改进的v-支持向量回归机的v解路径算法

v-支持向量回归机(v-support vector regression, v-SVR)的对偶形式与ε-支持向量回归机的对偶形式相比增加了一个额外的不等式约束,截止目前还没有找到有效且可行的v-SVR 的v解路径算法。针对Loosli等人提出的v-SVR的v解路径算法存在路径不可更新的问题,提出了改进的v-SVR的v解路径算法。该算法基于v-SVR的修改形式及Karush-Kuhn-Tucker(KKT)条件,通过引入新的变量和附加项的策略,能够有效地避免在绝缘增量调整过程中存在的冲突和异常,并最终经过有限次数迭代拟合出整个v-解路径。理论分析和仿真结果表明,该算法是有效且可行的。

Improved v solution path for v-support vector regression

In comparison with the dual formulation of ε-support vector machine, the dual of v-support vector regression (v-SVR) has an extra inequality constraint. To date, there is no effective and feasible v- solution path for v-SVR. To solve the infeasible updating path problem of the v solution path for v-SVR, which was first proposed by Loosli et al, an improved v- solution path for v-SVR is proposed. Based on the modified formulation of v-SVR and the Karush-Kuhn-Tucker (KKT) conditions, the strategy of using a new introduced variable and an extra term can avoid the conflicts and exceptions effectively during the adiabatic incremental adjustments. Finally, the proposed algorithm can fit the entire v-solution path within the finite number of iterations. Theoretical analysisand simulation results demonstrate that the proposed algorithm is effective and feasible.