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Fisher's linear discriminant analysis (LDA) is a traditional dimensionality reduction method that has been proven to be successful for decades. Numerous variants, such as the kernel-based Fisher discriminant analysis (KFDA), have been proposed to enhance the LDA's power for nonlinear discriminants. Although effective, the KFDA is computationally expensive, since the complexity increases with the size of the data set. In this correspondence, we suggest a novel strategy to enhance the computation for an entire family of the KFDAs. Rather than invoke the KFDA for the entire data set, we advocate that the data be first reduced into a smaller representative subset using a prototype reduction scheme and that the dimensionality reduction be achieved by invoking a KFDA on this reduced data set. In this way, data points that are ineffective in the dimension reduction and classification can be eliminated to obtain a significantly reduced kernel matrix K without degrading the performance. Our experimental results demonstrate that the proposed mechanism dramatically reduces the computation time without sacrificing the classification accuracy for artificial and real-life data sets.