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首页> 外文期刊>Journal of Chemometrics >Post-transformation of PLS2 (ptPLS2) by orthogonal matrix: a new approach for generating predictive and orthogonal latent variables
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Post-transformation of PLS2 (ptPLS2) by orthogonal matrix: a new approach for generating predictive and orthogonal latent variables

机译：通过正交矩阵对PLS2（ptPLS2）进行后变换：一种生成预测和正交潜在变量的新方法

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摘要

Partial Least Squares (PLS) is a wide class of regression methods aiming at modelling relationships between sets of observed variables by means of latent variables. Specifically, PLS2 was developed to correlate two blocks of data, the X-block representing the independent or explanatory variables and the Y-block representing the dependent or response variables. Lately, OPLS was introduced to further reduce model complexity by removing Y-orthogonal sources of variation from X in the latent space, thus improving data interpretation through the generated predictive latent variables. Nevertheless, relationships between PLS2 and OPLS in case of multiple Y-response have not yet been fully explored. With this perspective and taking inspiration from some basic mathematical properties of PLS2, we here present a novel and general approach consisting in a post-transformation of PLS2 (ptPLS2), which results in a decomposition of the latent space into orthogonal and predictive components, while preserving the same goodness of fit and predictive ability of PLS2. Additionally, we discuss the application of ptPLS2 approach to two metabolomic data sets extracted from earlier published studies and its advantages in model interpretation as compared with the 'standard' PLS approach. Copyright (C) 2016 John Wiley & Sons, Ltd.
机译：偏最小二乘（PLS）是一类广泛的回归方法，旨在通过潜在变量对观察变量集之间的关系进行建模。具体来说，开发了PLS2来关联两个数据块，其中X块代表自变量或解释变量，Y块代表因变量或响应变量。最近，引入OPLS来通过从潜在空间中的X移除Y正交变异源来进一步降低模型复杂度，从而通过生成的预测潜在变量改善数据解释。然而，在多个Y响应的情况下，PLS2和OPLS之间的关系尚未得到充分探索。从这个角度出发，并从PLS2的一些基本数学特性中获得启发，我们在这里提出了一种新颖而通用的方法，该方法包括PLS2（ptPLS2）的后转换，该转换将潜在空间分解为正交分量和预测分量，而保持与PLS2相同的拟合优度和预测能力。此外，我们讨论了ptPLS2方法在从较早发表的研究中提取的两个代谢组学数据集上的应用，以及与“标准” PLS方法相比在模型解释中的优势。版权所有（C）2016 John Wiley＆Sons，Ltd.

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