A multi-sphere approach for Multiple Instance Learning classification

Multiple Instance Learning (MIL) consists in classifying bags of instances. The main characteristic of a MIL problem is that, in the learning phase, only the labels of the bags are known, while the labels of the instances belonging to the bags are unknown. In the case of two types of instances and two types of bags (positive and negative), a very common assumption consists in considering a bag positive if it contains at least a positive instance and negative if it contains only negative instances. Starting from this assumption and initially inspired by a well-established SVM type approach, we present a spherical based instance-space algorithm where a finite and variable number of spheres is generated using the following criterion: a bag is considered positive if at least one of its instances belongs to the union of the spheres (i.e. it is contained in at least a sphere) and it is negative if all its instances are outside the union of the spheres (i.e. they are not contained in any sphere). Numerical results are presented on a set of benchmark datasets.