ultrametricadj.n.
/ʌltrəˈmɛtrɪk/ Mathematics.
A. adj.
Of a metric: satisfying the ultrametric inequality, which states that the distance between two points as defined by this metric must be less than or equal to the greater of the two distances between either of these points and any third point; of or pertaining to such a metric.
ΘΚΠ
the world > relative properties > number > algebra > [noun] > expression > inequality
inequation1855
inequality1875
Minkowski inequality1932
triangle inequality1941
Cauchy–Schwarz inequality1956
ultrametric inequality1967
the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to inequalities
ultrametric1967
1967 J. A. Hartigan in Jrnl. Amer. Statist. Assoc. 62 1141 Johnson..considers the idea of a distance function satisfying the ‘ultrametric’ inequality, which is equivalent to a similarity matrix with exact structure.
1967 Math. Biosciences I. 175 A 1-metric space is usually called a metric space and a 0-metric space an ultrametric space.
1972 Computer Jrnl. 15 212/1 The only consistent difference is between the ultrametric data-sets D, E, and F versus the non-ultrametric sets A, B, and C, with the ultrametrics faring somewhat better on the whole.
1988 Lit. & Ling. Computing 3 125/1 The tree representation model most widely applied to the structuring of large bodies of data is based on the use of ultrametric trees or dendrograms.
1988 Lit. & Ling. Computing 3 125/1 The ultrametric model has some advantages.
B. n.
A metric which satisfies this inequality.
ΘΚΠ
the world > relative properties > number > algebra > [noun] > expression > inequality > metric which satisfies
ultrametric1974
1974 P. H. A. Sneath in M. J. Carlile & J. J. Skehel Evol. in Microbial World 18 It can be seen that the number of PAM units from the root to any tip is about sixty-five, a fairly good ultrametric.
This entry has not yet been fully updated (first published 1993; most recently modified version published online September 2018).
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adj.n.1967