Multi-instance Support Vector Machine Based on Convex Combination∗

This paper presents a new formulation of multi-instance learning as maximum margin problem, which is an extension of the standard C-support vector classification. For linear classification, this extension leads to, instead of a mixed integer quadratic programming, a continuous optimization problem, where the objective function is convex quadratic and the constraints are either linear or bilinear. This optimization problem is solved by an iterative strategy solving a convex quadratic programming and a linear programming alternatively. For non-linear classification, the corresponding iterative strategy is also established, where the kernel is introduced and the related dual problems are solved. The preliminary numerical experiments show that our approach is competitive with the others.