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In kernel discriminant analysis, one common practice is to use a fixed level of smoothing (estimated from training data) for classifying all unlabeled observations. But, in classification, a good choice of smoothing parameters also depends on the observation to be classified. Therefore, instead of using a fixed level of smoothing over the entire measurement space, it may be more useful to estimate the smoothing parameters depending on that specific observation. Here, we propose a simple method for this case-specific smoothing. Some benchmark data sets are analyzed to illustrate the performance of the proposed method.