Learning Large Margin Mappings

We present a method to simultaneously learn a mixture of mappings and large margin hyperplane classifier. This method learns useful mappings of the training data to improve classification accuracy. We first present a simple iterative algorithm that finds a greedy local solution and then derive a semidefinite relaxation to find an approximate global solution. This relaxation leads to the matrix mixture of mappings formulation which generalizes both the mixture of mappings and the mixture of kernels framework. More efficient algorithms based on the extragradient method are introduced to work on larger problems and to extend the basic framework to a multitask setting. We then apply our method to the novel task of learning monotonic transformations which cannot be easily addressed in a kernel learning framework. Experiments directly comparing kernel learning and mapping learning demonstrate the usefulness of the technique.