High‐dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framework for Regularized PLS by solving a relaxation of the SIMPLS optimization problem with penalties on the PLS loadings vectors. Our approach enjoys many advantages including flexibility, general penalties, easy interpretation of results, and fast computation in high‐dimensional settings. We also outline extensions of our methods leading to novel methods for non‐negative PLS and generalized PLS, an adoption of PLS for structured data. We demonstrate the utility of our methods through simulations and a case study on proton Nuclear Magnetic Resonance (NMR) spectroscopy data. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012

中文翻译：

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正则化偏最小二乘法在 NMR 光谱中的应用。

基因组学、蛋白质组学和化学计量学中常见的高维数据通常包含复杂的相关结构。最近，偏最小二乘法 (PLS) 和稀疏 PLS 方法作为监督数据分析背景下的降维技术在这些领域受到了关注。我们通过解决对 PLS 载荷向量进行惩罚的 SIMPLS 优化问题的松弛来引入正则化 PLS 的框架。我们的方法具有许多优点，包括灵活性、一般惩罚、结果的简单解释以及高维设置中的快速计算。我们还概述了我们方法的扩展，导致非负 PLS 和广义 PLS 的新方法，将 PLS 用于结构化数据。我们通过模拟和质子核磁共振 (NMR) 光谱数据的案例研究证明了我们的方法的实用性。© 2012 Wiley Periodicals, Inc. 统计分析和数据挖掘，2012