On a recent algorithm for Multiple Instance Learning. Preliminary applications in image classification

We present an application of a Multiple Instance Learning (MIL) approach to image classification. In particular we focus on a recent MIL method for binary classification where the objective is to discriminate between positive and negative sets of points. Such sets are called bags and the points inside the bags are called instances. In the case of two classes of instances (positive and negative), a bag is defined positive if it contains at least a positive instance and it is negative if it contains only negative instances. For such kind of problems there exist in literature two different approaches: the bag-level approach and the instance level approach. While in the former the total entity of each bag is considered, in the latter a classifier is obtained on the basis of the characteristics of the instances, without looking at the whole entity of each bag. The presented method is an instance-level approach and it is based on the application of the Lagrangian relaxation technique to a Support Vector Machine (SVM) type model. Preliminary numerical tests are discussed on a set of simple grey-level images.