  There are many applications where it important to perform well on a set of
examples as opposed to individual examples. For example in image or video
classification the question is does an object appear somewhere in the image or
video while there are several candidates of the object per image or video. In
this context, it is not important what is the performance per candidate.
Instead the performance per group is the ultimate objective.
  For such problems one popular approach assumes weak supervision where labels
exist for the entire group and then multiple instance learning is utilized.
Another approach is to optimize per candidate, assuming each candidate is
labeled, in the belief that this will achieve good performance per group.
  We will show that better results can be achieved if we offer a new
methodology which synthesizes the aforementioned approaches and directly
optimizes for the final optimization objective while consisting of a convex
optimization problem which solves the global optimization problem. The benefit
of grouping examples is demonstrated on an image classification task for
detecting polyps in images from capsule endoscopy of the colon. The algorithm
was designed to efficiently handle hundreds of millions of examples.
Furthermore, modifications to the penalty function of the standard SVM
algorithm, have proven to significantly improve performance in our test case.
