Validity discriminant method

The validity discriminant discussed in this section is the descendant of an earlier cluster validity measure used by Gunderson ( ) to assess the quality of cluster configurations obtained in an application of the Fuzzy ISODATA algorithms. It is closely related to a method suggested by Sneath ( ) for testing the distinctness, i.e. separation, of two clusters, and also borrows from the ideas of Fisher s linear discriminant theory (see chapt. 4, Duda and Hart,(2 0). The validity discriminant attempts to measure the separation between the classes of a cluster configuration usually, but not necessarily, obtained by application of the FCV algorithms. A brief description follows ... 

Even quantitative assessment of pregnanetriol by visual comparison with standards would be adequate using carefully coded samples, and preferably duplicates. It is agreed from objective evaluations in a wide variety of fields that this method has a C.V. of 15 to 20% (B27). In the presence of 5- to 100-fold elevations of this steroid in the adrenogenital syndrome, the visual method would meet the usual requirements for a clinically valid discriminant (W3). 

A much simpler amplitude discrimination method was introduced by Hishida and Maeda (1990). In order to ensure that only particles traversing the center of the measurement volume are sampled, a minimum number of zero crossings in the Doppler signal was required for validation. 

E. Marengo and R. Todeschini, Linear discriminant hierarchical clustering a modeling and cross-validable divisive clustering method. Chemom. Intell. Lab. Syst., 19 (1993) 43-51. 

The VolSurf method was used to produce molecular descriptors, and PLS discriminant analysis (DA) was applied. The statistical model showed two significant latent variables after cross-validation. The 2D PLS score model offers a discrimination between the permeable and less permeable compounds. When the spectrum color is active (Fig. 17.2), red points refer to high permeability, whereas blue points indicate low permeability. There is a region in the central part of the plot with both red and blue compounds. In this region, and in between the two continuous lines, the permeability prediction is less reliable. The permeability model... 

Therefore, the development and validation of a scientifically sound dissolution method requires the selection of key method parameters that provide accurate, reproducible data that are appropriate for the intended application of the methodology. It is important to note that while more extensive dissolution methodologies may be required for bioequivalency evaluations or biowaivers (i.e., multiple media, more complex dissolution media additives, and multiple sampling time points), it is also essential for the simplified, routine quality control dissolution method to discriminate batch-to-batch differences that might affect the product s in vivo performance. 

Claros (1995) released an attractive program, MitoProt. In this program, various sequence features of a potential signal region are reported to assist in the user s decision making. Later, an objective prediction method that combines many sequence features by the discriminant analysis was proposed (Claros and Vincens, 1996). With a cross-validation test, its accuracy was estimated to be 75%. 

Two non-parametric methods for hypothesis testing with PCA and PLS are cross-validation and the jackknife estimate of variance. Both methods are described in some detail in the sections describing the PCA and PLS algorithms. Cross-validation is used to assess the predictive property of a PCA or a PLS model. The distribution function of the cross-validation test-statistic cvd-sd under the null-hypothesis is not well known. However, for PLS, the distribution of cvd-sd has been empirically determined by computer simulation technique [24] for some particular types of experimental designs. In particular, the discriminant analysis (or ANOVA-like) PLS analysis has been investigated in some detail as well as the situation with Y one-dimensional. This simulation study is referred to for detailed information. However, some tables of the critical values of cvd-sd at the 5 % level are given in Appendix C. 

For a more realistic estimate of the future error one splits the total data set into a training and a prediction part. With the training set the discriminant functions are calculated and with the objects of the prediction or validation set, the error rate is then calculated. If one has insufficient samples for this splitting, other methods of cross-validation are useful, especially the holdout method of LACHENBRUCH [1975] which is also called jackknifing or leaving one out . The last name explains the procedure For every class of objects the discriminant function is developed using all the class mem-... 

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