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We propose a new discriminative learning framework, called soft margin feature extraction (SMFE), for jointly optimizing the parameters of transformation matrix for feature extraction and of hidden Markov models (HMMs) for acoustic modeling. SMFE extends our previous work of soft margin estimation (SME) to feature extraction. Tested on the TIDIGITS connected digit recognition task, the proposed approach achieves a string accuracy of 99.61%, much better than our previously reported SME results. To our knowledge, this is the first study on applying the margin-based method in joint optimization of feature extraction and acoustic modeling. The excellent performance of SMFE demonstrates the success of soft margin based method, which targets to obtain both high accuracy and good model generalization.