Auto-scaling

To know how to carry out scaling, mean-centering, and auto-scaling... 

With the exception of mechanical rub, defective cables and transducers are the only sources of this ski-slope profile. When mechanical rub is present, the ski slope will also contain the normal rotational frequencies generated by the machine-train. In some cases, it is necessary to turn off the auto-scale function in order to see the rotational frequencies, but they will be evident. If no rotational components are present, the cable and transducer should be replaced. 

R X auto <- scale (X, center = TRUE, scale = TRUE)... 

Dual Display/ Multiple Display Auto Scale... 

Auto Scale This command recalculates the extreme values on occasions where a data set is loaded and the values for the maximum/minimum data points are not correct. 

FIGURE 8.6. (a) 3D plot using the scores calculated from PCA analysis using autoscale preprocessing with six factors for the opium samples from different locations, (b) 3D plot using the scores calculated from PCA analysis using auto-scale preprocessing with six factors for the poppy straw samples. See color insert. 

A two-way analysis shows that without centering across samples and scaling within variables (auto-scaling) there is no contribution to the model from the trace metals with their low concentrations, and without a stoichiometric scaling, leaving out centering, the ion balances of certain important sources are not really found. Thus, different ways of looking at the data may be needed for different purposes. 

Now to our subject. Modern software programs offer many options for the manipulation of the chromatogram, e.g. automated baseline subtraction, programmed change of integration parameter, auto-zero functions and auto scale, automated calibration for non-linear signal-to-concentration ratio, etc. It is worth while knowing these options and how to use them as they fit. 

In Figure 11 an example of oMEDA is shown. For this, a 100 x 100 data set with two clusters of data was simulated. The distribution of the observations was designed so that both clusters had significantly different values only in variable 10 and then data was auto-scaled. The oMEDA vector clearly highlights variable 10 as the main difference between both clusters. 

PCA is a least square method and therefore its results depend on data scaling. The initial variance of a column variable partly determines its importance in the model. In order to avoid the problem of over- or under-representation of variables, column variables are scaled to unit variance before analysis. The column average is then subtracted from each variable, which, from a statistical point of view, corresponds to moving the multivariate system to the center of the data, which becomes the starting point of the mathematical analysis. The same auto-scaling and centering procedures are applied in PLS discriminant analysis. 

Figure 13.4. Print preview of the IR spectrum of cortisone using the template Basicl.PLE. On the Options page the items Auto Scale to All Spectra and Use Compressed Wavenumbers were checked.

Auto scaling and calibration features for shaft sinking operations... 

AUTO SCALING AND CALIBRATION FEATURES FOR SHAFT SINKING OPERATIONS... 

B Log scale O Grid lines IS Numbered S Auto scale B Show markers S Auto grid Number of grids ... 

In general it is needed to auto-scale the data, i.e., to centre data and scale to unit variance. The choice of V should reflect the choice and be of same units as the scaled data. For further details see the appendix. 

When the data set X5 is loaded into the workspace (using load X5), go to File , select Load Data , load X-block and load X5. Data auto-scaling should be performed You could select Preprocess to change this. Now calculate the principal components by selecting calc , the window as shown in Fig. 22.3 will appear. 

The procedure for calculating the PLS model is given by several authors, amongst others, Geladi and Kowalski (1986). The procedure starts with assuming a score vector told that is any column of matrix X, for example Xi, and a score vector u which is any column of matrix T, for example j i. Assuming that X and Y are auto-scaled, the following steps are then carried out ... 

The program npls auto-scales the data firsf i.e. from each variable the mean is subtracted and divided by the standard deviation. Then the first 300 data points are used to develop a linear PLS model, the modehng results are shown in Fig. 23.4. 

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