An Outer-Product-of-Gradient Approach to Dimension Reduction and its Application to Classification in High Dimensional Space
提出高维梯度外积降维方法，结合随机投影构建集成分类器，理论证明与模拟、真实数据验证其优于现有方法。
Sufficient dimension reduction (SDR) has progressed steadily. However, its ability to improve general function estimation or classification has not been well received, especially for high-dimensional data. In this article, we first devise a local linear smoother for high dimensional nonparametric regression and then utilise it in the outer-product-of-gradient (OPG) approach of SDR. We call the method high-dimensional OPG (HOPG). To apply SDR to classification in high-dimensional data, we propose an ensemble classifier by aggregating results of classifiers that are built on subspaces reduced by the random projection and HOPG consecutively from the data. Asymptotic results for both HOPG and the classifier are established. Superior performance over the existing methods is demonstrated in simulations and real data analyses. Supplementary materials for this article are available online.