230 S. Silva et al.
For the comparison with the state-of-the-art classifiers, we have used Weka
3.6.10. Weka is also open source and freely available.^4 In Weka we have used the
default parameters and configurations for each algorithm.
7 Results and Discussion
This section is split in three parts. First we summarize the results of the comparison
between M2GP and a standard GP classifier, and between M2GP and a number
of state-of-the-art classifiers (previously published in Ingalalli et al. 2014 ). Then
we summarize the results of the comparison between M3GP and M2GP, and
between M3GP and the best state-of-the-art classifiers from the first part (previously
published in Muñoz et al. 2015 ). Finally, we present the new results obtained with
eM3GP, comparing them with the ones obtained by the previous methods.
7.1 Results of M2GP
With the goal of comparing the performance of M2GP with the performance of other
GP systems, we chose the range selection method with static threshold selection
mentioned in Sect. 2 (Zhang and Smart 2004 ;Lietal. 2007 ) as the benchmark for
comparison, since it is a fairly standard way of performing multiclass classification
with GP. However, in data sets with a higher number of classes we immediately
observed the often reported inadequacy of this standard GP method to perform
multiclass classification. It was losing the race too quickly, so we abandoned any
further comparison. Just to provide some numbers, on the WAV and SEG data sets
M2GP improved the accuracy upon the standard method in approximately 25 and
55 percentual points, respectively.
We then compared M2GP with a number of classifiers available in Weka.
Random Forests (RF) and Decision Trees (J48) are tree based classifiers; Random
Subspace (RS) and Multi-Class Classifier (MCC) are meta classifiers; Multilayer
Perceptron (MLP) and Support Vector Machines (SVM) are function based clas-
sifiers. Table 2 presents the results already reported in Ingalalli et al. ( 2014 ), the
median and the best accuracy values of the 30 different runs for the test data
sets. We have used the same set of 30 different partitions to perform 30 different
runs with all the classifiers. M2GP used 100 generations and the dimensiond
was automatically chosen during the process of initialization (as explained in
Sect. 3 ), except for the binary class data set (HRT) wheredD 1 , since this was
reported to be the best setting. For the rest of the classifiers, we have used the
default settings from Weka. SVM used the “one-against-one” approach to multi-