Scores normalisation

Fig. 34.13. Score plot (ti vs 12) of the spectra given in Fig. 34.2 after normalisation. The points A and B are the purest spectra in the data set. The points A and B are the spectra at the boundaries of the non-negativity constraint.

L contains normalised rows while T is weighted by the matrix S. This, however, is somewhat ambiguous as the decomposition of the transposed, Y1, is equally possible and then the score and loading matrices are simply exchanged. For this reason, we do not use the expressions scores and loadings. The Singular Value Decomposition maintains some kind of symmetry between the decompositions of Y and Yl. 

Figure 31 Dot plots of z-scores for normalised vitamin B2 data...

A useful trick is to normalise tire scores. This involves calculating... 

Figure 6.9 illustrates die scores of dataset A normalised over two PCs. Between times 3 and 21, die points in die chromatogram are in sequence on die arc of a circle. The extremes (3 and 21) could represent the purest elution times, but points influenced primarily by noise might lie anywhere on the circle. Hence time 25, which is clearly... 

The normalised scores of dataset B [Figure 6.10(a)] show a clearer pattern. The figure suggests the following ... 

Scores of dataset A normalised over the first two principal components... 

Scores of dataset B normalised over the first two principal components (a) Over entire region (b) Expansion of central regions... 

Scores corresponding to Figure 6.10(b) but normalised over three PCs and presented in three dimensions... 

Note that some people call this normalisation, but we will avoid that terminology, as this method is distinct from that in Section 6.2.2. The influence on PC scores plots has already been introduced (Chapter 4, Section 4.3.6.2) but will be examined in more detail in this chapter. 

Normalise the scores of die first two PCs obtained in question 4 by dividing by die square root of the sum of squares at each pH. Plot the graph of the normalised scores of PC2 vs PCI, labelling each point as in question 4, and comment. 

Calculate the two x loadings for the current PLS component of the overall dataset by normalising the scores and loadings of H, i.e. 

PCA is simple in Matlab. The singular value decomposition (SVD) algorithm is employed, but this should normally give equivalent results to NIPALS except diat all the PCs are calculated at once. One difference is that die scores and loadings are bodi normalised, so that for SVD... 

Figure 4. Partial least squares analysis of twelve glycoside hydrolysates, sensory attribute ratings and volatile compound concentration (normalised) a) component loadings, and b) sample scores. For explanation of codes see Tables II and IV.

The most comprehensive but most expensive method of objective hand evaluation was developed by Kawabata and co-workers " and is called KES-F (Kawabata Evaluation System-Fabrics). It consists of several different measuring instruments, for example for tensile and shear properties (KES-Fl), bending properties (KES-F2), compressibility (KES-F3), surface (KES-F4) and thermal (KES-F7) properties. The measured parameters and the area weight are normalised and correlated to the subjective handle scores. From this correlation, for every hand evaluation a transformation equation is developed, resulting in a primary... 

It is possible that more than one metric contributes to die poor status. In lakes it is common for quality elements of phytoplankton, macrophytes and fish to fall short of the quality criteria. In rivers, macrofauna and fish are likely to have inadequate scores. In both situations the steering factors form a complex. In the example of lakes, this is known as a eutrophication complex. In rivers it is caused by canalisation and normalisation. And, third, the complex causing an inadequate score for macrofauna and fish in the metric for transitional waters is called coastal defences. 

With regard to the CSl dataset employed in Chapter 5 to exemplify PLS, similar findings were obtained. Just to summarise, the 108 atomic absorbances were reduced to 10 principal components (99.92% of the variance), which were input to the ANN. The number of neurons in the hidden layer was varied from 2 to 6 ( tansig function) and 1 neuron ( purelin function) was set in the output layer. The other parameters in the setup were learning rate 0.0001 maximum number of epochs (iterations) 300000 maximum acceptable mean square error 25 (53 calibrators). The scores were normalised 0-1 (division by the absolute maximum score). Figure 6.8 depicts how the calibration error of the net evolved as a function of the number of epochs. It is obvious that the net... 

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