A theoretical and empirical analysis of support vector machine methods for multiple-instance classification

The standard support vector machine (SVM) formulation, widely used for supervised learning, possesses several intuitive and desirable properties. In particular, it is convex and assigns zero loss to solutions if, and only if, they correspond to consistent classifying hyperplanes with some nonzero margin. The traditional SVM formulation has been heuristically extended to multiple-instance (MI) classification in various ways. In this work, we analyze several such algorithms and observe that all MI techniques lack at least one of the desirable properties above. Further, we show that this tradeoff is fundamental, stems from the topological properties of consistent classifying hyperplanes for MI data, and is related to the computational complexity of learning MI hyperplanes. We then study the empirical consequences of this three-way tradeoff in MI classification using a large group of algorithms and datasets. We find that the experimental observations generally support our theoretical results, and properties such as the labeling task (instance versus bag labeling) influence the effects of different tradeoffs.