Partial least squares methods: partial least squares correlation and partial least square regression.
Partial least squares methods: partial least squares correlation and partial least square regression.
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DOI：
10.1007/978-1-62703-059-5_23
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发表时间：
2013-01-01
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影响因子：
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通讯作者：
Williams, Lynne J
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文献类型：
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作者：
Abdi, Herve;Williams, Lynne J
偏最小二乘（PLS）方法（有时也称为潜在结构投影）将两个数据表中的信息关联起来，这两个数据表收集了同一组观测值的测量值。PLS方法通过导出潜在变量来进行，这些潜在变量是数据表的变量的（最佳）线性组合。当目标是找到两个表之间的共享信息时，该方法相当于相关问题，该技术称为偏最小二乘相关（PLSC）（有时也称为PLS-SVD）。在这种情况下，有两组潜变量（每个表一组），这些潜变量需要具有最大协方差。当目标是预测一个数据表和另一个数据表时，该技术称为偏最小二乘回归。在这种情况下，存在一组潜变量（从预测器表导出），并且需要这些潜变量来给出最佳可能的预测。在本文中，我们提出并说明PLSC和PLSR，并显示这些描述性的多元分析技术可以扩展到处理推理问题，通过使用交叉验证技术，如引导和排列测试。
Partial least square (PLS) methods (also sometimes called projection to latent structures) relate the information present in two data tables that collect measurements on the same set of observations. PLS methods proceed by deriving latent variables which are (optimal) linear combinations of the variables of a data table. When the goal is to find the shared information between two tables, the approach is equivalent to a correlation problem and the technique is then called partial least square correlation (PLSC) (also sometimes called PLS-SVD). In this case there are two sets of latent variables (one set per table), and these latent variables are required to have maximal covariance. When the goal is to predict one data table the other one, the technique is then called partial least square regression. In this case there is one set of latent variables (derived from the predictor table) and these latent variables are required to give the best possible prediction. In this paper we present and illustrate PLSC and PLSR and show how these descriptive multivariate analysis techniques can be extended to deal with inferential questions by using cross-validation techniques such as the bootstrap and permutation tests.