  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.
