Pattern Recognition 40 (2007) 1498 – 1509 www.elsevier.com/locate/pr Self-generating prototypes for pattern classification Hatem A. Fayed a , Sherif R. Hashem a , Amir F. Atiya b, ∗ a Department of Engineering Mathematics and Physics, Cairo University, Giza, Egypt b Department of Computer Engineering, Cairo University, Giza, Egypt Received 15 February 2006; received in revised form 15 February 2006; accepted 17 October 2006 Abstract Prototype classifiers are a type of pattern classifiers, whereby a number of prototypes are designed for each class so as they act as representatives of the patterns of the class. Prototype classifiers are considered among the simplest and best performers in classification problems. However, they need careful positioning of prototypes to capture the distribution of each class region and/or to define the class boundaries. Standard methods, such as learning vector quantization (LVQ), are sensitive to the initial choice of the number and the locations of the prototypes and the learning rate. In this article, a new prototype classification method is proposed, namely self-generating prototypes (SGP). The main advantage of this method is that both the number of prototypes and their locations are learned from the training set without much human intervention. The proposed method is compared with other prototype classifiers such as LVQ, self-generating neural tree (SGNT) and K-nearest neighbor (K-NN) as well as Gaussian mixture model (GMM) classifiers. In our experiments, SGP achieved the best performance in many measures of performance, such as training speed, and test or classification speed. Concerning number of prototypes, and test classification accuracy, it was considerably better than the other methods, but about equal on average to the GMM classifiers. We also implemented the SGP method on the well-known STATLOG benchmark, and it beat all other 21 methods (prototype methods and non-prototype methods) in classification accuracy.  2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved. Keywords: Prototype classifiers; Nearest neighbor; Learning vector quantization; Self-generating neural trees; Gaussian mixture models 1. Introduction The simplest and most intuitive approach in pattern clas- sification is based on the concept of similarity [1,2]. Patterns that are similar (in some sense) are assigned to the same class. Prototype classifiers are one major group of classifiers that are based on similarity. A number of prototypes are de- signed so as they act as representatives of the typical pat- terns of a specific class. When presenting a new pattern, the nearest prototype determines the classification of the pattern. Two extreme ends of the scale for prototype classifiers are the nearest neighbor classifier, where each pattern serves as a prototype, and the minimum distance classifier, where there ∗ Corresponding author. Tel.: +20 2 3354773. E-mail addresses: h_fayed@eng.cu.edu.eg (H.A. Fayed), shashem@ieee.org, shashem@mcit.gov.eg (S.R. Hashem), amiratiya@link.net, amir@alumni.caltech.edu (A.F. Atiya). 0031-3203/$30.00  2006 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.patcog.2006.10.018 is only one prototype (the class center or mean) per class. Practically speaking, the most successful prototype classi- fiers are the ones that have a few prototypes per class, thus economically summarizing all data points into a number of key centers. Learning vector quantization (LVQ) [3] is prob- ably the most well-known prototype classifier. Other meth- ods also include self-generating neural tree (SGNT) [4,5], which is a hierarchical tree structure, where all the training patterns (or specifically the misclassified ones) are repeat- edly presented to the tree until the method correctly classifies all the patterns. Some other prototype classifiers have also been developed such as methods that compactly cover each class region by a set of hyperspheres [6,7] or ones that use a set of hyperellipsoids [8] or a set of hyperrectangles [9]. Another prototype classifier is the Gaussian mixture model (GMM), which is based on modeling the class-conditional densities as a Gaussian mixture [1,10]. The well-known EM algorithm is used to design such a classifier. Each