Vector-based representation, molecular similarity

Many methods exist for assessing 3-D molecular similarity. Lemmen and Lengauer (58) provide a comprehensive review of most of the methods in use today, a large class of which utilizes some form vector-based representation of... 

The names in parentheses are those commonly used for molecular-fingerprint-based similarity functions. All of the similarity functions are symmetric. Similarity functions for function-based representations are identical in form to those for vector-based representations except that the summations are replaced by integrations over the corresponding function spaces [41]. 

The remainder of this chapter covers set- and vector-based representations of structural and molecular data and how this information is converted into the various similarity, dissimilarity, and distance measures that have found wide application in chemical informatics. Examples of some of the types of structural and molecular descriptors are also presented, along with a discussion of their essential features. Significant emphasis is given to the concept of CS, a concept that plays... 

A brief introduction to the types of molecular representations typically encountered in MSA is presented at the beginning of Subheading 2. followed in Subheading 2.1. by a discussion of similarity measures based on chemical-graph representations. Although graph-based representations are the most familiar to chemists, their use has been somewhat limited in similarity studies due to the difficulty of evaluating the appropriate similarity measures. This section is followed by a discussion of similarity measures based on finite vector representations, the most ubiquitous types of representations. In these cases, the vector components can be of four types ... 

Vector-based methods can use combinations of ID, 2D, and 3D descriptors vide supra) and are considerably faster computationally than function-based methods (cf. [100]) for two reasons. First, summations over vector components are generally faster than integrations over whole molecules. In one case, fast 3D similarity searches were carried out using a vector-like representation whose components were derived from a set of molecular shape-based criteria [100]. 

Clearly, Equation 15.5.1 only strictly applies to set-based representations, although closely related asymmetric similarity functions can also be defined for graph-, vector-, and function-based representations (see Table 15.3 and Table 15.4 and the associated discussions in Sections 15.4.2 and 15.4.4). Because most applications employ set-based similarity functions and binary molecular fingerprints, the discussion in this section focuses on this category of MSA. Equivalent analyses can, however, be carried out with respect to other similarity measures (see e.g., [46]). 

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