Similarity city block metric

Distances in these spaces should be based upon an Zj or city-block metric (see Eq. 2.18) and not the Z2 or Euclidean metric typically used in many applications. The reasons for this are the same as those discussed in Subheading 2.2.1. for binary vectors. Set-based similarity measures can be adapted from those based on bit vectors using an ansatz borrowed from fuzzy set theory (41,42). For example, the Tanimoto similarity coefficient becomes... 

All INBSs with a city block metric similarity measure (3) ... 

The first three searches compared the performance of different similarity measures with the full INBS frequency data. When the performance of the frequency Tanimoto measure and the city block metric was compared, it was found that the hits ranked to the top using the Tanimoto measure were not as similar to the query structure as those ranked top by the city block metric. Generally it was found that the city block and Euchdean distance measures ranked the hits equally well, however in two cases the city block ranking was better than the Euclidean ranking, so use of the city block metric may be preferred. The fourth search used only the paths from the most connected atom in the structure in a city block metric calculation. A comparison of the performance of the INBS search for individual query structures using the city block metric for all paths and for the Morgan root atom alone is discussed below. 

It was found that the best method currently tested is that which compares the incremental rates of change in the distribution of the INBSs in a structure using the city block metric similarity measure. The performance of this measure did differ shghtly for each of the chosen query structures which were selected to represent a variety of molecular sizes and structural patterns. However, the success of the pattern search appears to be on the same level as the current 2-D similarity search available in the CSD System based on bit-screens. Interestingly, those structures which are considered most similar to the query are not the same in the two searches presumably because they are based on different attribute sets. 

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