On Classification with Bags, Groups and Sets

In recent years, the field of pattern recognition has seen many problems that are difficult to formulate as regular supervised classification problems where (feature vector, label) pairs are available to train a classifier that, in turn, can predict labels for previously unseen feature vectors. A subset of these problems contains learning scenarios where (part of) the objects are represented by sets or bags of feature vectors or instances. Such learning scenarios include multiple instance learning [11], set classification [42], group-based classification [47] and many others. In this paper we review these learning scenarios. There are several reasons why a bag representation might be chosen in a pattern recognition problem. The first reason is that a single feature vector is often too restrictive to describe an object. For example, in drug activity prediction, we are interested in classifying molecules as having the desired effect (active) or not. However, a molecule is not just a list of its elements: most molecules can fold into different shapes or conformations, which can influence the activity of that molecule.