Pattern Recognition Using Functions of Multiple Instances

The Functions of Multiple Instances (FUMI) method for learning a target prototype from data points that are functions of target and non-target prototypes is introduced. In this paper, a specific case is considered where, given data points which are convex combinations of a target prototype and several non-target prototypes, the Convex-FUMI (C-FUMI) method learns the target and non-target patterns, the number of nontarget patterns, and determines the weights (or proportions) of all the prototypes for each data point. For this method, training data need only binary labels indicating whether the data contains or does not contain some proportion of the target prototype; the specific target weights 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 detection of the skin in hyper spectral imagery and sub-pixel target detection in simulated data are presented.