Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory performance for the categorical response, especially for the binary-response. To address this issue, we propose a novel estimation method of sufficient dimension reduction subspace (SDR subspace) using optimal transport. The proposed method, named principal optimal transport direction (POTD), estimates the basis of the SDR subspace using the principal directions of the optimal transport coupling between the data respecting different response categories. The proposed method also reveals the relationship among three seemingly irrelevant topics, i.e., sufficient dimension reduction, support vector machine, and optimal transport. We study the asymptotic properties of POTD and show that in the cases when the class labels contain no error, POTD estimates the SDR subspace exclusively. Empirical studies show POTD outperforms most of the state-of-the-art linear dimension reduction methods.

翻译：为解决这一问题,我们提出了使用最佳运输方式(SDR 子空间)进行足够尺寸减少的新估计方法。拟议方法称为主要最佳运输方向(POTD),利用不同反应类别数据之间最佳运输连接的主要方向来估计特别提款权子空间的基础。拟议方法还揭示了三个似乎不相干的专题之间的关系,即,足够的尺寸减少、支持矢量机和最佳运输。我们研究了POTD的无孔不入特性,并表明在类别标签没有误差的情况下,POTD只估计了特别提款权子空间。经验性研究显示,POTD的功能超过了大多数最先进的线性减少方法。