A linear programming approach to multiple instance learning

Abstract

Multiple instance learning (MIL) aims to classify objects with complex structures and covers a wide range of real-world data mining applications. In MIL, objects are represented by a bag of instances instead of a single instance, and class labels are provided only for the bags. Some of the earlier MIL methods focus on solving MIL problem under the standard MIL assumption, which requires at least one positive instance in positive bags and all remaining instances are negative. This study proposes a linear programming framework to learn instance level contributions to bag label without emposing the standart assumption. Each instance of a bag is mapped to a pseudo-class membership estimate and these estimates are aggregated to obtain the bag-level class membership in an optimization framework. A simple linear mapping enables handling various MIL assumptions with adjusting instance contributions. Our experiments with instance-dissimilarity based data representations verify the effectiveness of the proposed MIL framework. Proposed mathematical models can be solved efficiently in polynomial time.