Multiple instance learning via margin maximization

In this paper, we consider the classification problem within the multiple instance learning (MIL) context. Training data is composed of labeled bags of instances. Despite the large number of margin maximization based classification methods, there are only a few methods that consider the margin for MIL problems in the literature. We first formulate a combinatorial margin maximization problem for multiple instance classification and prove that it is NP-hard. We present a way to apply the kernel trick in this formulation for classifying nonlinear multiple instance data. We also propose a branch and bound algorithm and present computational results on publicly available benchmark data sets. Our approach outperforms a leading commercial solver in terms of the best integer solution and optimality gap in the majority of image annotation and molecular activity prediction test cases.