Reflected discriminant analysis

The combination of PCA and LDA is often applied, in particular for ill-posed data (data where the number of variables exceeds the number of objects), e.g. Ref. [46], One first extracts a certain number of principal components, deleting the higher-order ones and thereby reducing to some degree the noise and then carries out the LDA. One should however be careful not to eliminate too many PCs, since in this way information important for the discrimination might be lost. A method in which both are merged in one step and which sometimes yields better results than the two-step procedure is reflected discriminant analysis. The Fourier transform is also sometimes used [14], and this is also the case for the wavelet transform (see Chapter 40) [13,16]. In that case, the information is included in the first few Fourier coefficients or in a restricted number of wavelet coefficients. 

Murray, I, Aucott, L. S. and Pike, I. H. (2001) Use of discriminant analysis on visible and near infrared reflectance spectra to detect adulteration of fish meal with meat and bone meal. 

Whitfield [13] was one of the first NIR spectroscopists to discuss the use of NIR diffuse reflection analysis for veterinary products in 1986. Even then, he recognized the need for specificity and included an identification step in the analysis. This discriminant analysis program, named DISCRIM (Technicon, Tarrytown, NY) was an early version of the types of algorithms available commercially now. 

Note that since the mean spectrum was subtracted from each individual spectrum in the initial stage of the discriminant analysis, the resulting discriminants reflect only the variations in the spectra that distinguished one sample class from another. The positive portion of D1 (D1+) was domi-... 

MOSS, B. w., MILLAR, s. J. and KILPATRICK, D. J. (2000). The use of discriminant analysis for the interpretation of the reflectance spectra of irradiated porcine longissmus dorsi. Meat Science, 55(3), 337-348. 

The adaptive wavelet algorithm outlined in Section 6 can be used for a variety of situations, and its goal is reflected by the particular criterion which is to be optimized. In this chapter, we apply the filter coefficients produced from the adaptive wavelet algorithm for discriminant analysis. It was stated earlier that the dimensionality is reduced by selecting some band(jg,xg) of wavelet coefficients from the discrete wavelet transform. It then follows that the criterion function will be based on the same coefficients i.e. Xl " (xg). 

The correct classification rate (CCR) or misclassification rate (MCR) are perhaps the most favoured assessment criteria in discriminant analysis. Their widespread popularity is obviously due to their ease in interpretation and implementation. Other assessment criteria are based on probability measures. Unlike correct classification rates which provide a discrete measure of assignment accuracy, probability based criteria provide a more continuous measure and reflect the degree of certainty with which assignments have been made. In this chapter we present results in terms of correct classification rates, for their ease in interpretation, but use a probability based criterion function in the construction of the filter coefficients (see Section 2.3). Whilst we speak of correct classification rates, misclassification rates (MCR == 1 - CCR) would equally suffice. The correct classification rate is typically formulated as the ratio of correctly classified objects with the total... 

P. Dardenne, R. Biston. Attempt to recognize wheat species by discriminant analysis. In Near Infrared Diffuse Reflectance/Transmittance Spectroscopy, Proceedings of the International NIR/NIT conference, Budapest, Hungary, May 12-16, 1986. J. Hollo, et al co-ed. Akademiai Kiado, Budapest, 1987, p. 51-60. 

Isaksson et al. showed that VIS/NIR reflectance could possibly be applied in salmon production plants to classify fillets into broad texture classes before further processing or sale. Spectra of fillets of farmed Atlantic salmon were correlated to Kramer shear force measurement and texture profile analysis (TPA). Samples were analyzed prerigor (2 h after slaughter) and postrigor (6 days after slaughter). Classification using linear discriminant analysis gave up to 79% correct classification into three... 

Near-infrared reflectance analysis is a useful technique for characterizing textile raw materials, fiber, yarns, and fabrics. It is a nondestructive quantitative analysis that is simple to use and allows rapid testing of the sample. Its ability to measure multiple components of the sample simultaneously and eliminate extensive sample preparation are major advantages of NIRA in the characterization of textile materials. Many innovative mathematical treatments, for example, discriminant analysis and spectral reconstruction, have been developed by instrument manufactures and software companies. These instruments not only aid in the quantitative analysis of the data but also allow morphological investigations of fibers and yarns and rapid, qualitative identification of specific sample sets. 

In the preceding section, we presented principles of spectroscopy over the entire electromagnetic spectrum. The most important spectroscopic methods are those in the visible spectral region where food colorants can be perceived by the human eye. Human perception and the physical analysis of food colorants operate differently. The human perception with which we shall deal in Section 1.5 is difficult to normalize. However, the intention to standardize human color perception based on the abilities of most individuals led to a variety of protocols that regulate in detail how, with physical methods, human color perception can be simulated. In any case, a sophisticated instrumental set up is required. We present certain details related to optical spectroscopy here. For practical purposes, one must discriminate between measurements in the absorbance mode and those in the reflection mode. The latter mode is more important for direct measurement of colorants in food samples. To characterize pure or extracted food colorants the absorption mode should be used. 

We found that it is necessary to run several sets of differential display primers prior to an analysis of the distribution of differential display bands. This allows for a comparison between different independent reactions using different PCR primers to assess the quality of individual cDNA samples and discriminate between sample-to-sample variability and potential positive bands that are consistently found in different repUcates. The presence or absence of a specific band in lanes corresponding to independent experimental samples indicates a reproducible difference in the relative amount of cDNA in a given sample, which should reflect differences in mRNA levels. However, the interpretation of the differential display results is not always straightforward. For example, a thick band can reflect quantitative differences in the initial concentration of a specific cDNA between samples or can represent comigration of two bands. Replication of the PCR reactions for samples that have differences in banding pattern will eliminate a significant number of false positive differential display differences. Also, in some cases, it may be informative to alter the electrophoresis conditions to maximize resolution of a band of interest prior to isolation, reamplification, and further analysis of potential positive bands. 

The number of probe sites (features) per unit surface area in a DNA array reflects its information density and versatility in terms of parallel analysis of different sequences. In order to maximize these parameters, the features and their spacing in the array should be as small as possible, while retaining full sensitivity and discrimination in terms of detection. Decreasing the size of the features has the additional advantage of reducing the amount of target sample required for analysis in the application. 

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