Distance Metric

For a distance coefficient to be defined as a ‘Distance Metric’ it should have the following properties:

1. Distance values must be zero or positive, and when the compound is compared with itself the distance value must be zero; D_AB ≠ 0, D_AA = D_BB = 0
2. When compound A is compared with B, and vice versa; distance values must be symmetric; D_AB = D_BA
3. Distance values must obey triangular inequality; D_AC + D_CB ≥ D_AB
4. Distance between non-identical compounds must be greater than zero. If A ≠ B, then D_AB ≥ 0.

If only properties 1-3 are followed then the distance coefficient is called ‘pseudo-metric’.
If only properties 1, 2 and 4 are followed then the distance coefficient is called ‘non-metric’.

See Also:

References:
Willett, P., Barnard, J. M. and Downs, G. M.  Chemical Similarity Searching, J. Chem. Inf. Comput. Sci., 38 (6), 983-996, 1998.

Cite This As:

Dogra, Shaillay K., "Distance Metric" From QSARWorld--A Strand Life Sciences Web Resource.
http://www.qsarworld.com/insilico-chemistry-distance-metric.php