In this paper, the Multi-target Extended Function of Multiple Instances (Multi-target eFUMI) method is developed and described. The method is capable of learning multiple target spectral signatures from weakly- and inaccurately-labeled hyperspectral imagery. Multi-target eFUMI is a generalization of the Function of Multiple Instances approach (FUMI). The FUMI approach differs significantly from standard Multiple Instance Learning (MIL) approach in that it assumes each data is a function of target and non-target “concepts.” In this paper, data points which are convex combinations of multiple target and several non-target “concepts” are considered. Moreover, it allows both “proportion-level” and “bag-level” uncertainties in training data. Training data needs only binary labels indicating whether some spatial area contains or does not contain some proportion of target; the specific target proportions for the training data are not needed. Multi-target eFUMI learns the target and non-target concepts, the number of non-target concepts, and the proportions of all the concepts for each data point. After learning the target concepts using the binary “bag-level” labeled training data, target detection can be performed on test data. Results for sub-pixel target detection on simulated and real airborne hyperspectral data are shown.