Multiple Instance Learning for bags with Ordered instances

Multiple Instance Learning (MIL) algorithms are designed for problems where labels are available for groups of instances, commonly referred to as bags. In this paper, we consider a new MIL problem setting where instances in a bag are not exchangeable, and a bijection exists between every pair of bags. We propose a neural network based MIL algorithm (MILOrd) that leverages the existence of such a bijection when learning to discriminate bags. MILOrd has an input node for each instance in the bag, an output node that captures the bag level prediction, and a hidden layer that captures the output from an instance level classifier for each instance in the bag. The bag level prediction is obtained by combining these hidden layer values using a function that models the importance of each instance, unlike the traditional schemes where each instance is considered equal. We demonstrate the utility of the proposed algorithm on the problem of burned area mapping using yearly bags composed of multispectral reflectance data for different time steps in the year. Our experiments show that MILOrd outperforms traditional MIL schemes that don’t account for the presence of a bijection.