Information Technology Reference
In-Depth Information
computed for both subsets. The results are shown in Figure 4(b) - respective
learning data sets are depicted with black lines while test data sets with grey
lines. Nevertheless quantization error for learning document sets are similar, the
difference lies in test sets and the hierarchical network is clearly
overfitted
. Again,
there's no room to go into detailed study here, but it can be shown that this un-
desirable behavior is the result of the noised information brought by additional
terms, which finally appears to be not meaningful in the particular context (and
thus are disregarded in contextual weights
w
dtG
).
4.7
Immune Network Structure Investigation
To compare robustness of different variants of immune-based models, in each
learning iteration, for each of the immune networks: contextual [Fig. 5(b)], hier-
archical [Fig. 5(c)], global [Fig. 5(d)] and MST built on SOM grid [Fig. 3(c)], the
distributions of the edge lengths have been computed. Next, the average length
u
and the standard deviation
s
of the length have been calculated and edges have
been classified into five categories, depending on their length,
l
: shortest edges
with
l
≤
u
−
s
,shortwith
l
∈
(
u
−
s, u
−
0
.
5
s
], medium with
l
∈
(
u
−
0
.
5
s, u
+0
.
5
s
],
long with
l
(
u
+0
.
5
s, u
+
s
] and very long edges with
l>u
+
s
.
Additionally, in Figure 5(a), we can see average length of the edges for hier-
archical and contextual immune networks (dashed and solid black lines, respec-
tively) and complete graphs on both models' antibodies (cliques - depicted with
grey lines). Actually, in both cases clustering structure has emerged and the aver-
age length of the edge in the immune network is much lower than in the complete
graph. However, the average length for the contextual network is lower, whereas
variance of this length is higher. It signifies more explicit clustering structure.
∈
idiotypic net [C]
clique graph [C]
idiotypic net [H]
clique graph [H]
u−s
u−.5s
u
u+.5s
u+s
u−s
u−.5s
u
u+.5s
u+s
u−s
u−.5s
u
u+.5s
u+s
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. 5.
Edge length distrib.: (a) complete (b) contextual (c) hierarchical (d) global net
There are quite a few differences in edge length distribution. One can notice
than in all models, the number of shortest edges diminishes with time. It is
coherent with the intention of gradual elimination of the redundant antibodies
from the model. However, such elimination is much slower in case of the global
model, what is another reason of slow convergence and high learning time. Also in
case of SOM model, which has a static topology and no removal of inecient cells
is possible, we can see that the model slowly reduces the number of redundancies,
represented by too similar referential vectors.
