Advanced Preprocessing: Multiway Centering and Scaling

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Introduction

When handling multi-way data (that is, data sets which have three or more modes), there are two specialized centering and scaling methods which can be used: multiway center and multiway scale. The details of how these methods work is beyond the scope of this chapter but details can be obtained from the multiway methods chapter (Chapter 10) of the Chemometrics Tutorial in PLS_Toolbox and Solo and from the help for the npreprocess command. The basic information on these methods is given below.

Note that when used together, multiway centering and scaling may need to be done iteratively if a true convergence is to be reached. The following general guidelines can be applied:

1. Centering across one mode tends to disturb scaling across all modes (except for particular scaling where the scaling is independent of the level/offset/center, such as in autoscaling.)
2. Scaling within a mode disturbs centering across the same mode but not across other modes.
3. Scaling affects scaling in other modes.

More details of these considerations can be found in Bro and Smilde, 2003.

Multiway Center

Performs centering across one or more modes of a multiway array. The result is a matrix which has a mean of zero for the given mode(s). In the Preprocessing window, the only setting defines which mode or modes should be centered. The npreprocess function can be used to perform this method at the command line.

Multiway Scale

Performs scaling of one or more modes of a multiway array. In the Preprocessing window, the only setting defines which mode or modes should be scaled. The npreprocess function can be used to perform this method at the command line.