Functions of Multiple Instances for Learning Target Signatures

Abstract

The functions of multiple instances (FUMI) approach for learning target and nontarget signatures is introduced. FUMI is a generalization of the multiple-instance learning (MIL) approach for supervised learning. FUMI differs significantly from standard MIL and supervised learning approaches because only data points which are functions of class concepts/signatures are available. In particular, this paper addresses the problem in which data points are convex combinations of target and nontarget signatures. Two algorithms, convex FUMI ( $c$ FUMI) and extended $c$ FUMI ( $e$ FUMI) , are presented and applied to the problem of hyperspectral unmixing and target detection. $c$ FUMI learns target and nontarget signatures (i.e., target and nontarget endmembers) , the number of nontarget signatures, and the proportion of each signature for every data point. The $e$ FUMI algorithm extends the $c$ FUMI to allow for additional “bag level” uncertainty in training labels. For these methods, training data need only binary labels indicating whether a data point (or some spatial area in the case of $e$ FUMI) contains or does not contain some proportion of the target; the specific target proportions for the training data are not needed. After learning the target signature using the binary-labeled training data, target detection can be performed on test data. Results for subpixel target detection on simulated and real airborne hyperspectral data are shown.