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In the past several decades, classifier-independent front-end feature extraction, where the derivation of acoustic features is lightly associated with the back-end model training or classification, has been prominently used in various pattern recognition tasks, including automatic speech recognition (ASR). In this paper, we present a novel discriminative feature transformation, named generalized likelihood ratio discriminant analysis (GLRDA), on the basis of the likelihood ratio test (LRT). It attempts to seek a lower dimensional feature subspace by making the most confusing situation, described by the null hypothesis, as unlikely to happen as possible without the homoscedastic assumption on class distributions. We also show that the classical linear discriminant analysis (LDA) and its well-known extension - heteroscedastic linear discriminant analysis (HLDA) can be regarded as two special cases of our proposed method. The empirical class confusion information can be further incorporated into GLRDA for better recognition performance. Experimental results demonstrate that GLRDA and its variant can yield moderate performance improvements over HLDA and LDA for the large vocabulary continuous speech recognition (LVCSR) task.