A Semiproximal Support Vector Machine Approach for Binary Multiple Instance Learning

We face a binary multiple instance learning (MIL) problem, whose objective is to discriminate between two kinds of point sets: positive and negative. In the MIL terminology, such sets are called bags, and the points inside each bag are called instances. Considering the case with two classes of instances (positive and negative) and inspired by a well-established instance-space support vector machine (SVM) model, we propose to extend to MIL classification the proximal SVM (PSVM) technique that has revealed very effective for supervised learning, especially in terms of computational time. In particular, our approach is based on a new instance-space model that exploits the benefits coming from both SVM (better accuracy) and PSVM (computational efficiency) paradigms. Starting from the standard MIL assumption, such a model is aimed at generating a hyperplane placed in the middle between two parallel hyperplanes: the first one is a proximal hyperplane that clusters the instances of the positive bags, while the second one constitutes a supporting hyperplane for the instances of the negative bags. Numerical results are presented on a set of MIL test data sets drawn from the literature.