Instance elimination strategy for non-convex multiple-instance learning using sparse positive bags

In some multiple instance learning (MIL) applications, positive bags are sparse (i.e. containing only a small fraction of positive instances). To deal with the imbalanced data caused by these situations, we present a novel MIL method based on a small sphere and large margin approach (SSLM-MIL). Due to the introduction of a large margin, SSLM-MIL enforces the desired constraint that for all positive bags, there is at least one positive instance in each bag. Moreover, our framework is flexible to incorporate the non-convex optimization problem. Therefore, we can solve it using the concave–convex procedure (CCCP). Still, CCCP may be computationally inefficient for the number of external iterations. Inspired by the existing safe screening rules, which can effectively reduce computational time by discarding some inactive instances. In this paper, we propose a strategy to reduce the scale of the optimization problem. Specifically, we construct a screening rule in the inner solver and another rule for propagating screened instances between iterations of CCCP. To the best of our knowledge, this is the first attempt to introduce safe instance screening to a non-convex hypersphere support vector machine. Experiments on thirty-one benchmark datasets demonstrate the safety and effectiveness of our approach.