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

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

Fundamentals and Analytical Applications of Multi-way Calibration

Elsevier

Año: 2015; p. 365 - 393

In the present chapter, the most relevant applications reported in the literature concerning unfolded and multi-way partial least-squares with residual multi-linearization modeling are presented. The chapter is organized in three sections according to the order of the data being handled: (1) second-order data, (2) third-order data, and (3) fourh-order data. In each part, a discussion about the different approaches implemented for data generation, considering instrumentation, detectors, strategies, etc. is presented. Attention was focused on the structure of the data and arrays regarding relevant properties such as bilinearity, trilinearity and quadrilinearity. The more flexible internal structure of the considered algorithms, compared to more rigid methodologies, make them more appropriate for processing multi-way data not strictly multilinear. Finally, several examples of complex analytical problems are discussed in detail with the aim of proving tools for further implementations.