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For high dimensional data, if no preprocessing is carried out before inputting patterns to classifiers, the computation required may be too heavy. For example, the number of hidden units of a radial basis function (RBF) neural network can be too large. This is not suitable for some practical applications due to speed and memory constraints. In many cases, some attributes are not relevant to concepts in the data at all. In this paper, we propose a novel separability-correlation measure (SCM) to rank the importance of attributes. According to the attribute ranking results, different attribute subsets are used as inputs to a classifier, such as an RBF neural network. Those attributes that increase the validation error are deemed irrelevant and are deleted. The complexity of the classifier can thus be reduced and its classification performance improved. Computer simulations show that our method for attribute importance ranking leads to smaller attribute subsets with higher accuracies compared with the existing SUD and Relief-F methods. We also propose a modified method for efficient construction of an RBF classifier. In this method we allow for large overlaps between clusters corresponding to the same class label. Our approach significantly reduces the structural complexity of the RBF network and improves the classification performance.