Single class discrimination

Rose, V.S., Wood, J. and MacFie, H.J.H. (1991). Single Class Discrimination Using Principal Component Analysis (Scd PCA). Quant.Struct.-Act.Relat., 10,359-368. 

Rose, V. S., Wood, J., MacFie, H. J. H. Single class discrimination using principal component analysis (SCD-PCA). Quant. Struct.-Act. Relat. 1991,10, 359-368. 

As a first step in this direction, a surface consisting of electric eel AChE and horse serum BChE was designed. Both of these enzymes are inhibited by TPPSi and the characteristic absorbance peaks for the porphyrin-enzyme complexes are different (421 vs. 446 nm). This allows for co-immobilization of the two enzymes from a simple mixture of equal concentrations onto the entire slide surface [25]. Exposure to those compounds inhibiting BChE competitively results in a loss in absorbance at 421 nm while compounds inhibiting AChE competitively result in a loss at 446 nm. Compounds inhibiting both enzymes result in a loss at both 421 nm and 446 nm. This combination of two enzymes allows for class discrimination of those compounds, which are inhibitors of BChE, inhibitors of AChE, inhibitors of both enzymes, and inhibitors of neither enzyme. Detection limits are approximately the same for the dual enzyme system as those observed for the single enzyme systems. 

For most applications in the "omics" fields, even the most simple multivariate techniques such as Linear Discriminant Analysis (LDA) cannot be applied directly. From Equation 2 it is clear that an inverse of the the covariance matrix 2 needs to be calculated, which is impossible in cases where the number of variables exceeds the number of samples. In practice, the number of samples is nowhere near the number of variables. For QDA, the situation is even worse to allow a stable matrix inversion, every single class should have at least as many samples as variables (and preferably quite a bit more). A common approach is to compress the information in the data into a low number of latent variables (LVs), either using PCA (leading... 

Evidence is provided by this analysis that (a) structural considerations discriminate among at least four practical classes of pi delocalization behavior, each of which has limited generality (b) the blend of polar and pi delocalization effect contributions to the observed effect of a substituent is widely variable among different reaction or data sets (the contributions may be opposite as well as alike in direction), depending upon structural considerations and the nature of the measurement (c) solvent may play an important role in determination of the observed blend of effects (d) it is the first three conditions which lead to the deterioration of the single substituent parameter treatment as a means of general and relatively precise description of observed electronic substituent effects in the benzene series. 

After all the careful filtering, there was neither a single molecular property from the profiles discussed above which could effectively discriminate the two classes nor a predictive model obtained from all those property descriptors. Only after... 

These weights depend on several characteristics of the data. To understand which ones, let us first consider the univariate case (Fig. 33.7). Two classes, K and L, have to be distinguished using a single variable, Jt,. It is clear that the discrimination will be better when the distance between and (i.e. the mean values, or centroids, of 3 , for classes K and L) is large and the width of the distributions is small or, in other words, when the ratio of the squared difference between means to the variance of the distributions is large. Analytical chemists would be tempted to say that the resolution should be as large as possible. 

In 1956, Doering et al. reported that methylene (CH2) inserted into the C H bonds of pentane, 2,3-dimethylbutane, and cyclohexene with no discrimination (other than statistical) between chemically different sites CH2 was classed as the most indiscriminate reagent known in organic chemistry. Doering and Kirmse also demonstrated that the C—H insertion reactions of CH2 in solution were direct, single barrier concerted processes with transition states that could be represented as 27 (Fig. 7.12). In particular, they did not proceed via initial H abstraction to give radical pair intermediates that subsequently recombined. (Triplet carbene C H insertions, however, do follow abstraction-recombination, radical pair mechanisms, as demonstrated in classic experiments of Closs and Closs and Roth (see Chapter 9 in this volume). 

Decision trees [135] can be used to identify and segment spectra when discriminating rules are known or desired (Fig. 8.8). A binary tree consists of nodes in which a single parameter is used as a discriminant. After a series of nodes are traversed, leaf nodes of the tree are encountered in which all the objects are labeled as belonging to a particular class. Decision trees can be axis parallel or oblique. Axis-parallel trees are called so because they correspond to... 

In supervised pattern recognition, a major aim is to define the distance of an object from the centre of a class. There are two principle uses of statistical distances. The first is to obtain a measurement analogous to a score, often called the linear discriminant function, first proposed by the statistician R A Fisher. This differs from the distance above in that it is a single number if there are only two classes. It is analogous to the distance along line 2 in Figure 4.26, but defined by... 

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