Rank estimates

Once ftE calibration and test sets are defined, SIMC. models are estimated using ini rank estimates Offom PCA) and default class volumes (from the software fKrkage). The samples in the test set arc predicted and the results evaimtedaa detennine if modification of the tanks and/or class volumes is needed (see Habit 4 for details of this evaluation). If the number of misclassifi-cations is anacccptable, the rank and class volume parameters are adjusted and the pswress repeated. 

When the PCA analysis is completed and the calibration and validation sets are chosen, the next step is to create SIMCA models for the calibration set samples. The initial rank estimates from PCA and software default class volumes are used, the performance of the models on the test samples is examined, and the SIMCA settings are adjusted as necessary. 

Percent Variance Table (Model Diagnostic) The percent variance explained as a function of the number of PLS factors shown in Tabic 5.20 indicates that much of the variation in the measurements (S>9.98%) and concentration (99.82%) have been explained using a tliree-factor model. This is consistent with a s> stcm containing three sources of variation (i,e., salt, caustic, and temperature). The remaining diagnostics are used to refine the rank estimate. 

The new subset is selected by first computing the SVD of the least squares matrix A. A rank estimate, f, is obtained by first determining the condition number of the matrix from the singular values and then deciding upon the number of parameters that must be eliminated to reduce k to an acceptable value. The QR scheme with column pivoting is then applied to... 

Fits are to HF/3-21G(" ) electrostatic potential calculated at 1000 points in a shell between 1.0 and 3.0 times the van der Waals surface of the molecule. The rank estimate is taken as the number of singular values for which the ratio s to Sj does not exceed 10. ... 

Table 4 SVD Rank Estimates for CHELP LLS as a Function of Sample Size ...

Figure 9 Rank estimates for LLS fits for alanine dipeptide, neopentane, phenol, and acetamide as a function of the size of the sampling envelope. Data from CHELP LLS fits at the HF/3-21G( ) level using a sample of 1000 points.

H.L. Shen, J.H. Wang, Y.Z. Liang, K. Pettersson, M. Josefson, J. Gottfries and F. Lee, Chemical Rank Estimation by Multiresolution Analysis for Two-way Data in the Presence of Background, Chemometrics Intelligent Laboratory Systems 37 (1997), 261-269. 

Intell. Lab. Syst., 37, 261-269 (1997). Chemical Rank Estimation by Multiresolution Analysis for Two-way Data in the Presence of Background. 

According to the sum of the rank estimates yyRank. the antioxidant activity of all compormd (XIII) clathrates should exceed the activity of the pure nonclathrated compormd (XIII). In this case, the comparable value of the antioxidant activity should decrease in the series (XIII-GA 1 4)>(XIII-GA l 3)>(Xni-GA 1 2) (XIII-GA 1 1)>(XIII). The clathrate (XIII-GA 1 4) should show the highest activity. The (XIII-GA 1 2) and (XIII-GA 1 1) complexes should show the lowest activities. 

The results of predicting the antiarrhythnuc activity of the compound (XIV) elathrates with glycyrrhizinic acid are shown in Table 12.17. According to the sum of the rank estimates yyRank, the expected antiarrl thmic activity of compound (XIV) elathrates did not differ significantly from the activity of the pure nonclath-rated compound (XIV) the maximum difference was oidy two units, whereas the minimum difference was 10 in the case of the antioxidant activity. Thus, the antiarrhythmic activity of all elathrates of compound (XIV) should be comparable with the activity of the pure nonclathrated compound (XIV). 

Calculating the mineral-matter-free basis for rank estimation is discussed in the following section. 

The introduction of local rank constraints in image analysis requires finding out the number and identity of the missing components in the pixels to be constrained. Therefore, only pixels with a robust rank estimation and clear constituent identification will be constrained. 

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