A local and global classification machine with collaborative mechanism

As an advanced local and global learning machine, the existing maxi–min margin machine (M 4 ) still has its heavy time-consuming weakness. Inspired from the fact that covariance matrix of a dataset can characterize its data orientation and compactness globally, a novel large margin classifier called the local and global classification machine with collaborative mechanism (C 2 M) is constructed to circumvent this weakness in this paper. This classifier divides the whole global data into two independent models, and the final decision boundary is obtained by collaboratively combining two hyperplanes learned from two independent models. The proposed classifier C 2 M can be individually solved as a quadratic programming problem. The total training time complexity is O ( 2 N 3 ) which is faster than O ( N 4 ) of M 4 . C 2 M can be well defined with the clear geometrical interpretation and can also be justified from a theoretical perspective. As an additional contribution, it is shown that C 2 M can robustly leverage the global information from those datasets with overlapping class margins, while M 4 does not use such global information. We also use the kernel trick and exploit C 2 M’s kernelized version. Experiments on toy and real-world datasets demonstrate that compared with M 4 , C 2 M is a more time-saving local and global learning machine.