IEEE Computational Intelligence Magazine - May 2018 - 27

proposed in [40], as in the previous study, but with the follow-
ing considerations:
❏ For assessing the scalability with respect to the number of
classes, the datasets are generated by varying the number of
classes from 3 to 15. In all cases, a set of 25 features and
1,500 samples are fixed.
❏ For assessing the scalability with respect to the number of
instances, the number of classes is fixed in 3 and the number
of features is kept in 25. The number of instances for each
dataset ranges from 800 to 6,000, with a step size of 400.

Fig. 6 depicts the behavior of MC2ESVM under these con-
ditions. Based on these figures, we can remark the following:
❏ The number of evaluations increases as either the number
of instances or the number of classes is increased. This is
an expected result, since MC2ESVM deals with more com-
plex problems.
❏ The number of classes seems to be more harmful in the scal-
ability of MC2ESVM. This may be due to the fact that, as
the number of classes grows, the complexity of the decision
boundaries is increased, making harder the recognition.

(a) Artificial Dataset

(b) MC2ESVM

(c) OVO

(d) OVA

(e) MSVM-WW

(f) MSVM-LLW

(g) MSVM-CS

(h) MSVM2

FigurE 5 decision boundary for each of the SVM multiclass extensions.

7,000
6,000
5,000
4,000

.105

1.5
Number of Evaluations

Number of Evaluations

8,000

3,000
400 1,200 2,000 2,800 3,600 4,400 5,200 6,000
Number of Instances
(a) Instances

1.0

0.5

0.0

3

5

7
9
11
Number of Classes
(b) Classes

13

15

FigurE 6 Scalability when either the number of classes or instances increases.

may 2018 | IEEE ComputatIonal IntEllIgEnCE magazInE

27



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