Dimension reduction based on constrained canonical correlation and variable filtering
Dimension reduction based on constrained canonical correlation and variable filtering
复制标题
DOI：
10.1214/07-aos529
复制
发表时间：
2008-08-01
影响因子：
4.5
通讯作者：
He, Xuming
中科院分区：
文献类型：
--
作者：
Zhou, Jianhui;He, Xuming
“维度的诅咒”一直是统计学中高维数据分析的一个挑战。分片逆回归(SIR)和典型相关(CANCOR)方法的目的是在不损失太多信息的情况下，用少量的复合方向代替解释变量来降低数据的维度。然而，估计的合成方向通常涉及所有变量，使得它们的解释变得困难。为了简化方向估计，Ni，Cook和Tsai提出了基于SIR的收缩切片逆回归(SSIR)。在本文中，我们提出了基于CANCOR的约束正则相关(C-3)方法，然后是一个简单的变量滤波方法。因此，每个复合方向由可解释性变量和预测力变量的子集组成。该方法的目的是在不牺牲无约束CANCOR估计的可取性质的情况下识别简单结构。仿真研究表明，与SSIR方法相比，C-3方法具有更好的性能优势。我们还用所提出的方法在两个例子中进行了说明。
The "curse of dimensionality" has remained a challenge for high-dimensional data analysis in statistics'. The sliced inverse regression (SIR) and canonical correlation (CANCOR) methods aim to reduce the dimensionality of data by replacing the explanatory variables with a small number of composite directions without losing much information. However, the estimated composite directions generally involve all of the variables, making their interpretation difficult. To simplify the direction estimates, Ni, Cook and Tsai [Biometrika 92 (2005) 242-247] proposed the shrinkage sliced inverse regression (SSIR) based on SIR. In this paper, we propose the constrained canonical correlation (C-3) method based on CANCOR, followed by a simple variable filtering method. As a result, each composite direction consists of a subset of the variables for interpretability as well as predictive power. The proposed method aims to identify simple structures without sacrificing the desirable properties of the unconstrained CANCOR estimates. The simulation studies demonstrate the performance advantage of the proposed C-3 method over the SSIR method. We also use the proposed method in two examples for illustration.