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论文类型：期刊论文

发表时间：2016-01-01

发表刊物：NEURAL COMPUTING & APPLICATIONS

收录刊物：SCIE、EI

卷号：27

期号：1,SI

页面范围：3-8

ISSN号：0941-0643

关键字：Interval computation; Interval neural network; Extreme learning machine; Interval extreme learning machine

摘要：Interval data offer a valuable way of representing the available information in complex problems where uncertainty, inaccuracy, or variability must be taken into account. Considered in this paper is the learning of interval neural networks, of which the input and output are vectors with interval components, and the weights are real numbers. The back-propagation (BP) learning algorithm is very slow for interval neural networks, just as for usual real-valued neural networks. Extreme learning machine (ELM) has faster learning speed than the BP algorithm. In this paper, ELM is applied for learning of interval neural networks, resulting in an interval extreme learning machine (IELM). There are two steps in the ELM for usual feed-forward neural networks. The first step is to randomly generate the weights connecting the input and the hidden layers, and the second step is to use the Moore-Penrose generalized inversely to determine the weights connecting the hidden and output layers. The first step can be directly applied for interval neural networks. But the second step cannot, due to the involvement of nonlinear constraint conditions for IELM. Instead, we use the same idea as that of the BP algorithm to form a nonlinear optimization problem to determine the weights connecting the hidden and output layers of IELM. Numerical experiments show that IELM is much faster than the usual BP algorithm. And the generalization performance of IELM is much better than that of BP, while the training error of IELM is a little bit worse than that of BP, implying that there might be an over-fitting for BP.