Extension neural network (ENN) is a new neural network that is a combination of extension theory and artificial neural network (ANN). The learning algorithm of ENN is based on supervised learning algorithm. One of important issues in the field of classification and recognition of ENN is how to achieve the best possible classifier with a small number of labeled training data. Training data selection is an effective approach to solve this issue. In this work, in order to improve the supervised learning performance and expand the engineering application range of ENN, we use a novel data selection method based on shadowed sets to refine the training data set of ENN. Firstly, we use clustering algorithm to label the data and induce shadowed sets. Then, in the framework of shadowed sets, the samples located around each cluster centers (core data) and the borders between clusters (boundary data) are selected as training data. Lastly, we use selected data to train ENN. Compared with traditional ENN, the proposed improved ENN (IENN) has a better performance. Moreover, IENN is independent of the supervised learning algorithms and initial labeled data. Experimental results verify the effectiveness and applicability of our proposed work. 1. Instruction There are some recognition and classification problems whose features are defined over an interval of values in our world. For example, boys can be defined as a class of men from age 1 to 12, and the permitted operation voltages of a specified motor may be between 100 and 120？V. For these problems, it is difficult to implement an appropriate classification method using the current artificial neural networks (ANNs). Therefore, a new topology of neural network, extension neural network (ENN), is proposed by Wang and Hung [1] to solve these problems. This new neural network is a combination of extension theory [2] and ANN. The ENN uses a modified extension distance to measure the similarity between the objects and the class centers. It can quickly and stably learn to categorize input patterns and permit the adaptive processes to access significant new information. Moreover, the ENN has shorter learning time and a simpler structure than traditional ANNs. There have been some successful applications based on ENN in the field of pattern recognition, fault diagnosis, classification, cluster analysis, and so on [1, 3–8]. Just like any other ANNs based on supervised learning, the training data set is the most important and critical factor to ensure the supervised learning performance of ENN. In other words, supervised
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