论文标题
使用主要最佳运输方向的足够降低尺寸以分类
Sufficient dimension reduction for classification using principal optimal transport direction
论文作者
论文摘要
足够的降低尺寸被普遍用作降低维度的方法。大多数现有的足够降低方法是为了连续响应而开发的数据，并且对分类响应的性能可能不令人满意，尤其是对于二进制响应。为了解决这个问题，我们提出了一种使用最佳传输的充分尺寸降低子空间（SDR子空间）的新型估计方法。所提出的方法，称为主要最佳运输方向（POTD），使用符合不同响应类别的数据之间的最佳传输耦合的主要方向估算了SDR子空间的基础。所提出的方法还揭示了三个看似无关的主题之间的关系，即足够的尺寸降低，支持向量机和最佳运输。我们研究了POTD的渐近特性，并表明在类标签不包含错误的情况下，POTD仅估计SDR子空间。经验研究表明，POTD优于大多数最先进的线性降低方法。
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.
