https://imedea.uib-csic.es/master/cambioglobal/Modulo_V_cod101615/Theory/lit_support/pca_wold.pdf

Principal component analysis

Partial leastgquares (PLS) methods for spectral analyses are related to other multlvarlate callbratlon methods such as classical least-squares (CLS), Inverse least-squares (ILS), and prlnclpal component regression (PCR) methods which have been used often In quantitative spectral analyses. The PLS method which analyzes one chemlcal component at a tbne Is presented, and the basis for each step In the algorithm Is explained. PLS callbratlon Is shown to be composed of a series of simpllfled CLS and ILS steps. This detalled understandlng of the PLS algorithm has helped to ldentlfy how chemically Interpretable qualltatlve spectral lnformatlon can be obtained from the lntennedlate steps of the PLS algorithm. These methods for extractlng qualitative Information are demonstrated by use of simulated spectral data. The qualltatlve Information directly available from the PLS analysis Is superlor to that obtained from PCR but is not as complete as that which can be generated during CLS analyses. Methods are presented for selecting optbnal numbers of loading vectors for both the PLS and PCR models In order to optimize the model while simultaneously reduclng the potential for overfittlng the caHbratlon data. Outlier detection and methods to evaluate the statlstlcal slgnlflcance of resuits obtalned from the dMerent cahatlon methods applied to the same spectral data are also discussed.

/pdf/partial-least-squares-methods-for-spectral-analyses-1-125ka44fdl.pdf

Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information

A generic preprocessing method for multivariate data, called orthogonal projections to latent structures (O-PLS), is described. O-PLS removes variation from X (descriptor variables) that is not correlated to Y (property variables, e.g. yield, cost or toxicity). In mathematical terms this is equivalent to removing systematic variation in X that is orthogonal to Y. In an earlier paper, Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175-185) described orthogonal signal correction (OSC). In this paper a method with the same objective but with different means is described. The proposed O-PLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in X is removed, making interpretation of the resulting PLS model easier and with the additional benefit that the non-correlated variation itself can be analyzed further. As an example, near-infrared (NIR) reflectance spectra of wood chips were analyzed. Applying O-PLS resulted in reduced model complexity with preserved prediction ability, effective removal of non-correlated variation in X and, not least, improved interpretational ability of both correlated and non-correlated variation in the NIR spectra.

Orthogonal projections to latent structures (O-PLS)

Data-driven Soft Sensors in the process industry

The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered. Multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches. This approach facilitates the analysis of operational and quality-control problems in past batches and allows for the development of multivariate statistical process control charts for on-line monitoring of the progress of new batches. Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches. The method is applied to data collected from an industrial batch polymerization reactor.

https://www.jstor.org/stable/pdfplus/1269152.pdf

Multivariate SPC charts for monitoring batch processes

Orthogonal signal correction of near-infrared spectra

The Lohmoller–Wold decomposition of multi-way (three-way, four-way, etc.) data arrays is combined with the non-linear partial least squares (NIPALS) algorithms to provide multi-way solutions of principal components analysis (PCA) and partial least squares modelling in latent variables (PLS).

The decomposition of a multi-way array is developed as the product of a score vector and a loading array, where the score vectors have the same properties as those of ordinary two-way PCA and PLS. In image analysis, the array would instead be decomposed as the product of a loading vector and an image score matrix.

The resulting methods are equivalent to the method of unfolding a multi-way array to a two-way matrix followed by ordinary PCA or PLS analysis. This automatically proves the eigenvector and least squares properties of the multi-way PCA and PLS methods.

The methodology is presented; the algorithms are outlined and illustrated with a small chemical example.

Multi‐way principal components‐and PLS‐analysis

When using hyphenated methods in analytical chemistry, the data obtained for each sample are given as a matrix. When a regression equation is set up between an unknown sample (a matrix) and a calibration set (a stack of matrices), the residual is a matrix R.

The regression equation is usually solved by minimizing the sum of squares of R. If the sample contains some constituent not calibrated for, this approach is not valid. In this paper an algorithm is presented which partitions R into one matrix of low rank corresponding to the unknown constituents, and one random noise matrix to which the least squares restrictions are applied. Properties and possible applications of the algorithm are also discussed.

In Part 2 of this work an example from HPLC with diode array detection is presented and the results are compared with generalized rank annihilation factor analysis (GRAFA).

Residual bilinearization. Part 1: Theory and algorithms

The partial least squares-residual bilinearization (PLS-RBL) approach to backgroung correction presented in Part 1 of this work is demonstrated a with an example from HPLC with diode array detection Data are also evaluated with generalized rank annihilation factor analysis (GRAFA) and results are compared

Residual bilinearization. Part 2: Application to HPLC—diode array data and comparison with rank annihilation factor analysis

Simultaneous determination of five different food proteins by high-performance liquid chromatography and partial least-squares multivariate calibration

Jerker Öhman

Papers

Orthogonal signal correction of near-infrared spectra

Multi‐way principal components‐and PLS‐analysis

Residual bilinearization. Part 1: Theory and algorithms

Residual bilinearization. Part 2: Application to HPLC—diode array data and comparison with rank annihilation factor analysis

Simultaneous determination of five different food proteins by high-performance liquid chromatography and partial least-squares multivariate calibration