基于二阶锥规划的鲁棒投影支持向量机

Robust Projection Support Vector Machine Based on Second-Order Cone Programming

【目的】投影支持向量机是通过将线性判别分析的思想应用到双子支持向量机,从而提出的一种新的非平行分类模型,旨在寻找两个不平行的投影方向而非超平面。然而该模型不够鲁棒,当训练数据集中存在大量的异常点或噪声时,投影支持向量机所学习的投影方向往往会受到影响而发生偏移,从而分类性能下降,需要进一步降低模型对异常点或噪声的敏感性,提升模型的鲁棒性。【方法】在模型中引入机会约束,在投影空间中允许部分投影样本到它的样本中心投影的距离大于它到另一类样本中心的投影距离,即给出了分错样本概率的一个上界。【结果】得到一个新的带有机会约束的鲁棒投影支持向量机,并等价地转化为二阶锥规划问题,从而只需求解一对线性二阶锥规划问题即可训练出两个非平行投影方向。【结论】在有关UCI数据集以及增加噪声的该数据集的数值实验中,上述基于二阶锥规划的鲁棒投影支持向量机与其他算法相比,准确率变化很小,相对稳定,具有更好的鲁棒性和泛化能力。

[Purposes]Projection support vector machine is a new non-parallel classification model proposed by applying the idea of linear discriminate analysis to twin support vector machine.which aims to find two non-parallel projection directions instead of hyperplanes.However,the model is not robust enough.When there are a large number of abnormal points or noise in the training data set,the projection direction learned by the projection support vector machine will often be affected by it and shift,and the classification performance will decrease.In order to reduce the sensitivity of the model to abnormal points or noise,the robustness of the model is improved.[Methods]The chance constraint is introduced into the model.In the projection space,the projection distance from a part of the projection sample to its sample center is allowed to be greater than the projection distance from it to another kind of sample center.In other words,an upper bound of the probability of wrong sample separation is given.[Findings]Obtain a new robust projection support vector machine with chance constraints,and equivalently transform it into a second-order cone programming problem,so that only apair of linear second-order cone programming problems can be solved to train two non-parallel projection directions.[Conclusions]In numerical experiments on UCI dataset and the dataset with increased noise,compared with other algorithms,the proposed robust projection support vector machine based on second-order cone programming has little change in accuracy,is relatively stable,and has better robustness and generalization ability.