In this paper, two methods for discriminative multiple instance target characterization, MI-SMF and MI-ACE, are presented. MI-SMF and MI-ACE estimate a discriminative target signature from imprecisely-labeled and mixed training data. In many applications, such as sub-pixel target detection in remotely-sensed hyperspectral imagery, accurate pixel-level labels on training data is often unavailable and infeasible to obtain. Furthermore, since sub-pixel targets are smaller in size than the resolution of a single pixel, training data is comprised only of mixed data points (in which target training points are mixtures of responses from both target and non-target classes). Results show improved, consistent performance over existing multiple instance concept learning methods on several hyperspectral sub-pixel target detection problems.