Preprocessing autoscaling

In data analysis, data are seldom used without some preprocessing. Such preprocessing is typically concerned with the scale of data. In this regard two main scaling procedures are widely used zero-centered and autoscaling. 

GLS preprocessing can be considered a more elaborate form of variable scaling, where, instead of each variable having its own scaling factor (as in autoscaling and variable-specific scaling), the variables are scaled to de-emphasize multivariate directions that are known to correspond to irrelevant spectral effects. Of course, the effectiveness of GLS depends on the ability to collect data that can be used to determine the difference effects, the accuracy of the measured difference effects, and whether the irrelevant spectral information can be accurately expressed as linear combinations of the original x variables. 

Interpreting plots of autoscaled data is difficult because the units have been removed. Graphically it appears tliat autoscaling has removed much of tlie in-fonnation because the patterns we arc comfortable seeing are gone. However, this preprocessing step can in fact improve the analysis results. 

From a chemometric point of view, the only constraint is that an appropriate column preprocessing, such as autoscaling, is required in order to eliminate systematic differences between variables of a different nature. Then, when the original variables are very numerous, it is possible to join the PCs computed separately for each variable block. 

For demonstration we use the data of a cooperative test [DOERFFEL and ZWANZIGER, 1987], In this interlaboratory comparison five laboratories were involved in the analysis of slag samples three times for seven chemical elements. So the (15, 7)-data matrix consists of 5 times 3 rows and 7 columns. The raw data in % are given in Tab. 5-2. The data have been preprocessed by standardization (autoscaling). 

Data preprocessed by autoscaling will assume mean = 0 and variance = 1 ... 

Two of the most commonly employed methods of preprocessing multivariate data are mean centering and variance scaling of the spectra. Taken together, the application of mean centering and variance scaling is autoscaling. 

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