Multi-instance learning (MIL) is a useful tool for tackling labeling ambiguity in learning because it allows a bag of instances to share one label. Bag mapping transforms a bag into a single instance in a new space via instance selection and has drawn significant attention recently. To date, most existing work is based on the original space, using all instances inside each bag for bag mapping, and the selected instances are not directly tied to an MIL objective. As a result, it is difficult to guarantee the distinguishing capacity of the selected instances in the new bag mapping space. In this paper, we propose a discriminative mapping approach for multi-instance learning (MILDM) that aims to identify the best instances to directly distinguish bags in the new mapping space. Accordingly, each instance bag can be mapped using the selected instances to a new feature space, and hence any generic learning algorithm, such as an instance-based learning algorithm, can be used to derive learning models for multi-instance classification. Experiments and comparisons on eight different types of real-world learning tasks (including 14 data sets) demonstrate that MILDM outperforms the state-of-The-Art bag mapping multi-instance learning approaches. Results also confirm that MILDM achieves balanced performance between runtime efficiency and classification effectiveness.