Descriptor 3- dimensional

We must now mention, that traditionally it is the custom, especially in chemo-metrics, for outliers to have a different definition, and even a different interpretation. Suppose that we have a fc-dimensional characteristic vector, i.e., k different molecular descriptors are used. If we imagine a fe-dimensional hyperspace, then the dataset objects will find different places. Some of them will tend to group together, while others will be allocated to more remote regions. One can by convention define a margin beyond which there starts the realm of strong outliers. "Moderate outliers stay near this margin. 

The profits from using this approach are dear. Any neural network applied as a mapping device between independent variables and responses requires more computational time and resources than PCR or PLS. Therefore, an increase in the dimensionality of the input (characteristic) vector results in a significant increase in computation time. As our observations have shown, the same is not the case with PLS. Therefore, SVD as a data transformation technique enables one to apply as many molecular descriptors as are at one s disposal, but finally to use latent variables as an input vector of much lower dimensionality for training neural networks. Again, SVD concentrates most of the relevant information (very often about 95 %) in a few initial columns of die scores matrix. 

The idea behind this approach is simple. First, we compose the characteristic vector from all the descriptors we can compute. Then, we define the maximum length of the optimal subset, i.e., the input vector we shall actually use during modeling. As is mentioned in Section 9.7, there is always some threshold beyond which an inaease in the dimensionality of the input vector decreases the predictive power of the model. Note that the correlation coefficient will always be improved with an increase in the input vector dimensionality. 

Usually, the denominator, if present in a similarity measure, is just a normalizet it is the numerator that is indicative of whether similarity or dissimilarity is being estimated, or both. The characteristics chosen for the description of the objects being compared are interchangeably called descriptors, properties, features, attributes, qualities, observations, measurements, calculations, etc. In the formiilations above, the terms matches and mismatches" refer to qualitative characteristics, e.g., binary ones (those which take one of two values 1 (present) or 0 (absent)), while the terms overlap and difference" refer to quantitative characteristics, e.g., those whose values can be arranged in order of magnitude along a one-dimensional axis. 

Table 8-2. Classification of descriptors by the dimensionality of their molecular representation.

Several research groups have built models using theoretical desaiptors calculated only from the molecular structure. This approach has been proven to be particularly successful for the prediction of solubility without the need for descriptors of experimental data. Thus, it is also suitable for virtual data screening and library design. The descriptors include 2D (two-dimensional, or topological) descriptors, and 3D (three-dimensional, or geometric) descriptors, as well as electronic descriptors. 

Cluster sampling methods, which first identify a set of compound clusters, followed by the selection of several compounds from each cluster [73]. Grid-based sampling, which places all the compounds into a low-dimensional descriptor space divided into many cells and then chooses a few compounds from each cell [74]. 

In the Fischer convention, the ermfigurations of other molecules are described by the descriptors d and L, which are assigned comparison with the reference molecule glyceraldehyde. In ertqrloying the Fischer convention, it is convenient to use projection formulas. These are planar representations defined in such a w as to convey three-dimensional structural information. The molecule is oriented with the major carbon chain aligned vertically in such a marmer that the most oxidized terminal carbon is at the top. The vertical bonds at each carbon are directed back, away fiom the viewer, and the horizontal bonds are directed toward the viewer. The D and L forms of glyceraldehyde are shown below with the equivalent Fischer projection formulas. 

The simplest and fastest techniques for grouping molecules are partitioning methods. Every molecule is represented by a point in an n-dimensional space, the axes of which are defined by the n components of the descriptor vector. The range of values for each component is then subdivided into a set of subranges (or bins). As a result, the entire multidimensional space is partitioned into a number of hypercubes (or cells) of fixed size, and every molecule (represented as a point in this space) falls into one of these cells [57]. 

Chen X, Rusinko A, Young SS. Recursive partitioning analysis of a large structure-activity data set using three-dimensional descriptors. J Chem Inf Comput Sci 1998 38 1054-62. 

Dearden JC, Netzeva TI. QSAR modelling of hERG potassium channel inhibition with low-dimensional descriptors. I Pharm Pharmacol 2004 56 Suppl S-82. 

Two-dimensional H-bond descriptors are included in Table 6.1. Considering information content, they may be classified as indirect descriptors (no direct link with the H-bonding process), H-bond indicators (atoms having potential H-bond capability) and thermodynamic factors (calculated on the basis of experimental thermodynamic data of H-bonding). 

I 6 H-bonding Parameterization in Quantitative Structure-Activity Relationships di Drug Design Tab. 6.1 Two-dimensional H-bond descriptors. 

Three-dimensional H-bond Descriptors 135 Tab. 6.3 Three-dimensional H-bonding parameters and descriptors. 

Pastor, M., Cruciani, G., McLay, L, Pickett, S., Glementi, S. GRid-INdependent descriptors (GRIND) a novel class of alignment-independent three-dimensional molecular descriptors. /. Med. Chem. 2000, 43, 3233-3243. 

Most of the models and descriptors discussed so far are based on the two-dimensional representation of the compounds, i.e. on their structural formula. 

The importance of methods to predict log P from chemical structure was described in Chapter 14, which is focused on fragment- and atom-based approaches. In this chapter property-based approaches are reviewed, which comprise two main categories (i) methods that use three-dimensional (3D) structure representation and (ii) methods that are based on topological descriptors. 

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