Speeding up local and global learning of M4

We construct a novel large margin classifier called the Collaborative Classification Machine with Local and Global Information (C²M) for speeding up the recently proposed Maxi-Min Margin Machine (M⁴). We divide the whole global data used in M⁴ into two independent models, and the final decision boundary is obtained by collaboratively combining the two hyperplanes learned from the two independent models. The proposed C²M model can be individually solved as a Quadratic Programming (QP) problem. The total training time complexity is O(2N³) which is faster than O(N⁴) of M⁴. We describe the definition of the C²M model, provide the geometrical interpretation and present theoretical justifications. Experiments on toy and real-world data sets demonstrate that the C²M is more robust and time saving than M⁴ as a local and global classification machine.