Transfer learning (TL) aims at solving the problem of learning an effective classification model for a target category, which has few training samples, by leveraging knowledge from source categories with far more training data. We propose a new discriminative TL (DTL) method, combining a series of hypotheses made by both the model learned with target training samples and the additional models learned with source category samples. Specifically, we use the sparse reconstruction residual as a basic discriminant and enhance its discriminative power by comparing two residuals from a positive and a negative dictionary. On this basis, we make use of similarities and dissimilarities by choosing both positively correlated and negatively correlated source categories to form additional dictionaries. A new Wilcoxon-Mann-Whitney statistic-based cost function is proposed to choose the additional dictionaries with unbalanced training data. Also, two parallel boosting processes are applied to both the positive and negative data distributions to further improve classifier performance. On two different image classification databases, the proposed DTL consistently outperforms other state-of-the-art TL methods while at the same time maintaining very efficient runtime.