Differential evolution based nearest prototype classifier with optimized distance measures for the features in the data sets David Koloseni a,d , Jouni Lampinen b,c , Pasi Luukka a,e,⇑ a Laboratory of Applied Mathematics, Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta, Finland b Department of Computer Science, University of Vaasa, P.O. Box 700, FI-65101 Vaasa, Finland c Department of Computer Science, VSB-Technical University of Ostrava, 17. listopadu 15, 70833 Ostrava-Poruba, Czech Republic d University of Dar es salaam, Department of Mathematics, P.O. Box 35062, Dar es salaam, Tanzania e School of Business, Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta, Finland article info Keywords: Differential evolution Classification Distance measures Distance selection for the feature Pool of distances abstract In this paper a further generalization of differential evolution based data classification method is pro- posed, demonstrated and initially evaluated. The differential evolution classifier is a nearest prototype vector based classifier that applies a global optimization algorithm, differential evolution, for determining the optimal values for all free parameters of the classifier model during the training phase of the classi- fier. The earlier version of differential evolution classifier that applied individually optimized distance measure for each new data set to be classified is generalized here so, that instead of optimizing a single distance measure for the given data set, we take a further step by proposing an approach where distance measures are optimized individually for each feature of the data set to be classified. In particular, distance measures for each feature are selected optimally from a predefined pool of alternative distance measures. The optimal distance measures are determined by differential evolution algorithm, which is also deter- mining the optimal values for all free parameters of the selected distance measures in parallel. After determining the optimal distance measures for each feature together with their optimal parameters, we combine all featurewisely determined distance measures to form a single total distance measure, that is to be applied for the final classification decisions. The actual classification process is still based on the nearest prototype vector principle; A sample belongs to the class represented by the nearest prototype vector when measured with the above referred optimized total distance measure. During the training process the differential evolution algorithm determines optimally the class vectors, selects optimal dis- tance metrics for each data feature, and determines the optimal values for the free parameters of each selected distance measure. Based on experimental results with nine well known classification benchmark data sets, the proposed approach yield a statistically significant improvement to the classification accu- racy of differential evolution classifier. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Differential evolution algorithm is gaining a fast popularity in classification problems. Some include bankruptcy prediction (Chauhan, Ravi, & Chandra, 2009), classification rule discovery (Su, Yang, & Zhao, 2010), feature selection, (Khushaba, Al-Ani, & Al-Jumaily, 2011), edge detection in images (Bastürk & Günay, 2009). Also in some methods classification techniques are used to improve optimization with differential evolution algorithm (Liu & Sun, 2011). The global optimization problems arises in many fields of science, engineering and business (Sun, Zhang, & Tsang, 2005). In order to achieve the best available classification perfor- mance, we typically need to find the best classification model for the current data set to be classified, and the best optimization algo- rithm for determining the values of its free parameters during the training phase. One of the emerged global optimization methods is the differential evolution (DE) algorithm (Price, Storn, & Lampinen, 2005) that belongs evolutionary computation approaches. DE has also been applied in many areas of pattern recognition, i.e. in re- mote sensing imagery (Maulik & Saha, 2009), hybrid evolutionary learning in pattern recognition systems (Zmudaa, Rizkib, & Tamburinoc, 2009), in neural network based learning algorithms (Fernandez, Hervas, Martinez, & Cruz, 2009; Magoulas, Plagianakos, & Vrahatis, 2004), in clustering (Bandyopdhyay & Saha, 2007; 0957-4174/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.eswa.2013.01.040 ⇑ Corresponding author at: Laboratory of Applied Mathematics, Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta, Finland. Tel.: +358 503694108. E-mail addresses: David.Koloseni@lut.fi (D. Koloseni), jouni.lampinen@uwasa.fi (J. Lampinen), Pasi.Luukka@lut.fi (P. Luukka). Expert Systems with Applications 40 (2013) 4075–4082 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa