Multiway methods

MULTISENSOR SYSTEMS ELECTRONIC TONGUE BASED ON LOW-SELECTIVE SENSORS AND MULTIWAY METHODS OF RECEIVED DATA TREATMENT... 

Multiway methods For analyzer data where a single sample generates a second order array (ex. GC/MS, LC/UV, excitation/emission fluorescence), multiway chemometric modehng methods, such as PARAFAC (parallel factor analysis) [121,122], can be used to exploit the second order advantage to perform effective calibration transfer and instrument standardization. 

Multivariate Image Analysis Strong and Weak Multiway Methods Strong and weak -way methods analyze 3D and 2D matrices, respectively. Hyperspectral data cube structure is described using chemometric vocabulary [17]. A two-way matrix, such as a classical NIR spectroscopy data set, has two modes object (matrix lines) and V variables (matrix columns). Hyperspectral data cubes possess two object modes and one variable mode and can be written as an OOV data array because of their two spatial directions. 

Even if strong A -way methods are used to reduce image noise, compress data, and improve data cube visualization, weak multiway methods are more often used as they facilitate classification using classical single-point spectra. 

Weak Multiway Methods Figure 7 shows the three steps in weak N-way analysis Unfold the data cube, perform the selected chemometric methods, and refold the matrix in order to display distribution maps. Weak N-way analysis comprises two main variants ... 

Multiway methods can be extended far beyond trilinear PLS1, and there are many cases in chemistry where such approaches are appropriate. However, in the case of calibration of analytical signals to determine concentrations, trilinear PLS1 is adequate in the majority of situations. 

Chemometrics finds widespread use in spectroscopy, and there are a number of reviews that describe advances in this area. In a review by Geladi [41], some of the main methods of chemometrics are illustrated with examples. A series of three reviews addresses the topic of chemometrics in spectroscopy [42-44], Part 1 has 199 references and focuses specifically on chemometric techniques applied to spectroscopic data [42], Part 2 has 68 references and focuses on data-preprocessing methods and data transformations aimed at reducing noise, removing effects of baseline offsets, and filtering to remove noise [43], Part 3 focuses on multiway methods of analysis applied to spectroscopic data [44],... 

With least-squares (LS) algorithms for non-linear problems such as multiway methods, the problem of local minima solutions6 is well known and it is common practice to repeat the calculation a number of times using different starting estimates for the components. This way the results of several models are compared and if the calculated models are sufficiently similar, it is likely that the global LS minimum has been found, whereas if the models are dissimilar, local LS minima are likely to be present. In case of local LS minima, more repetitions can be made in order to see if a consistent pattern... 

Bro R, Heimdal H, Enzymatic browning of vegetables. Calibration and analysis of variance by multiway methods, Chemometrics and Intelligent Laboratory Systems, 1996,34, 85-102. 

Methods for simultaneous Af-way regression can be based on the decomposition of the X array by multiway methods introduced in Section 5.2 (parallel factor analysis (PARAFAC) or Tucker models) and regressing the dependent variable on the components of those models. A drawback with this approach is that the separately estimated components are not necessarily predictive for Y. This caused the development of improved algorithms for multiway regression analysis of that kind. 

Guimet et al. used two potential multiway methods for the discrimination between virgin olive oils and pure olive oils the unfold principal component analysis (U-PCA) and parallel factor analysis (PARAFAC), for the exploratory analysis of these two types of oils. Both methods were applied to the excitation-emission fluorescence matrices (EEM) of olive oils and followed the comparison of the results with the ones obtained with multivariate principal component analysis (PCA) based on a fluorescence spectrum recorded at only one excitation wavelength. 

In contrast to multiway methods, multiset MCR methods provide only two matrices with the qualitative information of compounds, and C, which... 

Since both in quantitative analysis coming from the multiway method and in multiset analysis, the last step is the construction of univariate calibration lines, analogous figures of merit have been proposed that have been successfully used to provide results with suitable xmcertainty [51] and to comply with regulatory issues [52]. 

In this chapter, the main multiway methods used for data decomposition and for calibration will be briefly presented and described, together with some examples of their application. Here it must be stressed that while, for the sake of an easier presentation, the discussion will be mainly focused on three-way methods, generalization to higher-order arrays is straightforward. 

This chapter has highlighted the main features of three-way methods and their straightforward extension to multiway methods. The description has been based on both algorithmic and practical frameworks. The practical examples have been focused on food analysis to strengthen the importance of multiway methods in as complicated a matrix as food. With this, there is still room for several remarks that deserve attention. So far, the main use of three-way methods is in academia and research. From our perspective, a huge effort... 

---