Multiclass sub-pixel target detection using functions of multiple instances

The Multi-class Convex-FUMI (Multi-class C-FUMI) method is developed and described. The method is capable of learning prototypes for multiple target classes from hyperspectral imagery. Multi-class C-FUMI is a non- traditional supervised learning method based on the Functions of Multiple Instances (FUMI) concept. The FUMI concept differs significantly from traditional supervised by the assumption that only functions of target patterns are available. Moreover, these functions are likely to involve other non-target patterns. In this paper, data points which are convex combinations of multiple target and several non-target prototypes are considered. Multi-class C-FUMI learns the target and non-target patterns, the number of non-target patterns, and the weights (or proportions) of all the prototypes for each data point. For hyperspectral image analysis, the target and non-target prototypes estimated using Multi-class C-FUMI are the endmembers for the target and non-target (background) materials. For this method, training data need only binary labels indicating whether a data point contains or does not contain some proportion of a target endmember; the specific target proportions for the training data are not needed. After learning the target prototype using the binary-labeled training data, target detection is performed on test data. Results showing sub-pixel target detection on highly mixed simulated hyperspectral data generated from the ASTER spectral library are presented.