A collaborative classifier for local and global learning

Inspired by covariance matrix stating data direction globally, we construct a novel large margin classifier called collaborative classification machine with local and global information (C2M). By the median rule of combining classifiers, this model collaboratively learns the decision boundary from two hyperplanes with global information. The proposed C2M algorithm can be individually solved as a quadratic programming (QP) problem, and has O(2N3) time complexity that is faster than O(N4) of existing maxi-min margin machine (M4). We describe the C2M model definition, provide the geometrical interpretation, and present theoretical justifications. As a major contribution, we show that C2M can robustly utilize the global information when M4 loses the global information on those data sets with confused classes margin. We also exploit kernelization trick and extend C2M to nonlinear classification. Moreover, we show that C2M can be transformed into standard support vector machine (SVM) model and can be solved by other quick algorithms widely used by SVM. Furthermore, we propose four indicators to evaluate the global impact of covariance matrix on classification. Experiments on toy and real-world data sets demonstrate that the C2M has comparable performance with SVM that utilizes only local information, while the C2M is more robust and time saving than M4.