Hodgkin similarity index

As has been pointed out numerous times, if vA = kvb => SCar(vA,vB) = 1, for all K. This prompted Hodgkin and Richards (49) to define a slightly modified form of the similarity, usually called the Hodgkin similarity index, that does not suffer from this problem, namely,... 

As discussed in the previous section for vectors, if F and Fg differ only by a constant, that is, if F = K Fg, then SCar(F ,Fg) = 1 regardless of the specific form of the functions. While this is not a likely occurrence in practical applications, Hodgkin and Richards (49) nonetheless defined a slightly altered similarity measure, usually referred to as the Hodgkin similarity index, which is not affected by this problem and is given by... 

Hodgkin similarity index -> simiiarity/diversity HoiogramQSAR -> substructure descriptors... 

The final vector comprising of the seven invariant moments represents the distribution of the property P on the bidimensional map. This representation was used to compare bidimensional molecule projections by Carbo similarity index and Hodgkin similarity index. 

When using the smoothed Coulomb potential description, one first wished to emphasize the overlap of the electrostatic potential acting in regions of space remote from the molecular skeleton itself, that is, beyond the so-called solvent accessible surface of the molecule. In that case, one first used the overlap similarity measure with the Hodgkin similarity index as Good et al. [44] reported that this last index is sensitive to the magnimde of the 3D descriptor field. It, however, appeared that the Laplacian-Tanimoto combination was more efficient. 

There are many different types of similarity indexes, including the association coefficients (e.g., Tanimoto coefficient [27], Jaccard coefficient [38], Hodgkin-Richards coefficient [39,40]), the correlation coefficients or cosinelike indexes, and the distance coefficients or dissimilarity indexes (e.g., Hamming distance) [26],... 

The variation of 7 (n) with < b( ) is illustrated in Fig. 5, from which it is evident that the Tanimoto-like index is somewhat more discriminating than the Hodgkin-like index when dealing with high values (i.e. with very similar systems). Of course, this conclusion is not specific to p-space indices. 

In the Carbo index, the denominator is the geometric mean of the self-similarities. Naturally, we could also think about using the arithmetic mean, which gives rise to the Hodgkin-Richards index " " " originally developed for comparisons of electrostatic potentials ... 

In all three of these approaches, the similarity indices should be maximized. Both the Carbo index and the Hodgkin-Richards index were used by Boon et al. % whereas in the applications of AIM, the Cioslowski similarity measure was For the atom-centered approach, we can use all... 

Dice similarity coefficient Also known as the Hodgkin index c. 2 El 1 ... 

Fields can be utilized in virtual screening applications for assessing the similarity (alignment) or complementarity (docking) of molecules. Two similarity measures have achieved the most attention. These are the so-called Garbo- [195] and Hodgkin indexes [196] respectively. Others are Pearson s product moment correlation coefficient [169] and Spearman s rank correlation coefficient [169]. 

The value of SI(II) also varies in the range 0 to 1. When pA = npB (n is constant and 0) is substituted into Eq. (15), the Carbo index will be unity, which means that the Carbo index represents the similarity of the shapes of electron density distributions but not of the magnitudes. When pA = npB is substituted into Eq. (16), the result will be SI(H) = 2n/(l + n2), which means that the Hodgkin index characterizes the similarity in the shape as well as in the magnitude of the electron density functions [104],... 

Figure 12 reveals that when VAi = a VBi(Vi) (a is a constant and i- 0) the Petke MEP-SI is an even more sensitive measure of similarity than the Hodgkin index. This is true particularly in the region ae[- 1, 1] where MEP-SI(P) varies linearly with a. The Sis defined by Eqs. (17), (18) and (22) may be called cumulative indices since in each case the SI is computed by accumulating products of MEP values for a number of grid points [116]. 

In a more detailed study of technique validation and of the comparison of different similarity evaluation methods [1065], several Carbo indices (also using Gaussian function approximations), the Hodgkin index (eq. 213),... 

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