Collective Classification for Spam Filtering - Computational Intelligence in Security for Information Systems - page 22

T

1

H GRE
T

≤ − 4(1 − t ) 2 . (2)

t =1

Basedon[12],wehavealso:

exp

t ) 2

T

1

T

− − t ) 2 ≤ − −

4(1 2 (1 (3)

t =1 t =1

Finally, for t < 1 / 2, we have:
exp

t ) 2
T →∞

T

− 2 (1 − → 0 (4)

t =1

(4) ensures that the distribution P t will not be modified once reaching a sucient
number of iterations, and so the convergence of the process. (4) shows that, sim-
ilarly as for AdaBoost, Greedy-Boost decreases the learning error exponentially
fast. Greedy-Boost stops when its error is equal to 0. Practically, Greedy-Boost
reduces the error with a speedy way (only after few iterations). Consequently,
Greedy-Boost performs the classification quickly in real time.

4 Experiments and Results

The used data are a sampling from KDD99 benchmark intrusion detection
dataset. It's a standards data which were prepared and controlled by the MIT
Lincoln laboratories for the DARPA 1998 program. These data are also used for
the intrusion detection challenge of KDD 99 [10]. In this section, we compare
the precision and the recall of AdaBoost, C4.5 and Greedy-Boost applying 10
cross-validation to evaluate the model. We use 10 iterations for AdaBoost and
Greedy-Boost experiments.
Results in table1 show the superiority of Greedy-Boost concerning the pre-
cision of the minority classes (Probe, U2R and R2L). Indeed, the precision of
the prediction of these classes varies between 88% and 100% for Greedy-Boost.
However, for Boosting and C4.5, the prediction precision of these classes cannot
even be calculated since these methods are unable to label a connection of these
classes. Moreover, the precision ensured by Greedy-Boost (Normal and DOS) are
close to 100%. These results are higher than those assured by C4.5 and Boosting.
We calculated the recalls of the various classes ensured by each of the 3 algo-
rithms. Table 2 shows the superiority of greedy-Boost compared with C4.5 and
Boosting, concerning the recall of minority classes. Whereas this recall is null
for C4.5 and Boosting, Greedy-Boost obtains between 44% and 97,1% of recall
for each one of these classes, which constitutes a clear improvement. In the case
of the two most classes, the rates of recall of greedy-Boost are close to 90%,
whereas that of Boosting goes down to 82.0% for the Normal class and that of
C4.5 falls to 89.2% for the DoS class!
Based on the costs matrix table used on KDD99 challenge, the results obtained
on 3 shows that Greedy-Boost presents the lowest average costs compared to