Principal weighted support vector machines for sufficient dimension reduction in binary classification
提出主成分加权支持向量机框架，解决二分类问题中现有充分降维方法（如切片逆回归）只能估计一个方向的问题，并给出线性与非线性版本的理论和算法。
Sufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions. However, most existing methods may work poorly for binary classification. For example, sliced inverse regression (Li, 1991) can estimate at most one direction if the response is binary. In this paper we propose principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification. Its asymptotic properties are studied, and an efficient computing algorithm is proposed. Numerical examples demonstrate its performance in binary classification.