Instance Influence Estimation for Hyperspectral Target Signature Characterization using Extended Functions of Multiple Instances

The Extended Functions of Multiple Instances (eFUMI) algorithm is a generalization of Multiple Instance Learning (MIL). In eFUMI, only bag level (i.e. set level) labels are needed to estimate target signatures from mixed data. The training bags in eFUMI are labeled positive if any data point in a bag contains or represents any proportion of the target signature and are labeled as a negative bag if all data points in the bag do not represent any target. From these imprecise labels, eFUMI has been shown to be effective at estimating target signatures in hyperspectral subpixel target detection problems. One motivating scenario for the use of eFUMI is where an analyst circles objects/regions of interest in a hyperspectral scene such that the target signatures of these objects can be estimated and be used to determine whether other instances of the object appear elsewhere in the image collection. The regions highlighted by the analyst serve as the imprecise labels for eFUMI. Often, an analyst may want to iteratively refine their imprecise labels. In this paper, we present an approach for estimating the influence on the estimated target signature if the label for a particular input data point is modified. This "instance influence estimation" guides an analyst to focus on (re-)labeling the data points that provide the largest change in the resulting estimated target signature and, thus, reduce the amount of time an analyst needs to spend refining the labels for a hyperspectral scene. Results are shown on real hyperspectral sub-pixel target detection data sets.