Random set framework for multiple instance learning

Multiple instance learning for hyperspectral image analysis

“…RSF-MIL and MI-RVM have the best reported [4] classification results on Musk data sets (MI benchmarks) [10]. Results are compared to the WhitenDewhiten (WDW) transform, developed my Mayer et al [11], that uses target and background statistics of the training and testing data to calculate target confidence.…”

“…A more general MIL solution, Random Set Framework for Multiple Instance Learning (RSF-MIL) has recently been introduced by the authors and used for feature learning in GPR image analysis [4]. RSF-MIL provides a random set-model to perform analysis on bags.…”

“…Using this operator, similarities between bags can be analyzed, models can be learned, and posterior probabilities can be calculated. Details of various models that can be used to evaluate (4) are discussed in [4].…”

“…In this model, a germ, ξ j ∈ R d , and grain, λ j ∈ R d , pair are used to characterize the jth constituent random set, Ξ j . It is assumed that the random radii, R j of each the random grains Ξ j have a cumulative distribution P (R j ≤ r j ) = 2 1+exp(−r T j diag(λj )rj ) − 1 ; therefore, the probability of intersection given one sample, x, and the jth germ and grain pair (which is one minus the cumulative distribution of a grain) is calculated as [4]. Given this model, the capacity functional of Ξ) is calculated as in (7) using Λ j which is a diagonal matrix with λ j on the diagonal [4].…”

“…In the following, RSF-MIL and MI-RVM are used to learn a target emissivity signal for the purposes of landmine detection, which has not previously been done. These two MIL approaches have the highest classification performance given benchmark data sets [4] and will help identify the benefits of using MIL approaches for the purposes of HSI image analysis.…”