Global similarity measure

Each member in an ensemble uses a local aggregation function (such as average) to generate a schema matching similarity measure from the similarity measures of the attribute correspondences. Local similarity measures can then be aggregated using a global similarity measure (e.g., max) to become the ensemble similarity... 

Whatever the precise fragment definition that is used, the resulting molecular representations are input to dictionary-or fingerprint-based procedures analogous to those described previously for 2D similarity searching, with the final global similarity measure being obtained by means of a Tanimoto-like calculation. 

On the other hand, the analyst might not be interested in global retention indices. Indeed, by increasing the temperature for SF3, he would obtain similar retention indices as for the other two. He will then observe that the relative retention time, i.e. the retention times of the substances compared with each other, are the same for SF, and SF3 and different from SFj. Chemically, this means that SF3 has different polarity from SFj, but the same specific interactions. This is best expressed by using the correlation coefficient as the similarity measure. Indeed, rj3 = 1, indicating complete similarity, while r 2 23 much lower. Since both... 

Molecular diversity is thus plagued not only with the problems inherent in molecular similarity/dissimilarity [5, 6] but also with those problems associated with molecular populations [7]. One of the foremost problems is that computed molecular similarity values are not invariant to the molecular representation and to the similarity measure used [5]. Nearest-neighbor (NN) relationships, which are employed extensively in many aspects of HTS, are thus problematic, and it is difficult, and in many cases impossible, to obtain consistent subsets [8]. The structure of chemistry space can also be altered significantly in a global sense. As molecular diversity also depends on these factors, it too can be problematic and inconsistencies will no doubt arise. 

Most of the research accomplished to date on source flux rates has been directed toward landmines. This is generally because global publicity has focused attention, and hence funding, on them. Other ERWs are acknowledged, but similar measurements are more limited. We can recognize that many of the same processes will be operative. However, since landmines are intended to be placed, most often, by hand, they can be manufactured effectively from various polymer materials, rather than steel. 

When searching for local similarities of two molecules, the decoded local shape matrices Ib(a,b,Mi) of molecule M) are compared to various diagonal blocks of the global shape matrix s(a,b,M2) of molecule M2. In the most general case, the local shape matrix Ib(a,b,Mi) is used as a template, and it is compared to k-dimensional blocks of s(a,b,M2) obtained by all possible simultaneous row and column permutations. If the size ordering is considered important then only those permutations are taken which preserve the monotonicity of size ordering in the permuted diagonal block that is compared to the template. A local similarity measure... 

We have noted previously that similarity measures can be either local or global in character, depending upon whether they involve the generation of an alignment of the target structure with a database struaure, and we shall use this characteristic to provide an initial subdivision of the 3D similarity measures that have been reported to date in the literature. The next section also considers the extension of these measures to encompass flexible 3D molecules and the subject of docking, which is probably the most important application, thus far, of 3D similarity measures in the design of novel bioactive compounds. 

Much research has been done into similarity searching, and it is often assumed that diversity, or dissimilarity, is the converse (i.e, 1 — similarity). Any similarity measure involves three main components the structural descriptors that are used to characterize the molecules, the weighting scheme used to differentiate important from less important characteristics, and the similarity coefficient that is used to quantify the degree of similarity between pairs of molecules. Three types of descriptor have been used fragment substructures, topological indexes, and global physical properties. One of the most common similarity coefficients is that due to Tanimoto. There are three main methods of compound selection cluster-based, dissimilarity-based, and partition-based. 

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