Multiclass Classification Through
Multidimensional Clustering
Sara Silva, Luis Muñoz, Leonardo Trujillo, Vijay Ingalalli, Mauro Castelli,
and Leonardo Vanneschi
Abstract Classification is one of the most important machine learning tasks in
science and engineering. However, it can be a difficult task, in particular when a
high number of classes is involved. Genetic Programming, despite its recognized
successfulness in so many different domains, is one of the machine learning
methods that typically struggles, and often fails, to provide accurate solutions for
multiclass classification problems. We present a novel algorithm for tree based GP
that incorporates some ideas on the representation of the solution space in higher
dimensions, and can be generalized to other types of GP. We test three variants
of this new approach on a large set of benchmark problems from several different
sources, and observe their competitiveness against the most successful state-of-the-
art classifiers like Random Forests, Random Subspaces and Multilayer Perceptron.
Keywords Classification • Multiple classes • Clustering
1 Introduction
In the last two decades, Genetic Programming (GP) (Koza 1992 ) has established
itself as a solid research field, not only because of the numerous practical successes
that have been reported in many different application domains (Poli et al. 2008 ; Koza
2010 ) but also due to the strengthening of its theoretical foundations (Langdon and
Poli 2002 ).
S. Silva ()
Faculty of Sciences, BioISI – Biosystems & Integrative Sciences Institute, University
of Lisbon, Lisbon, Portugal
e-mail:[email protected]
L. Muñoz • L. Trujillo
Tree-Lab, Posgrado en Ciencias de la Ingeniería, Instituto Tecnológico de Tijuana, Blvd.
Industrial y Av. ITR Tijuana S/N, Mesa Otay C.P. 22500, Tijuana, B.C., Mexico
V. I n g a l a l l i
LIRMM, Montpellier, France
M. Castelli • L. Vanneschi
NOVA IMS, Universidade Nova de Lisboa, 1070-312 Lisbon, Portugal
© Springer International Publishing Switzerland 2016
R. Riolo et al. (eds.),Genetic Programming Theory and Practice XIII,
Genetic and Evolutionary Computation, DOI 10.1007/978-3-319-34223-8_13
219