Topological structure, autocorrelation

Autocorrelation of Topological Structure Moreau and Broto [24,25] have suggested the autocorrelation vector of a molecular graph as the source for molecular descriptors. This method assumes that each atom i in the graph is uniquely associated with a numeric quantity, qit such as the atomic number, atomic mass, (v)(, (ds), Sv, or electronegativity. The intrinsic atom values of the electrotopological state [26] and the atomic Rd and log Kow parameters [27,28] are other potential atomic descriptors suitable to construct autocorrelation vectors. Generally, the fcth element of the autocorrelation vector is defined as... 

Spatial autocorrelation is a quantitative measure of the probability of finding objects of defined properties within a distance of interest [9, 10]. The concept of autocorrelation is mainly applied in fields such as geography, economics, ecology or meteorology to describe the spatial distribution of features. The idea of a molecular descriptor based on the autocorrelation concept was first introduced into the field of cheminformatics by Moreau and Broto in 1980 [11] with the ATS (autocorrelation of a topological structure) descriptor. For this approach, the atoms of a molecule were represented by properties such as atomic mass or partial charge. The distance between atoms was measured as the number of bonds between the respective atoms (topological distance). 

Moreau-Broto autocorrelation (. Autocorrelation of a Topological Structure, ATS) This is a spatial autocorrelation defined on a molecular graph C as ... 

Moreau, G. and Broto, P. (1980b). The Autocorrelation of a Topological Structure A New Molecular Descriptor. Nouv.J.Chim., 4,359-360. 

Autocorrelation Vectors (topological autocorrelation vectors, autocorrelation of a topological Structure, ATS) are molecular descriptors for a property distribution along the topological structure. 

Moreau-Broto autocorrelation (= Autocorrelation ofia Topological Structure, ATS)... 

Autocorrelation of a Topological Structure = Moreau-Broto autocorrelation autocorrelation descriptors... 

Broto-Moreau autocorrelation of a topological structure- lag7/ weighted by atomic masses... 

In order to transform the information fi om the structural diagram into a representation with a fixed number of components, an autocorrelation function can be used [8], In Eq. (19) a(d) is the component of the autocorrelation vector for the topological distance d. The number of atoms in the molecule is given by N. 

We denote the topological distance between atoms i and j (i.e., the number of bonds for the shortest path in the structure diagram) dy, and the properties for atoms i and j are referred to as pi and pj, respectively. The value of the autocorrelation function a d) for a certain topological distance d results from summation over all products of a property p of atoms i and j having the required distance d. 

Bauknecht et al. [48] and Sadowski et al. [49] have also developed molecular descriptors that are based on the physicochemical properties of the atoms in a molecule. They calculate several different electronic properties for each atom in a molecule and then use autocorrelation to generate a fixed-length vector that is independent of the size of the molecule. Autocorrelation was first applied to the topology of a molecular structure by Moreau and Broto [50] using the following function ... 

Moreau has proposed the autocorrelation of topological molecular structure (ATS) value. The function is defined in (13). 

For this reason, molecular interaction potentials based on three-dimensional structures are calculated for the compounds of the test dataset. The potentials include all possibibhes of interaction between the small molecule and the en-2ymes, as well as the shape of the molecule. Twenty autocorrelation coefficients are derived from these potentials for each molecule and used as a descriptor set. The new descriptors are mapped in the same way as the topological descriptors by means of a self-organizing map. 

Topological autocorrelation vectors are calculated from the two-dimensional structure of a molecule that can be expressed as molecular graph. One of the original... 

Atom-type topological indices are used to describe a molecule by information related to different atom types in the molecule. An atom-type index is usually derived from some properties of all the atoms of the same type and their structural environment. Atom-type Estate indices of Kier and Hall, perturbation connectivity indices, atom-type path counts, and atom-type autocorrelation descriptors are examples of these molecular descriptors. 

Gasteiger et al. [20,21] have used autocorrelation vectors as molecular descriptors in diversity studies and also in library comparisons. Autocorrelation is a method for converting information of variable length into fixed-length information. Moreau and Broto [22] were the first to apply an autocorrelation function to the topology of a molecular structure ... 

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