Unfolded and multi-way partial least-squares with residual multi-linearization. Fundamentals

OLIVIERI A C; G ESCANDAR,; GOICOECHEA H C; MUÑOZ DE LA PEÑA, A

Fundamentals and Analytical Applications of Multi-way Calibration

ELSEVIER SCI LTD

Año: 2015; p. 347 - 365

In the present chapter the theory of second- and higher-order multivariate calibration methods based on latent variables is reviewed. Unfolded partial least-squares (U-PLS) and its multi-way version (N-PLS) are powerful techniques employed to model calibration data sets based on multi-way analytical signals. In order to achieve the important second-order advantage, they are complemented with procedures generally known as residual multi-linearization (RML), which involve RBL (bilinearization for second-order data), RTL (trilinearization for third-order data) and RQL (quadrilinearization for fourth-order data). Additional methodologies based on classical calibration, but closely related to U-PLS/RML are also revised.