Department of Chemistry, Idaho State University, Pocatello, Idaho 83209, USA.
Appl Spectrosc. 2010 Dec;64(12):1388-95. doi: 10.1366/000370210793561655.
Tikhonov regularization (TR) is a general method that can be used to form a multivariate calibration model and numerous variants of it exist, including ridge regression (RR). This paper reports on the unique flexibility of TR to form a model using full wavelengths (RR), individually selected wavelengths, or multiple bands of selected wavelengths. Of these three TR variants, the one based on selection of wavelength bands is found to produce lower prediction errors. As with most wavelength selection algorithms, the model vector magnitude indicates that this error reduction comes with a potential increase in prediction uncertainty. Results are presented for near-infrared, ultraviolet-visible, and synthetic spectral data sets. While the focus of this paper is wavelength selection, the TR methods are generic and applicable to other variable-selection situations.
季霍诺夫正则化（TR）是一种通用的方法，可用于建立多元校准模型，并且存在许多变体，包括岭回归（RR）。本文报道了 TR 形成模型的独特灵活性，可使用全波长（RR）、单独选择的波长或多个选定波长的波段。在这三种 TR 变体中，基于选择波长带的变体被发现可产生更低的预测误差。与大多数波长选择算法一样，模型向量大小表明这种误差减少伴随着预测不确定性的潜在增加。结果呈现了近红外、紫外-可见和合成光谱数据集。虽然本文的重点是波长选择，但 TR 方法是通用的，可适用于其他变量选择情况。
