220 S. Silva et al.
Probably the most straightforward formulation for a GP search is to apply it in
supervised machine learning problems, particularly symbolic regression and data
classification. In general, for a supervised classification problem some patternx 2
Rphas to be classified in one ofMclasses! 1 ;:::;!Musing a training setXof
N p-dimensional patterns with a known class label. Then, the goal is to build a
mappingg.x/WRp!M, that assigns each patternxto a corresponding class!i,
wheregis derived based on the evidence provided byX. In these problems fitness
is usually assigned in two general ways. One approach is to use awrappermethod,
where GP is used as a feature extraction method that performs the transformation
k.x/W Rp! Rd, and then another classifier is used to measure the quality of
the transformation based on accuracy or another performance measure. The second
approach is to use GP to evolvegdirectly, performing the feature transformation
step implicitly.
However, various references report on the poor performance of GP in multiclass
classification (i.e., whereM>2) when compared to other state-of-the-art classifiers
(see for instance Castelli et al. 2013 ). Very recently, we have introduced a novel
method in Ingalalli et al. ( 2014 ), and an improved variant in Muñoz et al. ( 2015 ),
which has finally allowed GP to be considered as a competitive option for multiclass
classification. The current work summarizes these two previous contributions, and
introduces yet another variant of the method, reporting comparative results between
the three of them, and also putting them against the most popular state-of-the-art
classification methods.
The remainder of this chapter is organized as follows. Section 2 describes the
state-of-the-art of multiclass classification with GP that is related to the work
presented here. Sections 3 – 5 describe the three variants of the novel method
mentioned above, called M2GP, M3GP and eM3GP, respectively. Section 6 specifies
the data set, tools and parameters used to perform the experiments. Section 7
reports and discusses the results achieved by each of the three variants, comparing
them between each other and with the state-of-the-art classifiers. Finally, Sect. 8
concludes and proposes the future directions for this work.
2 Related Work
Espejo et al. ( 2010 ) present a comprehensive discussion on GP-based classification
methods. Here we outline several GP methods that have been proposed in order to
specifically tackle multiclass classification problems.
Several works (Bojarczuk et al. 2000 ; Sakprasat and Sinclair 2007 ; Shen et al.
2003 ; Falco et al. 2002 ; Tan et al. 2002 ) in this area are based on a common and
straightforward approach that consists in evolving a single rule in each GP run. In
particular,cruns are performed for ac-class classification problem. In this way,
the final classifier has a single rule for each class. All these works evolve multiple
comprehensible IF-THEN classification rules.