Discriminant function testing

In discriminant analysis, in a manner similar to factor analysis, new synthetic features have to be created as linear combinations of the original features which should best indicate the differences between the classes, in contrast with the variances within the classes. These new features are called discriminant functions. Discriminant analysis is based on the same matrices B and W as above. The above tested groups or classes of data are modeled with the aim of reclassifying the given objects with a low error risk and of classifying ( discriminating ) another objects using the model functions. 

In the case of two groups one describes the groups by the discriminant scores of one discriminant function. The coordinates of the two class means with their variances are known and the new object may easily be discriminated, in other words classified to one of the groups. This is achieved simply by attributing the unknown object to that class into which confidence region it falls. This may be tested using ... 

The principle of multivariate analysis of variance and discriminant analysis (MVDA) consists in testing the differences between a priori classes (MANOVA) and their maximum separation by modeling (MDA). The variance between the classes will be maximized and the variance within the classes will be minimized by simultaneous consideration of all observed features. The classification of new objects into the a priori classes, i.e. the reclassification of the learning data set of the objects, takes place according to the values of discriminant functions. These discriminant functions are linear combinations of the optimum set of the original features for class separation. The mathematical fundamentals of the MVDA are explained in Section 5.6. 

Previous experience has shown that some markers are important, while others are only of minor value. Sensitivity may be improved to over 80% with certain combinations of single tests, in particular when the principle of discriminant functional analysis is applied (D.M. Chalmers el ah, 1981). In order to examine chronic alcohol consumption, a triple test combination would be of advantage, which, in the individual case, could be supported by additional values derived from the set of four tests, (s. tab. 28.6) When determining and differentiating acute alcohol consumption, the values of the triple test combination can be upgraded by additional tests for better clinical reliability. This would also help to determine important, so-called alcohol-typical emergency situations, including Zieve s syndrome, (s. tab. 28.6)... 

These results show that pattern recognition can be used as an effective tool to characterize polycyclic aromatic hydrocarbon carcinogens. Using a set of only 28 molecular structure descriptors, linear discriminants can be found to correctly dichotomize 191 out of 200 randomly selected PAH s. This same set of 28 descriptors supports a linear discriminant function that has an average predictive ability of over ninety percent when subjected to randomized predictive ability tests. 

As with multiple regression analysis, the most commonly used selection procedures involve stepwise methods with the F-test being applied at each stage to provide a measure of the value of the variable to be added, or removed, in the discriminant function. The procedure is discussed in detail in Chapter 6. 

Decision limit 32, 33 Degrees of freedom, 8 Dendrogram, 97, 105 Detection limit, 32, 33 Determination limit, 32, 33 Differentiation, 55 Savitsky-Golay, 57 Discriminant function, 124, 130 Discriminant score, 130 Discrimination, 123 Dispersion matrix, 82 Distance measures, 99 Dixon s Q-test, 13... 

Z2. Zieve, L., and Hill, E., An evaluation of factors influencing the discriminative effectiveness of a group of liver function tests. III. Relative effectiveness of hepatic tests in cirrhosis. Gastroenterology 28, 785-802 (1955). 

The accuracy of the discriminant function based on these characteristics was calculated on the recognition of 451 exon and 246 693 pseudo-exon sequences from the test set. The general accuracy of exact internal exon prediction is 77% with a specificity of 79%. At the level of individual nucleotides, the sensitivity of exon prediction is 89% with a specificity of 89% and the sensitivity of the intron prediction positions is 98% with a specificity of 98%. This accuracy is better than in the dynamic programming and neural network-based method [46], which has 75% accuracy of the exact internal exons prediction with a specificity of 67%. The method has 12% fewer false exon assignments with the better level of correct exon prediction. 

All ORF regions that were flanked by GT (on the left) and finished with a stop codon were considered as potential last exons. The structure of such exons is presented in Figure 3.9. The characteristics of their discrimimant function and their Mahalonobis distances are presented in Table 3.12. The accuracy of the discriminant function was tested on the recognition of the last 322 exon and 247 644 pseudo-exon sequences. The gene sequences were scanned and the 3 -exon with the maximal weight was selected for each of them. The function can identify exactly 60% of the annotated last exons. 

The incidence of aminoglycoside nephrotoxicity rises with advancing age from 7% in patients under age 30 to 15% in patients over 70 years of age [16]. It is likely that dosage may be excessive in older patients based on overestimates of drug excretory capacity by insensitive renal function tests such as the serum urea nitrogen or serum creatinine. This age effect has been confirmed in a retrospective stepwise discriminant analysis of 214 patients in randomized prospective trials [17]. The mechanism of this age effect is unclear since experimental studies show a decrease in drug uptake in older animals compared to similarly dosed younger animals [18]. 

A numerical procedure may also be used for classifying the groups. This utilizes only a part of the data as a craining set for which the discriminating functions are derived. The remainder of the data is used as a testing set with which the calculated functions may be optimized so as to minimize the number of misclassificadons. 

The first analytical application of a pattern recognition method dates back to 1969 when classification of mass spectra with respect to certain molecular mass classes was tried with the LLM. The basis for classification with the LLM is a discriminant function that divides the -dimensional space into category regions that can be further used to predict the category membership of a test sample. 

In the simplest case, a discriminant analysis is performed in order to check the affiliation (yes/no decision) of an unknown to a particular class, e.g. in case of a pur-ity/quality check or a substance identification. A sample may equally well be assigned between various classes (e.g., quahty levels) if a corresponding series of mathematical models has been estabhshed. Models are based on a series of test spectra, which has to completely cover the variations of particular substances in particular chemical classes. From this series of test spectra, classes of similar objects are formed by means of so-called discriminant functions. The model is optimized with respect to the separation among the classes. The evaluation of the assignment of objects to the classes of an established model is performed by statistically backed distance and scattering measures. 

As explained above, it is important for the formation of the discriminant function to know whether a corporation belongs to the group of good or poor credit quality before the analysis starts. This means that corporations must already be rated to be appropriate for building and testing the model. The requirement of an existing rating by at least... 

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