A Strategy of Maximizing the Sum of Weighted Margins for Ranking Multi Classification Problem
Linkai Luo, Chengde Lin, Hong Peng, Qifeng Zhou · 2006
This paper discusses the strategies of maximizing the sum of margins for ranking multi classification problem. First, the strategy of maximizing the sum of margins (MSM) is extended to maximizing the sum of weighted margins (MSWM). Using MSWM, a mathematical model is established to deal with the ranking multi classification problems where the importance of margins between classes is different, and its dual model is deduced. Then, by introducing the concept of algebraic margin, which is a generalization of geometric margin, the MSWM is further extended to maximizing the sum of weighed algebraic margins (MSWAM). Based on the MSWAM, the deduced mathematical model of the ranking multi classification problem not only has positive generalization ability, but is also a simple linear programming model