基于有效迭代算法的鲁棒L1范数非平行近似支持向量机

针对鲁棒L1范数非平行近似支持向量机（L1-NPSVM）求解算法无法保证获取可靠解的问题，提出一个新颖的迭代算法来解L1-NPSVM的目标问题。首先，根据L1-NPSVM原目标问题对解具有规模不变性，将其转换为一个等价的带等式约束的最大化问题。该迭代算法在每次迭代中利用更新权机制获取每次迭代的更新解；每次迭代中，问题归结为解两个快速的线性方程问题。从理论上证明了算法的收敛性。在公共UCI数据集上，实验显示，所提算法不仅在分类性能上要远远好于L1-NPSVM，且具有相当的计算优势。

Robust L1-norm non-parallel proximal support vector machine via efficient iterative algorithm

Considering that robust L1-norm Non-parallel Proximal Support Vector Machine (L1-NPSVM) can not guarantee a reliable solution, a new iterative algorithm was proposed to solve the objective of L1-NPSVM. Since the objective problem of L1-NPSVM is invariant to the scale of solution, such that it can be transformed into a maximization problem with an equality constraint. And then the proposed iterative algorithm was used to solve it. The iterative algorithm in each iteration obtained updated solution of each iteration by using weight updating mechanism, and the problem was reduced to solve two fast linear equations in each iteration. The convergence of the algorithm was proved theoretically. Experiments on the common UCI datasets show that the proposed algorithm is not only superior to L1-NPSVM in classification performance, but also has considerable computational advantage.