School of Behavioral and Brain Sciences, The University of Texas at Dallas, Richardson, TX 75080-3021, USA.
Neuroimage. 2011 May 15;56(2):455-75. doi: 10.1016/j.neuroimage.2010.07.034. Epub 2010 Jul 23.
Partial Least Squares (PLS) methods are particularly suited to the analysis of relationships between measures of brain activity and of behavior or experimental design. In neuroimaging, PLS refers to two related methods: (1) symmetric PLS or Partial Least Squares Correlation (PLSC), and (2) asymmetric PLS or Partial Least Squares Regression (PLSR). The most popular (by far) version of PLS for neuroimaging is PLSC. It exists in several varieties based on the type of data that are related to brain activity: behavior PLSC analyzes the relationship between brain activity and behavioral data, task PLSC analyzes how brain activity relates to pre-defined categories or experimental design, seed PLSC analyzes the pattern of connectivity between brain regions, and multi-block or multi-table PLSC integrates one or more of these varieties in a common analysis. PLSR, in contrast to PLSC, is a predictive technique which, typically, predicts behavior (or design) from brain activity. For both PLS methods, statistical inferences are implemented using cross-validation techniques to identify significant patterns of voxel activation. This paper presents both PLS methods and illustrates them with small numerical examples and typical applications in neuroimaging.
偏最小二乘法（PLS）方法特别适合分析大脑活动测量值与行为或实验设计之间的关系。在神经影像学中，PLS 指两种相关的方法：（1）对称 PLS 或偏最小二乘相关（PLSC），和（2）非对称 PLS 或偏最小二乘回归（PLSR）。目前神经影像学中应用最广泛（迄今为止）的 PLS 版本是 PLSC。它有几种变体，基于与大脑活动相关的数据类型：行为 PLSC 分析大脑活动与行为数据之间的关系，任务 PLSC 分析大脑活动与预定义类别或实验设计之间的关系，种子 PLSC 分析脑区之间的连通模式，以及多块或多表 PLSC 将这些变体中的一种或多种整合到共同分析中。与 PLSC 相反，PLSR 是一种预测技术，通常用于从大脑活动预测行为（或设计）。对于这两种 PLS 方法，统计推断都是使用交叉验证技术来识别体素激活的显著模式。本文介绍了这两种 PLS 方法，并通过小数值示例和神经影像学中的典型应用进行了说明。
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