Orthogonal descriptors

By applying this method, they demonstrated that the removal of insignificant variables increases the quality and reliability of the models despite the fact that the correlation coefficient, r, always decreases, although only shghtly. For example, the characteristics of a model with six orthogonalized descriptors were r = 0.99288, s = 0.9062, F = 127.4 and the quality of this model was sufficiently improved after removal of the two least significant descriptors, to r = 0.9925, s = 0.8553,... 

Fig. 1. Median partitioning and compound selection. In this schematic illustration, a two-dimensional chemical space is shown as an example. The axes represent the medians of two uncorrelated (and, therefore, orthogonal) descriptors and dots represent database compounds. In A, a compound database is divided in into equal subpopulations in two steps and each resulting partition is characterized by a unique binary code (shared by molecules occupying this partition). In B, diversity-based compound selection is illustrated. From the center of each partition, a compound is selected to obtain a representative subset. By contrast, C illustrates activity-based compound selection. Here, a known active molecule (gray dot) is added to the source database prior to MP and compounds that ultimately occur in the same partition as this bait molecule are selected as candidates for testing. Finally, D illustrates the effects of descriptor correlation. In this case, the two applied descriptors are significantly correlated and the dashed line represents a diagonal of correlation that affects the compound distribution. As can be seen, descriptor correlation leads to over- and underpopulated partitions.

Orthogonalized descriptors are used in similarity/diversity analysis and quantitative -> structure/response correlations with the aim of eliminating the bias provided by the interdependence of common molecular descriptors. Moreover, the interpretation of regression models should be facilitated, as the information encoded in each descriptor is unique. 

The similarity/diversity analysis based on previously orthogonalized descriptors is usually called orthosimilarity [Randic, 1996b]. 

Lucic, B., Nikolic, S., Trinajstic, N. and Juretic, D. (1995a). The Structure-Property Models can be Improved Using the Orthogonalized Descriptors. J.Chem.Inf.Comput.Sci.,35,532-538. 

Mracec, M., Muresan, S., Simon, Z. and Naray-Szabo, G. (1997). QSARs with Orthogonal Descriptors on Psychotomimetic Phenylalkylamines. QuantStruct.-ActRelat, 16,459-464. 

Randic, M. (1991f). Resolution of Ambiguities in Structure-Property Studies by Use of Orthogonal Descriptors. J.Chem.Inf.ComputSci.,31, 311-320. 

Soskic, M., Plavsic, D. and Trinajstic, N. (1996a). 2-Difluoromethylthio-4,6-bis-(monoalkyl-amino)-l,3,5-triazines a Inhibitor of Hill Reaction A QSAR Study with Orthogonalized Descriptors. J.Chem.Inf.Comput.Sci., 36,146-150. 

These are obtained by applying an orthogonalization procedure to a selected set of molecular descriptors. A descriptor is made orthogonal to another descriptor Xi simply by regressing it against X and using as the new orthogonal descriptor the residual — Xj, where Xj is the value... 

A basis of descriptors can be viewed as a representation of the molecular structure suitable for use in different applications. An interesting characteristic of a basis of descriptors is that they can be orthogonalized, thus providing a new basis of orthogonalized descriptors. 

Fernandez, F.M., Duchowicz, P.R. and Castro, E.A. (2004) About orthogonal descriptors in QSPR/ QSAR theories. MATCH Commun. Math. Comput. Chem., 51, 39-57. 

This distance in descriptor space measures how similar the investigated compound is to the training set compounds. The Mahalanobis distance is superior to the corresponding, and more familiar, Euclidian distance since the former takes correlations between the variables into account, that is, the Mahalanobis distance does not assume orthogonal descriptors as does the euclidian distance, that normally exists. 

In Table 4 we show the similarity/dissimilarity matrix based on orthogonal descriptors of Table 3. Observe how the degeneracy of the similarity/dissimilarity table for path numbers has almost completely disappeared. The most similar pairs of isomers are listed in Table 5 and are illustrated in Figure 13. 

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