Local Learning vs. Global Learning: An Introduction to Maxi-Min Margin Machine

We present a unifying theory of the Maxi-Min Margin Machine (M 4) that subsumes the Support Vector Machine (SVM), the Minimax Probability Machine (MPM), and the Linear Discriminant Analysis (LDA). As a unified approach, M 4 combines some merits from these three models. While LDA and MPM focus on building the decision plane using global information and SVM focuses on constructing the decision plane in a local manner, M 4 incorporates these two seemingly different yet complementary characteristics in an integrative framework that achieves good classification accuracy. We give some historical perspectives on the three models leading up to the development of M 4. We then outline the M 4 framework and perform investigations on various aspects including the mathematical definition, the geometrical interpretation, the time complexity, and its relationship with other existing models.