent
σ
d
: (a) edge length variance (b) network size (c) quantization
error (d) learning time
Comparing network sizes, Fig. 1(b), and quantization error, Fig. 1(c), we
observe that for the highest values of
σ
d
, the set of antibodies reduces to just
a few entities; on the other hand - for the lowest values almost all antibodies
(universal and over-specialized) are retained in the system's memory. It is not
surprising that the quantization error for a huge network (e.g.
σ
d
=0
.
1) is
much lower than for smaller nets. Still, the time-dependent
σ
d
(
t
) gives similarly
low quantization error for moderate network size. Also, both measures stabilize
quickly during learning process. Learning time, Figure 1(d), is - to some extent
- a function of network size. Thus, for the reference model, it is not only low
but very stable over all iterations.
sigma (t)
sigma=0.05
sigma=0.10
sigma=0.15
sigma=0.20
sigma=0.25
sigma (t)
sigma=0.05
sigma=0.10
sigma=0.15
sigma=0.20
sigma=0.25
sigma (t)
sigma=0.05
sigma=0.10
sigma=0.15
sigma=0.20
sigma=0.25
sigma (t)
sigma=0.05
sigma=0.10
sigma=0.15
sigma=0.20
sigma=0.25
20
40
60
80
100
20
40
60
80
100
20
40
60
80
100
20
40
60
80
100
Iterations
Iterations
Iterations
Iterations
Fig. 2.
Time-dependent
σ
s
: (a) edge length variance (b) network size (c) quantization
error (d) learning time
In the next experiment - dually - we compare reference model and another
five models with constant
σ
s
(and varying
σ
d
). Analogically to the first case,
the values of
σ
s
varied from the initial value 0
.
05 up to the final value in the
reference model 0
.
25 by 0
.
05 step. The results are presented in Fig. 2. Due to the
space limitations, we restrict the discussion of the results to the conclusion that
also in this case time-dependent parameter
σ
s
(
t
) had a strong, positive influence
on the resulting immune model.
A weakness of the approach seems to be the diculty in selecting appropriate
values of the parameters for a given dataset. We investigated independently
changes to the values of both parameters, but it turns out that they should be
changed ”consistently”; that is the antibodies should not be removed too quickly,
